department of civil, environmental and natural...

DOCTORA L T H E S I S

Department of Civil, Environmental and Natural Resources EngineeringDivision of Operation, Maintenance and Acoustics Reliability and Life Cycle Cost Modelling

of Mining Drilling Rigs

Hussan Saed Hamodi Al-Chalabi

ISSN 1402-1544ISBN 978-91-7583-043-8 (print)ISBN 978-91-7583-044-5 (pdf)

Luleå University of Technology 2014

Hussan Saed H

amodi A

l-Chalabi R

eliability and Life Cycle C

ost Modelling of M

ining Drilling R

igs

ISSN: 1402-1544 ISBN 978-91-7583-XXX-X Se i listan och fyll i siffror där kryssen är

Reliability and Life Cycle Cost Modelling of Mining Drilling Rigs

Hussan Saed Hamodi Al-Chalabi

Division of Operation, Maintenance and Acoustics Luleå University of Technology

SE -- 971 87 Sweden

Printed by Luleå University of Technology, Graphic Production 2014

ISSN 1402-1544 ISBN 978-91-7583-043-8 (print)ISBN 978-91-7583-044-5 (pdf)

Luleå 2014

www.ltu.se

Dedicated

to my parents, Khalida and Saed, to my family, Amani, Abdulmalek and Yaman, for allowing me to be part of their life and love.

V

ACKNOWLEDGMENTS

The research work presented in this thesis has been carried out during the period 2011 to 2014 at the Division of Operation, Maintenance and Acoustics at Luleå University of Technology (LTU). The research programme was financed by Atlas Copco, Boliden Mineral AB and LTU.

First of all, I would like to express my deepest gratitude to my main supervisor, Professor Jan Lundberg, who has enriched my knowledge through stimulating discussions and fruitful guidance. You have always believed in me and shown a positive attitude.

I would like to express my sincere gratitude to Alireza Ahmadi and Behzad Ghodrati, my co-supervisors, for their invaluable guidance, suggestions and support.

My sincerest gratitude is extended to Professor Uday Kumar, Head of the Division of Operation, Maintenance and Acoustics at LTU, for providing me with the opportunity to pursue my research at the Division of Operation and Maintenance Engineering.

I would like to express my sincere gratitude to the Iraqi Ministry of Higher Education and Scientific Research for providing a scholarship which made it possible for me to pursue doctoral research at LTU.

I am grateful to all the group members in the drilling rig project for their valuable time in meetings, sharing their experiences and suggestions for design improvement. Specific gratitude is extended to Arne Vesterberg, Tommy Öhman, Curt Lindblad, Mats Johansson, Mikael Anderson, Lars Karlsson, Andreas Nordbrandt, Ulf Sundberg and Jesus Retuerto for sharing their expertise.

I would like sincerely and gratefully to acknowledge my colleagues (present and past) at the Division of Operation, Maintenance and Acoustics for providing a friendly and open-minded working environment. Special thanks are due to Malin Shooks, Rajiv Dandotiya, Mustafa Aljumaili, Christer Stenström, Stephen Famurewa, Yasser Ahmed and Yamur Aldouri for their discussions. Gratitude is also extended to my friend Hassan Ali. The administrative support from Cecilia Glover and Marie Jakobsson is also gratefully acknowledged.

I wish to express my sincere gratitude to my dearest parents, Saed and Khalida, who have always offered their full support throughout my life and who taught me the meaning of life. Gratitude is extended to my siblings too. I am really thankful for all the support given to me.

Finally, I would like to express my deepest gratitude to my loving wife, Amani, and our beloved sons, Abdulmalek and Yaman, for their enormous understanding and endless support during my studies and research. It would not have been possible to complete this journey without you by my side.

Hussan Saed Hamodi Al-Chalabi December, 2014 Luleå, Sweden

VII

ABSTRACT

In the context of mining, drilling is the process of making holes in the face and walls of underground mine rooms, to prepare those rooms for the subsequent operation, which is the charging process. Due to the nature of the task, drilling incurs a high number of drilling rig failures. Through a combination of a harsh environment (characterised by dust, high humidity, etc.), the operating context, and reliability and maintainability issues, drilling rigs are identified as a major contributor to unplanned downtime.

The purpose of the research performed for this thesis has been to develop methods that can be used to identify the problems affecting drilling rig downtime and to identify the economic lifetime of drilling rigs. New models have been developed for calculating the optimum replacement time of drilling rigs. These models can also be used for other machines which have repairable or replaceable components. Based on an analysis performed in a case study, a life cycle cost (LCC) optimization model has been developed, taking the most important factors affecting the economic replacement time of drilling rigs into consideration. To this end, research literature studies and case studies have been performed, interviews have been held, observations have been made and data have been collected. For the data analysis, theories and methodologies within reliability, maintainability, ergonomics and optimization have been combined with the best practices from the related industries.

Firstly, this thesis analyses the downtime of the studied drilling rigs, with the precision and uncertainty of the estimation at a given confidence level, along with the factors influencing the failures. Secondly, the thesis identifies components that significantly contribute to the downtime and the reason for that downtime (maintainability and/or reliability problems). Based on the failure analysis, some minor suggestions have been made as to how to improve the critical components of the drilling rig. Thirdly, a new method is proposed that can help decision makers to identify the replacement time of reparable equipment from an economic point of view. Finally, the thesis proposes a method using the artificial neural network (ANN) for predicting the economic lifetime of drilling rigs through a series of basic weights and response functions. This ANN-based method can be made available to engineers without the use of complicated software.

Most of the results are related to specific industrial and scientific challenges, such as planning for cost-effectiveness. The results of the case study are promising for the possibility of making a significant reduction in the LCC by optimizing the lifetime. The results have been verified through interaction with experienced practitioners from both the manufacturer and the mining company using the drilling rig in question.

Keywords: Cost-optimization; Decision making; Drilling rig; Economic model; Life cycle cost analysis; Mining industry; Optimal replacement time; Reliability analysis; Replacement decision; Underground mining rig

IX

SAMMANFATTNING

Borrning är den process inom gruvdrift som åstadkommer hål i berg för att förbereda för laddning och sprängning. Denna process innebär hård belastning på de borriggar som utför borrningarna, vilket resulterar i oplanerade och kostsamma driftstopp. Dessa driftstopp beror bland annat på damm och hög luftfuktighet, handhavande, samt borriggarnas inbyggda funktionssäkerhet och underhållsmässighet.

Huvudsyftet med detta forskningsprojekt är att utveckla metoder att beräkna ekonomisk livslängd för borriggar i gruvmiljö. Dessa metoder skall även lämpa sig för beräkning av ekonomisk livslängd av andra typer av maskiner som består av utbytbara eller reparabla komponenter. Därvid har en livscykelkostnadsmodell tagits fram baserat på en fallstudie, där de viktigaste maskinpåverkande faktorerna tagits i beaktande. För att kunna utveckla dessa metoder och denna modell har litteraturstudier, fallstudier, intervjuer, observationer, datainsamlingar och modellering genomförts. Den så utvecklade modellen baseras på rådande teorier och metoder inom driftsäkerhet, underhållsmässighet, ergonomi och optimering för industriella applikationer.

De komponenter som väsentligt bidrar till driftstopp med avseende på funktionssäkerhet och underhållsmässighet har kartlagts. Baserat på analys av tillgänglighet, ges också några förslag på hur dessa kritiska komponenter kan förbättras. Slutligen föreslås en metod för att förutsäga den ekonomiska livslängden hos borriggar, genom användning av så kallad viktning, och utan krav på komplicerad programvara.

Resultaten är i första hand relaterade till industriella applikationer och förväntas hjälpa beslutsfattare att ta kostnadseffektiva beslut. Resultaten från fallstudien gör det också möjligt att uppnå betydande besparingar genom optimering av livslängden på borriggar. Resultaten har verifierats genom kontinuerlig interaktion med både tillverkare av borriggar och gruvbolag. Ur vetenskaplig synvinkel har också kunskapen ökats beträffande kritiska komponenters tillförlitlighet.

Nyckelord: Optimering av kostnad; beslutsfattande; borrigg; borrmaskin; ekonomisk modell; livscykelkostnadsanalys; gruvindustri; livslängd; tillförlitlighet; tillgänglighet; funktionssäkerhet; underhållsmässighet; underjordsbrytning

XI

LIST OF APPENDED PAPERS

Paper I

Al-Chalabi, H., Lundberg, J., Wijaya, A. and Ghodrati, B. (2014), ‘‘Downtime analysis of drilling machines and suggestions for improvements’’, published in the Journal of Quality in Maintenance Engineering, 20(4), 306-332. http://dx.doi.org/10.1108/JQME-11-2012-0038

Paper II

Al-Chalabi, H., Lundberg, J., Jonsson, A. and Ahmadi, A. (2014), ‘‘Case Study: Model for economic lifetime of drilling machines in the Swedish mining industry’’, published in the Engineering Economist. http://dx.doi.org/10.1080/0013791X.2014.952466

Paper III

Al-Chalabi, H., Ahmadzadeh, F., Lundberg, J. and Ghodrati, B. (2014), ‘‘Economic lifetime prediction of a mining drilling machine using artificial neural network’’, published in the International Journal of Mining, Reclamation and Environment, 28(5), 311-322. http://dx.doi.org/10.1080/17480930.2014.942519

Paper IV

Al-Chalabi, H., Lundberg, J., Al-Gburi, M., Ahmadi, A. and Ghodrati, B. (2014), ‘‘Model for economic replacement time of mining production rigs including redundant rig costs’’, submitted for publication in the Journal of Quality in Maintenance Engineering.

XIII

DISTRIBUTION OF WORK

The content of this section has been shared and accepted by all the authors who have contributed to the papers. The contributions of each named author to the scientific papers included in this thesis can be divided into the following main activities:

1. formulating the fundamental ideas of the study (initial idea and model development); 2. performing the study (data collection and analysis); 3. writing the paper and analysing the results; 4. revision of important intellectual content; 5. final approval for inclusion in the PhD thesis.

Table 1. Contributions of the main authors and co-authors of the appended papers

Pap

er I

Pap

er I

I

Pap

er I

II

Pap

er I

V

Hussan Al-Chalabi 1, 2, 3 1, 2, 3 1, 2, 3 1, 2, 3 Jan Lundberg 1, 4, 5 1, 4, 5 1, 4, 5 1, 4, 5 Alireza Ahmadi 4 4 4Behzad Ghodrati 4 4 4 4Andi Wijaya 4Adam Jonsson 1, 4Majid Al-Gburi 2 2 Farzaneh Ahmadzadeh 3

XV

ABBREVIATIONS

ANN Artificial neural networkBPP Branching Poisson processCMMS Computerised maintenance management systemDFR Design for reliability DMC Decreasing maintenance cost (%)DOC Decreasing operating cost (%)DRC Decreasing redundant rig cost (%)ERT Economic replacement time (months)GSI Geological strength indexGUI Graphical user interfaceHME Heavy mobile equipmentIAC Increasing acquisition cost (%)IFPP Increasing factor of the purchase price (%)iid Independent and identically distributedIPP Increasing purchase price (%)K-S Kolmogorov-Smirnov test LCC Life cycle cost MC Maintenance cost (cu) NHPP Non-homogenous Poisson process OC Operating cost (cu) ORT Optimal replacement time (months)PP Purchase price (cu) RFMC Reduction factor of the maintenance cost (%)RFOC Reduction factor of the operating cost (%)TBF Time between failures (h)TOC Total ownership cost (cu)TOCvalue Total ownership cost value (cu)TTF Time to failures (h) TTR Time to repairs (h)

XVII

NOTATION α Significant level cu Currency unit µx Mean time to repair (h) µy Mean time to failure (h) DTLL Lower limit of downtime (h)DTM Mean downtime (h) DTUL Upper limit of downtime (h)TTRLL Time to repair lower limit (h)MTTR Mean time to repair (h) TTRUL Upper limit of time to repair (h)mLL Lower limit of number of failures mM Mean number of failures mUL Upper limit of number of failures cu/h Currency unit per hour

XIX

TABLE OF CONTENTS

ACKNOWLEDGMENTS .................................................................................................... V

ABSTRACT ...................................................................................................................... VII

SAMMANFATTNING ...................................................................................................... IX

LIST OF APPENDED PAPERS ......................................................................................... XI

DISTRIBUTION OF WORK ......................................................................................... XIII

ABBREVIATIONS ........................................................................................................... XV

NOTATION .................................................................................................................. XVII

1 INTRODUCTION ........................................................................................................ 1

1.1 Background .............................................................................................................. 1

1.1.1 Mining drilling rig ............................................................................................. 2

1.1.2 Reliability literature review ................................................................................ 3

1.1.3 Optimal replacement time literature review ....................................................... 4

1.2 Basic concepts and definitions ................................................................................... 5

1.2.1 System reliability and performance ..................................................................... 5

1.2.2 System availability .............................................................................................. 5

1.2.3 System maintainability ....................................................................................... 6

1.2.4 System life cycle costing ..................................................................................... 6

1.2.5 Life cycle costing fundamentals .......................................................................... 7

1.3 Industrial motivation of the study .............................................................................. 8

2 THE APPROACH OF THE THESIS .......................................................................... 11

2.1 Research problem description ................................................................................. 11

2.2 Overall research goal ............................................................................................... 11

2.3 Research questions.................................................................................................. 12

2.4 Scope and limitations of the study ........................................................................... 12

3 RESEARCH METHODS ............................................................................................ 15

3.1 Data collection and analysis ..................................................................................... 15

3.1.1 Research objects .............................................................................................. 18

3.1.2 Failure and cost data......................................................................................... 18

3.2 Method used in Paper I........................................................................................... 21

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3.3 Method used in Papers II-IV ................................................................................... 21

4 SUMMARY OF APPENDED PAPERS ...................................................................... 23

4.1 Paper I .................................................................................................................... 23

4.2 Paper II .................................................................................................................. 23

4.3 Paper III ................................................................................................................. 24

4.4 Paper IV ................................................................................................................. 24

5 RESULTS AND DISCUSSIONS ................................................................................. 25

5.1 Results and discussion related to research question 1 ............................................... 25




6 CONCLUSIONS ......................................................................................................... 41

7 SCIENTIFIC & INDUSTRIAL CONTRIBUTIONS ................................................. 43

8 SCOPE OF FURTHER RESEARCH ......................................................................... 45

REFERENCES .................................................................................................................... 47

1

1 INTRODUCTION

1.1 Background

Mining is ranked as the second basic industry of early civilization after agriculture. Since prehistoric times, mining has been an essential part of human existence, i.e. mining in the broadest sense of the term, meaning the extraction of any naturally occurring mineral substances from the earth or other heavenly bodies for utilitarian purposes (Hartman, 1987). Humans began mining approximately 450,000 years ago (Hartman and Mutmansky, 2002). Nowadays, mining is the foundation of the world’s industrial development.

Minerals have been mined in Sweden for over 1,000 years. Metals from these minerals and other substances are important for society and are used in daily life. The mining industries contribute nine percent of the Swedish gross domestic product and employ 0.5 percent of the total industrial labour force (Lithander, 2004). In 2010, mining accounted for 13 percent of all industrial investments and contributed SEK 26 billion to Sweden's gross domestic product. In 2012, the Swedish Trade Council stated that the Swedish mining industry had annual sales of approximately SEK 70 billion and more than 30,000 employees, making the mining industry an important engine for growth in Sweden (Swedish Trade Council, 2012). The year 2013 was a record year for the Swedish ore production, as it reached almost 80 million tons that year, an increase of ten percent compared with 2012. Today, there are 17 mines in production in Sweden, 15 metal mines and two clay mines.

In modern mining, there are five stages in a mine’s life in the utilization of a mineral deposit. The first stage is the search for ores or other valuable minerals, which is called the prospecting stage. The second stage in the life of a mine is determining as precisely as possible the value and volume of the mineral deposit found. This stage is called the exploration stage. Development is the third stage in the mine’s life and it involves the work of opening a mineral deposit for exploitation. Exploitation, the fourth stage of mining, is associated with the actual recovery of minerals from the earth. The final stage in the operation of most mines is reclamation, the process of closing the mine (Hartman, 1987).

Mining can be classified into two main types based on the excavation technique. Type one is surface mining, which is performed on the surface by removing layers of bedrock to reach stone, coal, or ore deposits. Type two is underground mining, which concerns the exploitation of geological materials or other minerals by extracting them beneath the surface of the earth. Underground mining consists of making incisions into the earth in the form of underground tunnels to reach ore deposits, and can be classified into three main types based on the access type: slope mining, shaft mining and drift mining. Slope mining is a form of underground mining used where the mineral deposits are located very deep. This type of mining is normally carried out when there are problems drilling shafts vertically downward. Shaft mining is a type of underground mining where shafts are driven vertically into the earth to access ore deposits (Wijaya, 2012). Drift mining involves the use of a drift or horizontal access tunnel driven into the earth for extracting or transporting ore or minerals; drilling rigs are used for face drilling in this type of underground mining. This thesis focuses on drilling rigs used in underground mines. A typical drift mining process cycle consists of six processes, namely drilling, charging, blasting, scaling, loading and rock bolting. These processes form a cycle illustrated in Figure 1.1.

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Figure 1.1. A typical drift mining process cycle

The process cycle starts with drilling, the process of making blasting holes in the mining room face by crushing the rock. The next process, charging, is the process of filling the blasting holes with an explosive, for example dynamite. The subsequent process is blasting, the action of breaking rock using the charged explosives. After this the scaling process will start, in which loose material is cleared from the roof, face and walls to make the mining room completely safe. This is followed by the loading process, in which the broken rock is gathered and loaded onto trucks for removal to a central loading area. After the loading process is finished, the mining room has been cleared from broken rocks and prepared for the final process, which is bolting. Bolting involves the insertion of steel rods into holes drilled into the mining room’s roof or walls to provide support for the roof or sides of the mining room.

1.1.1 Mining drilling rig

A mining drilling rig is a machine used to create holes in the ground. Mobile drilling rigs can be used to make tunnels and underground facilities, and small or medium-sized mobile drilling rigs are utilized in mineral exploration, for example. Mining drilling rigs are used for two main purposes, namely production drilling (for processes in the mining production cycle such as bolting) and exploration drilling (for identification of the location of minerals).

As the description of the process cycle for drift mining shows, drilling is an extremely important step in the workplace. From an economic viewpoint, drilling rigs make an important contribution to the mine’s production rate, have a high acquisition, maintenance and operating cost, and represent a possible critical bottleneck for production. The L2C drilling rig is used as the object of a case study in this thesis and its components are presented in Figure1.2. This rig is manufactured by Atlas Copco and is used by Boliden AB in Sweden.

In 1898 Atlas manufactured its first drill, driven by compressed air, and then in 1915 the company produced drills equipped with four-cylinder single-acting piston motors. These drills had a design that offered many advantages over those of Atlas’ competitors, including fewer parts and good balance. The first mobile rig arrangement for underground drilling was designed for sub-level caving in Kiruna in 1952. In 1973 Atlas Copco presented the first heavy-duty impact hydraulic rock drill. The hydraulic rock drilling technique made it possible to increase the drilling output. In 1998 the company launched a new generation of underground drill rigs called boomers. Based on a modular design, this rig concept set new standards for automation, computerization and performance.

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Figure 1.2. Mining drilling rig (source: Atlas Copco Rock Drills AB)

Economic competition has pressurized mining companies into achieving higher production rates by enhancing the techniques of drilling and blasting and increasing mechanisation and automation. Boliden’s historical data over a period of one year (2008) from one of their underground mines in Sweden show that more than 15% of the unplanned downtime of mobile rigs is related to drilling rigs, the greater part of whose downtime is attributed to the poor reliability of their components. Thus, the drilling rig is a bottleneck in the production cycle and is becoming an important object of research in underground mining. Due to a combination of a harsh environment, the operation context, and reliability and maintainability issues, the drilling rig is a major contributor to unplanned downtime.

In the following subsections, an account is given of literature reviews performed to identify the current status of research on reliability and optimal replacement times, as documented in the available literature.

1.1.2 Reliability literature review

A mine production system consists of many subsystems. To make a mining system profitable, the optimization of each subsystem in relation to other subsystems should be considered (Barabady and Kumar, 2008). To achieve this aim, reliability and maintainability analysis should be performed for each subsystem in the mine production system. Since the mid-1980s, reliability analysis techniques have been essential tools in automatic mining systems (Blischke and Murthy, 2003).

Many researchers have studied the reliability and maintainability of mining equipment and its failure behaviour. For example, Kumar et al. (1989) analysed the operational reliability of a fleet of diesel-operated load-haul-dump (LHD) machines in Kiruna Mine in Sweden. They divided the LHD machines into four main subsystems. They did separate failure analyses and the reliability of the fleet was modeled. Kumar et al. (1992) performed reliability analysis on the power transmission cables of electric mine loaders in Sweden. They used a proportional hazards model to investigate the effects of two different designs on the reliability of a power transmission cable of an electric mine loader. They have found that the proportional hazards model can be used as an explanatory tool to seek explanations for undiscovered facts and on that basis decisions for selecting the suitable design for a component can be taken. Kumar and Klefsjö (1992) analysed the maintenance data of one subsystem (the hydraulic system) of a fleet of six LHD machines divided into three independent groups at Kiruna Mine.

1 Cabin 6 Front jacks 11 Cable reeling unit 2 Boom 7 Hydraulic pump 12 Diesel engine 3 Rock drill 8 Rear Jack 13 Hydraulic oil reservoir4 Feeder 9 Electric cabinet 14 Operator panel 5 Service platform 10 Hose reeling unit

4

Reliability assessment of mining equipment was performed by Vagenas and Nuziale (2001); using genetic algorithms, they developed and tested reliability assessment models for mobile mining equipment. They found that the application of genetic algorithms in reliability engineering may contribute to a better understanding of the reliability characteristics of industrial systems. Vayenas and Xiangxi (2009) used reliability-based maintenance to study the availability of 13 LHD machines in an underground mine. They were interested in the influence of machine downtime on the productivity and operation costs of these machines. They found that mechanical breakdowns and planned maintenance consume most of the repair time of the fleet. Wijaya et al. (2011) developed a method for visualising downtime by using a jack-knife diagram; they applied the method on a scaling machine at a mine in Sweden. Gustafson et al. (2012) analysed the reliability of automatic and manual LHD machines and performed a comparison between them. They found that the hydraulic and electric systems are the biggest reasons for the downtime of both manual and automatic LHD machines.

In addition, many studies have considered reliability, maintainability and optimum replacement decisions; readers are referred to Ahmadi and Kumar (2011) and Dandotiya and Lundberg (2012), for example, for further studies on the recent literature in this field. The first study to have been made regarding the downtime analysis of mining drilling rigs is presented in this thesis.

1.1.3 Optimal replacement time literature review

Standard models for economic replacement time (ERT) decisions contain an estimation of the discounted costs by minimising the total cost of the equipment. The assumption of these models is that equipment will be replaced at the end of its economic lifetime by a continuous sequence of identical equipment (Hartman and Tan, 2014). Bellman (1955) developed the first optimal asset replacement model for a variable lifetime of assets. Wagner (1975) offered dynamic programming formulation for the equipment replacement problem in which the state of the system is the time period and the decision at each period is to keep the equipment for N periods. His formulation has been extended by researchers to deal with the realities of technological changes, for example see Oakford et al. (1984), Bean et al. (1985), Hartman and Rogers (2006), and Hritonenko and Yatsenko (2008). These authors assumed a finite horizon in their approaches to the problem of equipment replacement under non-stationary costs.

In 1976, Elton and Gruber (1976) showed that an equal life policy was optimal on an infinite horizon under technological changes. In contrast, Hartman and Murphy (2006) studied an asset replacement problem for a stationary finite horizon; they illustrated how a bound on the number of times an asset is retained in its economic life can be obtained, thus suggesting that it is optimal to replace the asset during its economic lifetime.

Dynamic programming models have been utilized in real cases of calculating equipment replacement time because of the important uncertainties associated with life cycle costs (Richardson et al., 2013). The net present value of all the life cycle costs associated with an infinite sequence of equipment life cycles has also been used to make equipment replacement decisions (Bethuyne, 1998; Scarf and Bouamra, 1999; Hartman, 2005; Yatsenko and Hritonenko, 2005). Other researchers have used different equipment replacement models to analyse a variety of equipment, such as forklifts, buses, and aircraft (Eilon et al., 1966; Keles and Hartman, 2004; Bazargan and Hartman, 2012). Although Tanchoco and Leung (1987) found that replacement decisions could be influenced by capacity considerations, others have noted that technological changes can encourage decision makers to utilize equipment beyond its economic lifetime (Cheevaprawatdomrong and Smith, 2003). The first study to have been made regarding the optimal replacement time of mining drilling rigs is presented in this thesis.

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1.2 Basic concepts and definitions

1.2.1 System reliability and performance

In this section we present the basic definitions of reliability and discuss the relationship between reliability and performance. System or product reliability is defined as the ability of a product or system to perform as intended (i.e. without failure and within specified performance limits) for a specified period of time and in its life cycle conditions (Kapur, 2014). Reliability is an important attribute of a system or product. In the case of the drilling rig, the user expects the rig to operate properly for a specified period of time beyond its purchase date, which usually depends on the purpose and cost of the rig. At a low cost, a throwaway rig may be used as a redundant rig just for a limited period of operation. A reliable rig may be expected to last for many years of operation when it is properly maintained. The behaviour or the future performance of the system depends on its reliability. Thus, reliability has been considered as a term that concerns quality (Kapur, 1986; O'Connor, 2000). In the past few decades, system reliability has been defined in many ways, including the probability that a system, product, or device will not fail for a given period of time under specified operating conditions (Shishko and Aster, 1995). System reliability can be defined as the capability of a product to meet customer expectations of product performance over period of time (Stracener, 1997).

The performance of equipment is typically associated with the functionality of that equipment, what the equipment can do and how well it can do it. For example, the functionality of an underground mining drilling rig involves drilling holes in the face and walls of mining rooms. How it drills the holes and the quality of the holes involve functional performance parameters such as rotational speed, feeding speed, ease of drilling hard rocks, and steering adjustments. Improving the performance of equipment usually requires adding technology and complexity. This can make the desired reliability difficult to achieve.

To summarize the relationship between reliability and performance, it can be stated that the reliability of equipment refers to its ability to perform its function without failure for a certain period of time in its life cycle application under specified working conditions and within certain limits of performance. The performance parameters usually describe the functional capabilities of the equipment. Finally, it can be stated that the performance of equipment is related to its reliability.

1.2.2 System availability

Availability is defined as a percentage measure of the degree to which machinery and equipment are in an operable and committable state at the point in time when they are needed. This definition includes committability and operability factors which are contributed to by the equipment itself, the process being performed, and the surrounding facilities and operations (Katukoori, 1995). There are different classifications of availability and different ways to calculate it. A common classification is based on the span of time to which the availability refers and the types of downtime used in the computation. There are a number of different classifications of availability, such as the following:

point availability, defined as the probability that the system is in an operable state at a specified time;

interval availability, defined as the expected fraction of an interval of a specified length of time during which the system or equipment is in an operable state;

steady state availability, defined as the expected fractional amount of time in a continuum of operating time during which the system or equipment is in an operable state.

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For further discussion about the classifications and ways to calculate the system availability, see Katukoori (1995), Kumar and Akersten (2008), and Stapelberg (2009).

1.2.3 System maintainability

The maintainability of an item is defined as its ability, under stated conditions of use, to be retained in, or restored to, a state in which it can perform its required function when maintenance is performed under stated conditions and using prescribed procedures and resources (Rausand, 2004). System maintainability is a main factor which can be used to determine the availability of the system.

The maintainability of a system depends on design factors such as ease of reinstallation, ease of dismantling, ease of access to the system, and so on. Maintainability is primarily determined by the design of the system or the item and can be greatly enhanced if the repair procedure and fault detection and isolation are worked out during the design stage of the system itself. The objective of maintainability is to restore the function of the system in a minimum period of time.

1.2.4 System life cycle costing

The life cycle cost of a system can be defined as the sum of all the acquisition and ownership costs incurred during the useful life span of the system. These costs include direct, indirect, recurring, nonrecurring, and other related costs incurred, or estimated to be incurred, in design, research and development, investment, operations, maintenance and other support of the system, and retirement of the system. The ownership costs represent the total of all costs other than the acquisition or initial cost during the life span of a system. The term life cycle costing was used for the first time in 1965 in a report entitled "Life Cycle Costing in Equipment Procurement" (Dhillon, 2010). This report was prepared by the Logistics Management Institute, Washington, D.C., for the Assistant Secretary of Defense for Installations and Logistics, the U.S. Department of Defense, Washington, D.C. According to many studies, the system ownership cost (i.e. operating and logistic cost) can vary considerably and amount to 10-100 times the original acquisition cost (Ryan, 1968). Determining the system’s life cycle cost is an important issue, because the acquisition is a small part in relation to the total costs associated with owning and operating the system.

The life cycle cost of a system can be determined through one of three general methods (Farr, 2011). These methods are the engineering build-up, the analogy and the parametric method. The engineering build-up method involves direct estimation at the component level leading to a detailed engineering build-up cost estimate of the system. This can be achieved by using machine element and mechanics theories for estimating the lifetime of equipment and practical lifetime tests, see, for instance, Norton (2011). The engineering build-up methodology can be used for individual estimates for each item, element, or component, and these estimates are then combined into the overall cost estimate. Therefore, this methodology is sometimes classified as a "bottom-up" estimating method. It involves computation of the cost of each element by estimating costs at the lowest level of detail and computing quantities and levels of effort to determine the total system cost.

In the analogy method an estimate is made using historical results from a similar system or product. Analogy estimates are performed on the basis of comparison and extrapolation using similar systems or items. In many instances this can be accomplished using simple relationships or equations representative of detailed engineering build-up estimates of past projects. The preferred means to conduct a cost estimate early in the system life cycle is to use data from programmes that are technically representative of the programme to be estimated. The cost

7

data are then subjectively adjusted upward or downward, depending on whether the subject system is felt to be more or less complex than the analogous programme (Farr, 2011).

The parametric method is based on mathematical models or equations. Simple mathematical relationships such as nonlinear and linear regression are mostly utilized. Excel software, for example, can be easily utilized to fit these relationships (Farr, 2011). In this thesis, the parametric method is used to calculate the total ownership cost of the drilling rig and to estimate its economic lifetime.

1.2.5 Life cycle costing fundamentals

Life cycle costing can be defined as a method for estimating the total life cycle cost of an acquired item or acquired equipment. The total life cycle cost includes equipment procurement and ownership costs. The equipment ownership cost could be quite significant and in most cases exceeds the procurement cost. For example, various studies indicate that the operating and maintenance costs over the life span of equipment could be many times greater than its procurement cost (Ryan, 1968). There are many reasons why the industrial sector all around the world is being compelled increasingly to use life cycle costing to make different types of decisions that indirectly or directly concern engineering systems. Examples of these reasons are increasing operation and maintenance costs, budget limitations, competition, and the high cost of investment (Seldon, 1979). There are six primary areas where life cycle costing can be used: comparing competing projects, controlling on-going projects, long-term planning and budgeting, selecting a successful candidate among bidders competing for a project, comparing logistics concepts, and deciding the optimal replacement of aging equipment (Seldon, 1979). The focus of this thesis is directed on the economic replacement time of mining drilling rigs. To perform life cycle costing studies, different types of information are required, such as the costs connected with the acquisition, operation, maintenance, installation, and transportation (delivery) of the equipment, the taxes to be paid, the disposal cost, the second-hand value, and the useful operational life of the equipment or systems ( Brown, 1979).

There are many activities associated with life cycle costing, including the following (Earles, 1981):

o conducting appropriate sensitivity analysis; o defining activities that generate a product’s or an item's ownership costs; o establishing discounted life cycle costs; o identifying all the cost drivers; o defining a product's or an item's life cycle.

Over the years, many authors have proposed steps for performing life cycle cost analysis (Wynholds and Skratt, 1977; Coe, 1981; Dhillon, 2013). The following ten steps have been considered quite effective in performing life cycle cost analysis (Greene and Shaw, 1990):

1. determine the life cycle cost analysis objective, 2. define the scope of the system, 3. choose the effective models for estimating the life cycle cost, 4. obtain all the essential data and make the appropriate inputs into the selected model, 5. conduct sanity checks for outputs and inputs, 6. conduct essential sensitivity analysis, 7. formulate the life cycle cost analysis results, 8. document the life cycle cost analysis, 9. present the life cycle cost analysis as is appropriate, 10. update the life cycle cost analysis as is appropriate.

8

In order to perform effective life cycle cost analysis, availability of reliable cost data is necessary. This means that the existence of good cost data banks is very important. Thus, in developing a new cost data bank, careful attention must be given to factors regarding the data such as uniformity, volume, responsiveness, flexibility and comprehensiveness (Dhillon, 2010). Although data for life cycle cost analysis can be obtained from many sources, their quality and amount may vary quite considerably. Therefore, prior to starting a life cycle cost study, it is vital to examine carefully factors such as data applicability, data availability and data bias (Dhillon, 1999).

In 2010 Dhillon discussed the advantages and disadvantages of life cycle costing, stating that the important benefits of life cycle costing are that they are useful for the following purposes:

o reducing the total cost, o controlling programmes, o comparing the cost of competing projects, o making decisions associated with equipment replacement, planning, and budgeting.

In contrast, some of the main disadvantages of life cycle costing include the following:

o it is costly; o it is time-consuming; o the acquisition of data for analysis is a trying task, o it has doubtful data accuracy.

For more details, see Dhillon (2010). The specific purposes of life cycle costing in product acquisition management are to estimate the total ownership cost (TOC) of the product and to decide when to buy a new one. Reducing the TOC by using LCC analysis is an important issue in the development process of the product, and understanding TOC implications is necessary to decide whether to continue to the next development phase, as well as to control costs and assist the procurement decisions (Farr, 2011).

Life cycle cost analysis is an economic estimation technique that determines the total cost of owning, operating, maintaining and disposing of a system over its life span. It must be used to understand fully how to determine and interpret the total ownership cost of a system (Farr, 2011). A simple process for developing an LCC model is shown in Figure 1.3.

1.3 Industrial motivation of the study

Industrial companies, or more specifically mining companies, put huge funds, often millions of dollars, into their annual budgets to purchase heavy mobile equipment (HME) such as drilling rigs, scaling rigs, wheel dozers, wheel loaders, dump trucks, etc. Given the enormous costs of acquiring, operating, and maintaining their HME, it is important for mining companies to optimise their replacement and procurement strategies (Richardson et al., 2013). With increased mine production, the HME operating hours will increase and, as a result, the operating and maintenance cost will increase also. At some point in the equipment’s life span, these costs will be too high and, since it will then no longer be economically viable to continue using the old equipment, it should be replaced (Verheyen, 1979). An essential economic consideration in industrial companies is that a model must be found for identifying this point (i.e. the point at which the equipment replacement time is expected to yield a minimal life cycle cost). Obviously, for mining companies, one of the most important decisions concerns determining the ERT of capital equipment; this can be accomplished with the help of life cycle cost analysis. The main reason for the increasing use of the life cycle costing concept for HME is that at some point the operating and maintenance costs will exceed the acquisition costs.

9

Figure 1.3. Process for developing an LCC model (adapted from Farr, 2011)

Since the 1960s most of the research conducted in the field of mining equipment has concerned the reliability and maintenance of such equipment. Nowadays, modern mining machines have a higher technology level and a higher complexity in comparison with the old ones (Hoseinie, 2012). Reliability analysis techniques have been gradually accepted as standard tools for the planning and operation of complex and automatic mining equipment (Barabady and Kumar, 2008). Generally, the downtime costs of mining equipment are too high due to high production losses (Dandotiya, 2012). In order to enhance equipment reliability and to reduce mining equipment downtime, a large amount of research has been conducted using various methods to ensure the improvement of equipment design and maintenance procedures. Reliability analysis can be used in identifying the sensitive subsystems and critical components of mining machinery. Moreover, reliability analysis has been acknowledged as the basic requirement for all maintenance planning, prediction of the remaining useful life, and life cycle cost analysis of machinery. Therefore, we need to analyse the reliability of operating machinery at the first stage of any comprehensive field studies.

A preliminary study performed by the author of this thesis in one underground mine in Sweden revealed that more than 15 percent of the unplanned downtime of mobile equipment is related to drilling rigs. This high amount of unplanned downtime leads to monetary losses, which need to be minimized. Since drilling is the first process of a typical mining cycle and is a key factor for production, it is also important to find solutions for drilling rig problems and reduce the downtime. To minimize losses related to downtime, the reliability of the drilling rig should be improved and the economic replacement time of the rig should be determined. The replacement of rigs should be carried out in a cost-effective way.

The present study has focused on the development of a model that can be used by the manufacturer and the operator companies for easy estimation of the optimal replacement time of drilling rigs from an economic point of view. This model can in principle be used for other machinery used in the mining industry or other industries. Furthermore, the study has also aimed to calculate the downtime of drilling rigs to assist the manufacturer and operator companies in identifying the problems affecting rig downtime and to provide solutions that will reduce it. This collaborative research has been jointly conducted by Luleå University of Technology, a mining company operating the drilling rig and the manufacturing company which developed the rig.

Understand the manufacturer and operator requirements

Define the scope

Collect data

Sensitivity analysis

Conduct LCC

analysis

Evaluate and normalize the

data

Select the variables

Data analysis and correlation

Regression and curve fit

11

2 THE APPROACH OF THE THESIS

2.1 Research problem description

Meeting an increasing demand for higher production, reducing the production equipment’s downtime and increasing its productivity are the major concerns of the collaborating mining company. Economic competition is pressurizing the mining company into achieving higher production rates by enhancing its drilling and blasting techniques and increasing its mechanisation and automation. This means that improving the availability of the company’s production rigs should be investigated.

The production rigs are those rigs which contribute directly to the mine production rate and create value for the company. One of these production rigs is the drilling rig. The maintenance department at the mining company aims to reduce the number of failures and the downtime of production rigs. The financial department at the company aims to reduce the costs associated with the drilling rig’s acquisition, operation and maintenance by implementing a cost-cutting strategy. There are many reasons why the mining company is being compelled increasingly to use life cycle costing to make different types of decisions that indirectly or directly concern production rigs. Examples of these reasons are increasing operation and maintenance costs, budget limitations, competition, and the high cost of investment. The overall goal of the mining company is to increase its mine production and the company profit.

To achieve the goal of the maintenance department, the engineers at this department asked the following questions: which components of the drilling rig have mostly contributed to its downtime and which problems have the greatest effect on the downtime of the rig? To achieve the goal of the financial department, the financial experts at this department asked the following question: what is the best time to replace the rig and buy a new one from an economic point of view, with a view to reducing the total ownership cost of the rig? To achieve the overall goal of the mining company, downtime analysis should be performed for the drilling rig to identify the rig components that contribute most to its downtime, to identify the problems affecting the downtime of those components, and, if possible, to make suggestions for the solution of these problems. Another measure which would help the company to achieve its overall goal would be to perform life cycle cost analysis for the drilling rig in order to estimate the optimal replacement time of this rig, with a view to reducing the ownership cost from an economic point of view and increasing the company profitability.

The main reason for an increased use of the life cycle costing concept for production machinery is that at some point of its life span the operating and maintenance costs will exceed the acquisition costs. To this end one should consider focusing one’s attention on optimization models, techniques and tools which can help the decision makers in the mining company to optimize their equipment lifetime.

2.2 Overall research goal

The overall research goal has been to develop methods for downtime analysis and replacement time optimization. These methods should be useful for machinery in general and specifically for drilling rigs in mining applications.

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2.3 Research questions

To fulfil the overall research goal of the thesis, the following research questions (RQs) have been formulated.

1. Which critical components make a large contribution to the downtime of the drilling rig? What are the dominant problems influencing the drilling rig downtime, reliability problems and/or maintainability problems?

2. How should a model be constructed that can calculate the optimum replacement time of a drilling rig? Moreover, which cost factors have the largest impact on the replacement time?

3. How should the above model be improved with respect to easy and accurate prediction of the economic lifetime of this rig, with a high level of certainty and with a view to enhancing decision making in this regard?

4. How should a model be constructed for estimation of the economic lifetime of mining production rigs when also the costs from one redundant rig are considered?

These research questions are answered by the four appended papers, each of which makes its own contributions toward the research questions (see Table 2.1).

Table 2.1. Relationship between the appended papers and research questions

Pape

r I

Pape

r II

Pape

r II

I

Pape

r IV

Research question 1 (RQ 1) XResearch question 2 (RQ 2) X X XResearch question 3 (RQ 3) XResearch question 4 (RQ 4) X

The research framework appears in Figure 2.1. Paper I analyses and compares the downtime of four drilling rigs used in two underground mines in order to identify the critical components of these rigs. Paper II develops a practical model to calculate the optimal replacement time of the drilling rigs. Paper III develops a new model for easy and accurate prediction of the economic replacement time of mining drilling rigs by using an artificial neural network technique. Paper IV develops a model to determine the economic replacement time of production rigs used in the mining industry when also the costs from one redundant rig are considered.

2.4 Scope and limitations of the study

The scope of this thesis is limited to the drilling rig and, more specifically, to the study of the replacement time of drilling rigs used in underground mines in Sweden, as well as the issues related to the downtime of these rigs. The thesis is based on manually entered failure, repair and cost data from the collaborating mines.

The limitations of this thesis can be described as follows. Firstly, the reliability of human beings is an important area to consider, but is beyond the scope of this thesis. Secondly, the data are related to specific mobile mining equipment, with specific environmental and operating characteristics and working in specific underground mines. Thirdly, the results obtained from this research are limited to the information that could be extracted from the collected data.

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Fourthly, the results are limited to case studies of L2C drill rigs. Fifthly, the operating conditions, for example the working environment, are not considered in the downtime analysis. Sixthly, the influence of production performance of the drilling rig is not considered in the model of the optimal replacement time. The model is only considering the costs. Finally, in the present thesis, the replacement time analysis was performed based on the cost data obtained from only one drilling rig operated in a single underground mine in Sweden. Consequently, the operating conditions should be taken into consideration before applying the study’s results, especially when the operating conditions are not similar to those in the present study.

Figure 2.1. Research framework

Reliability and Life Cycle Cost Modelling of Mining

Drilling Rigs

Paper I

Downtime analysis and

comparison between different subsystems

Paper II

Optimal replacement time estimation

Paper III

Economic replacement time prediction using

artificial neural network

Paper IV

Model for ERT considering different cost

factors

15

3 RESEARCH METHODS

3.1 Data collection and analysis

The data were collected from the database of the computerized maintenance management system (CMMS) of the mining company participating in the present study. The literature survey was carried out based on relevant peer-reviewed papers in conference proceedings and journal articles from online databases. Some of the papers and articles were searched for on the basis of references of other relevant articles, and some of the known papers and articles were retrieved directly from the journal databases. Relevant books and reports were searched for in Lucia (Luleå University Library’s online catalogue), and PhD and licentiate theses from various universities were studied. Specific keywords were used to search for information in well-known online databases, including Science Direct, Elsevier, Emerald, Springer and Google Scholar. Moreover, discussions were held with reference groups.

The present research was performed on two underground mines in the north of Sweden. Failure and repair data for two years (August 2009-August 2011) were collected to answer research question one. These data were collected from the two mines for four drilling rigs. Three rigs were working in the first mine and the fourth rig was working in the second mine. Cost data for around four years (March 2009-January 2013) were collected to answer research questions two, three and four. The cost data were collected for a single rig operating in the second mine.

The analysis of failure data which can be used in reliability analysis should be based on the assumption that the times between failures (TBFs) are independent and identically distributed in the time domain. The magnitude of the recorded TBF data was valid for fitting the various distributions for representing the population of the TBFs. However, before any reliability analysis for Paper I was performed, trend and serial correlation tests had to be carried out to check whether the usual assumption of independent and identically distributed TBF data in the data sets would be contradicted or not (Kumar, 1989; Kumar and Klefsjö, 1992). The Laplace trend test was used in this study to test the hypothesis that a trend did not exist within the TBF data. We calculated the test statistic U for the TBFs of the drilling rig subsystems to be at a significant level of 0.05. From the standard normal tables, with a significant level of 0.05, the critical value is equal to 1.96. If -1.96<U<1.96, then we would accept the hypothesis of no trend within the TBF data. After applying the trend test for the critical components of the studied rigs, we found that there was no trend within the TBF data; for example, U was equal to 0.55 in the feeder of the drilling rig used in the second mine.

The serial correlation test of the TBF data of the drilling rigs and their subsystems was carried out to check the dependence of the TBF data. This test was performed by plotting the ith TBF against the (i-1)th TBF. We tested the significance of the correlation by calculating the (r) value and comparing it with the critical (r) value, which could be obtained from the correlation tables. For example, the results of the serial correlation test of the above component (i.e. the feeder) are given in Figure 3.1. Since the points are randomly scattered, the failure data can be assumed to be independently distributed. The (r) value is equal to 0.05, while the critical value of (r) from the correlation tables at the significance level alpha = 0.05 and a degree of freedom of 30 for a two-tailed test is equal to 0.364. We can conclude that the correlation between the TBFs of this subsystem is statistically not significant (i.e. no correlation

16

exists), since r < the critical r. Different types of statistical distributions were examined and their parameters were estimated by using the Easy Fit and Minitab software.

0

100

200

300

400

0 50 100 150 200 250 300 350 400

ith

TB

F

(i-1)th TBF

Serial correlation test

Figure 3.1. Serial correlation test for the feeder of the drilling rig

As mentioned earlier, the cost data for the single machine used in one mine were collected for a period of around four years. Figures 3.2 and 3.3 illustrate the maintenance and operating cost for this period.

Figure 3.2. Maintenance cost Figure 3.3. Operating cost

With reference to Papers II-IV, since the user company planned to use the machine for 120 months, extrapolation was performed on the operating and maintenance cost data. Figures 3.4 and 3.5 illustrate the maintenance and operating costs determined by data extrapolation.

Figure 3.4. MC after extrapolation Figure 3.5. OC after extrapolation

In Figures 3.4 and 3.5, the dots represent the real historical data for the maintenance and operating costs. Curve fitting was performed using the Table Curve 2D software to show the behaviour of these costs before and after the time when the data were collected. Note that the fitting would have been better if more data had been available for a time period of more than

Maintenance cost

70 80 90 100 110 120Time (month)

0

25

50

75

100

125

150

Mai

nten

ance

cos

t (cu

)

Operating cost

70 80 90 100 110 120Time (month)

15

25

35

45

55

Ope

ratin

g co

st (

cu)

Maintenance cost

0 50 100 150 200Time (month)

-200

-100

0

100

200

300

400

Mai

nten

ance

cos

t (cu

)

Operating cost

0 50 100 150 200Time (month)

-50

0

50

100

150

Ope

ratin

g co

st (

cu)

17

four years. This software uses the least squares method to find a robust (maximum likelihood) optimisation for nonlinear fitting. It is worth mentioning that the drilling rig in this case study had no multi-level preventive maintenance programme. The main reason why the maintenance cost was quite low in the earlier months was that the rig was new at the start of its utilization. The history shows that the user company began to keep track of cost data by using CMMS when the maintenance costs started growing. This observation can be compared with the three phases in the conventional bathtub curve (see Figure 3.6) used in reliability studies (Blischke and Murthy, 2003).

Figure 3.6. Bathtub curve (adapted from Blischke and Murthy, 2003)

The first phase of this curve represents the period with a relatively large number of early failures. This phase is not included in Figure 3.4 because the failures are considered to have been identified and resolved before the delivery of the rig to the mining company. The rig is assumed to have been delivered to the mining company while in the second phase. In this phase the rig has random failures at a low and almost constant failure rate. This phase is visible in the period between 0 and 76 months in Figure 3.4, where the cost is low and relatively constant. The final phase represents a period with an increasing number of failures that are related to the aging of the system. This corresponds to the period between 76 and 120 months in Figure 3.4.

There was no information regarding the number of failures and the maintenance cost at the beginning of the lifetime of this rig and up to the time when the company started to record these data in its CMMS. Therefore, the ‘‘Lorentzian Cumulative’’ equation was used to perform the extrapolation for the maintenance cost data.

The fitted curve for the maintenance and operating costs (in the second and third phases) using the Lorentzian extrapolation is assumed to represent the behaviour of our data adequately, since r2 (adj.) = 0.97 and 0.91 for the two costs, respectively. In Figures 3.4 and 3.5, the inflection point after 120 months of operation is due to a change in the usage profile of the rig, as the rig was to be used as a redundant rig. This was confirmed by the engineers at the collaborating mine. The rig was to be used after 120 months of operation only when any of the production drilling rigs should fail, and therefore the planned service and corrective maintenance were assumed to be relatively constant.

In Paper IV, MATLAB code was used to generate data sets for different time scales for using a redundant rig, after discussion with an expert group at the collaborating mining company (see Figure 4 and Table 3 in Paper IV).

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3.1.1 Research objects

The present research was performed on four drilling rigs working in two different underground mines in Sweden. The first underground mine began operating in 1940 and is classified as one of the oldest operating mines in Sweden. The predominant mining method used in this mine is cut-and-fill mining with hydraulic backfill (Krauland et al., 2001). The geology of the mine is irregular and complex. The complex ore is presently extracted at a depth of 900-1,400 m below the surface. The ores extracted from the first mine are lead, gold, copper, zinc, gold-copper and silver ores (Rådberg et al., 1992). In this mine, the uniaxial compressive strength of the intact host rock varies from 65-150 MPa and the geological strength index (GSI) varies between 50 and 80 (Edelbro, 2008). The second underground mine began operating in 1952 and is located in northern Sweden. The extraction process in this mine is the cut-and-fill method. The extracted ore is polymetallic and contains copper, gold, silver, lead and zinc. The geological strength index of the rock varies between 70 and 80 at a depth level of •1115-1130 m and the rock mass is of high quality, while at a depth level of •1130-1185 m, the rock mass quality is lower, with a geological strength index equal to 30-50 (Edelbro, 2009).

The drilling rig investigated in the present research is the L2C drilling rig, which is a model typically used in underground mining in Sweden. The dimensions of this rig are as follows: length 14.5-16.6 m; width 2.5 m; width of the rig with side platforms 2.9 m; height of the rig with the cabin 3.15 m; weight 26-33 tons (see Figure 1.2). The rig has four retractable stabilizer legs and an articulated four-wheel drive chassis. It can be operated by a water-cooled turbocharged diesel engine with 120 kW at 2,300 rpm or by electric power with a capacity of 158 kW (Atlas Copco Rock Drills AB, 2010).

3.1.2 Failure and cost data

The failure data used in this research (see Paper I) were collected over a period of two years (2009-2011). The source of the data is the database of the two underground mines in Sweden participating in the study. This database belongs to the MAXIMO system, which is a computerized maintenance management system (CMMS). In this research study, the time to failure data (TTF data) and the time to repair data (TTR data) of four drilling rigs and their subsystems were arranged in chronological order so that statistical analysis could be used to determine if there was any trend in the failure and repair data. The framework for the basic methodology used in this study for the analysis of the failure and repair data is presented step-by-step in Figure 3.7.

The first step in analysing the data was calculation of the times between failures (TBFs) for the system. In the CMMS, the failure data are recorded based on calendar time. Since drilling is not a continuous process, the TBFs were estimated by considering the utilization of each rig. Reliability and maintainability data analysis is usually based on the assumption that the TBF and TTR data are independent and identically distributed (iid) in the time domain. Therefore, it was critical to conduct a formal verification analysis of the assumption that the TBF and TTR data were iid; otherwise completely wrong conclusions could be drawn (Ascher and Feingold, 1984; Kumar and Klefsjö, 1992). The next step, after sorting and classifying the TBF and TTR data based on the component level, was validation of the iid assumption. The failure data were tested for trends using the Laplace trend test. This trend test is used to determine whether the data set is identically distributed (Klefsjö and Kumar, 1992). If such a trend is observed, then classical statistical techniques for reliability analysis may not be appropriate. Therefore, a non-stationary model such as the non-homogenous Poisson process (NHPP) must be fitted (Ascher and Feingold, 1984; Kumar and Klefsjö, 1992; Modarres, 2006; Birolini,

19

2007; Louit et al., 2009; Ghosh and Majumdar, 2011). Otherwise, the serial correlation test can be used to test the dependence of the failure data. A dependence test determines whether successive failures are dependent in data without a long-term trend (Klefsjö and Kumar, 1992). If a dependence between successive failure data is observed, a branching Poisson process (BPP) model can be used in this case (Ascher and Feingold, 1984). If a dependence is not observed, then the iid assumption is valid. After testing the validity of the iid assumption, different types of statistical distributions were examined and their parameters were estimated by using the Easy Fit and Minitab software. The goodness of fit of the distribution was tested by using the Kolmogorov-Smirnov (K-S) test with the Easy Fit software. In the present study, all the statistical tests were conducted by using a significance level (α) equal to 0.05.

Figure 3.7. Flowchart for analysing failure data (adapted from Asher and Feingold (1984))

The cost data used in the present research (see Papers II-IV) were collected over a period of around four years. The CMMS is the source of the cost data for the single rig operating in the second collaborating mine in this study, as mentioned earlier. The cost data contain corrective maintenance costs, preventive maintenance costs and repair times. The corrective and preventive maintenance costs contain costs for spare parts and labour (repair personnel). It is important here to mention that all the cost data used in this study concern real costs without inflation. Due to the company regulations, all the cost data were encoded and expressed in currency units (cu) for this research. A sample of the cost data can be seen in Table 3.1.

Table 3.1. Sample of cost data (Date format: ‘‘year-month-day’’)

Work description Working time (h)

Materials cost (cu)

Labour (cu)

Service cost (cu)

Total cost (cu)

Date Component Description

Work type

Extension 2 bolts of V-feeder

1 28.148 0.45 0 28.598 20xx-03-15 13:23

Feeder PM

FU1 Atlas L2C/2 5 9.836 0 4.182 14.018 20xx-03-15 13:24

PM

Mounting the sensor cables

6 0 2.7 0 2.7 20xx-03-15 22:41

Steering system CM

Atlas Copco L2C 16 0 7.2 0 7.2 20xx-03-16 13:17

Electrical system

CM

Replacing the hose feeding

0.5 0 0.225 0 0.225 20xx-03-19 07:30

Hoses CM

20

Figure 3.8 shows the flow chart for the data collection and analysis process for the LCC optimization model in Papers II-IV.

Figure 3.8. Flow chart for the data collection and analysis process used for the LCC model

21

3.2 Method used in Paper I

Paper I analyses the failure and repair data of four drilling rigs working in two different mines in order to estimate the downtime interval of each component for each rig. The aim of the downtime interval estimation is to identify the problems affecting the rig availability, to determine whether they are reliability problems and/or maintainability problems. Downtime analysis usually involves different groups of people who have different knowledge and backgrounds (Wikoff, 2008). For example, the present study involved three main groups, personnel representing the manufacturing company, personnel representing the company using the drilling rig, and representatives of academia. Given the groups’ diversity, it was vital to make the communication between them more effective and clear. To do so, a downtime visualization method developed by Wijaya in 2011 was used in this paper. This visualization method is based on the jack-knife diagram and presents a point estimation (a single value) of the downtime (Knights, 2001). To overcome the shortcomings of the point estimation of the downtime, an interval estimation of the downtime was used in this paper. This downtime interval involved three estimation points, namely the mean, the upper limit and the lower limit of the downtime.

In making the interval estimation, the method assumed that the failure times followed the Weibull distribution and the repair times followed the lognormal distribution. The failure and the repair data for the iid assumption and the goodness of fit of probability distributions were tested (see Figure 3.7). The confidence interval of the estimated downtime for a given uptime was solved by finding a confidence interval for the ratio of the mean time to repair (µx) to the mean time to failure (µy). In this study, the ‘‘exact method’’ (Masters et al., 1992) was implemented to estimate the confidence interval of μx/μy. The interval estimation of the downtime was then plotted on a log-log diagram as a function of the log number of failures (the vertical axis) and the log repair time (the horizontal axis). The used method was then applied to identify the critical components that made a greater contribution to the rig downtime. These components could be ranked based on the three estimation points of the downtime in order to highlight the component which should be prioritized and improved first. Based on discussions with the reference group, interviews with operators and field observations, some minor suggestions were made as to how to improve the critical components of the drilling rigs used in the collaborating mines.

3.3 Method used in Papers II-IV

Papers II-IV propose an approach to life cycle cost optimization of a single drilling rig for one mine in Sweden. The proposed approach is based on the calculations of the operating and maintenance cost of the case study. Extrapolation for the maintenance and operating cost was performed to generate data for the unavailable period during the life cycle of the rig. A declining balance depreciation method was used to estimate the resale value of the case study after each month of operation. In this method, a fixed percentage of the book value at the beginning of the month represented the monthly depreciation of the rig (Luderer et al., 2010; Eschenbach, 2010; Dhillon, 2010). The rig resale value is the rig’s value if/when the firm wants to sell it at any time during its lifetime. A life cycle optimization model was developed to estimate the optimal replacement time (ORT) of our case study. In Paper II, after the ORT was calculated, a single-variable sensitivity analysis and a multivariable sensitivity analysis were carried out to determine the effect of the input factors for the optimization model on the ORT of the new model of the drilling rig. A linear regression analysis was also performed on the results obtained from the MATLAB codes, and this analysis was used to carry out a sensitivity analysis resulting in a mathematical model which could be used for the new model

22

of the ORT estimation. The graphical user interface method was used to visualize the results of the optimization model and the sensitivity analysis.

In Paper III, the same approach as in Paper II was followed, but in Paper III artificial neural network techniques were used for the following two main reasons.

One aim was to help the engineers and decision makers in the user company to estimate the ORT of new drilling rigs without needing to use complicated software.

Another aim was to determine the relative importance of factors which were used in the optimization model and which would affect the ORT of new drilling rigs. The factor which has the highest impact on the ORT of new rigs should be prioritized in the development process of new drilling rigs.

Paper IV presents a practical model for determining the economic replacement time of production rigs. The objective is to minimise the total cost of this type of capital equipment, and included in the total cost are acquisition, operating and maintenance costs, and costs related to the rig’s downtime. The costs related to the rig’s downtime are represented by the costs of using a redundant rig. The same approach as that used in Papers II and III was followed in Paper IV, but in this paper our attention was focused on the loss of production due to the rig downtime. Data generation was performed for different time scales used in the calculations of the redundant rig cost for the lifespan of the rig.

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4 SUMMARY OF APPENDED PAPERS

This chapter presents a summary of the four appended papers. Each paper makes its own contribution towards the research questions and reports the findings of the case studies. The relation between the papers and the research questions is illustrated in Table 2.1. For detailed information, the reader is referred to the appended papers.

4.1 Paper I

Purpose: The purpose of Paper I is as follows: 1) to estimate the downtime of the drilling rigs’ components at a given confidence level; 2) to identify the critical components of drilling rigs; 3) to analyse the reliability and downtime of several drilling rigs to determine what kinds of problems affect their downtime; 4) to specify which strategies, i.e. design for maintainability and/or design for reliability, should be applied to reduce the drilling rigs’ downtime; and 5) to suggest some improvements for the components that contribute most to the rigs’ downtime.

Findings: The visualization method used to analyse the downtime of the drilling rigs reveals the following: 1) there are notable differences in the downtime of most of the studied components for all the rigs; 2) the rigs' components are ranked based on three estimation points for the downtime; 3) the hoses, feeder and rock drill have relatively the highest downtime compared with the other components of the drilling rigs; 4) the downtime of the studied components is due to reliability problems, and therefore design for reliability (DFR) should be adopted to reduce their downtime; and 5) no maintainability problems have been detected for the rigs’ significant components, and therefore a design for maintainability strategy is not required.

4.2 Paper II

Purpose: Paper II presents a practical model that can be used to identify the replacement age of drilling rigs from an economic point of view, using available data from the mining company.

Findings: According to the results obtained from the optimisation curve, the absolute ORT of the drilling rig at the case study’s mine is 115 months of operation. However, the ORT has a range of 110 to 122 months during which the total cost remains almost constant. This means that the company has the flexibility of being able to make replacements within the optimum replacement age range, i.e. 12 months. Therefore, there is no fixed date or age at which the total cost is at a minimum. In general, a range of months provides the minimum total cost. The results of the sensitivity analysis performed to identify various factors’ effect on and correlation with the optimal replacement time indicate that increasing the purchase price and decreasing the operating and maintenance costs have a positive effect on increasing the ORT. The results of the regression analysis using three factors, namely the increasing factor of the purchase price (IFPP), the reduction factor of the operating cost (RFOC), and the reduction factor of the maintenance cost (RFMC), show that the ORT of the new rig depends linearly on its IFPP, RFOC and RFMC. These results confirm the computation and the results of the sensitivity analysis. The results of the regression analysis show that the maintenance cost has the largest impact on the ORT, followed by the purchase price and the operating cost. Hence, the manufacturer must make a greater effort to improve the reliability and maintainability of the

24

drilling rig to reduce the costs associated with maintenance and to increase the ORT. The personnel at the financial department of the user company can easily use the graphical user interface (GUI) to estimate the ORT of a new rig and see the behaviour of its ORT for different values of its IFPP, RFOC and RFMC. These factors will provide a clear view of the ORT of the new rig. This knowledge will help the user company determine when to buy a new rig and assist them in any negotiations with the manufacturer concerning the purchase price.

4.3 Paper III

Purpose: This study presents a new model for easy prediction of the ORT of drilling rigs using ANN techniques. The ANN was used to design a model which can be employed to calculate the ORT of a drilling rig. The model is based on a series of basic weights and response functions which make the ORT estimation easy for any engineer to use without resorting to complicated software. An Excel spreadsheet can be used as a substitute for fast and accurate calculation of the ORT.

Findings: The study finds that increasing the purchase price and decreasing the operating and maintenance costs will increase a rig’s ORT linearly. Decreasing the maintenance cost has the largest impact on the ORT, followed by increasing the purchase price and decreasing the operating cost by the same percentages. The ANN gives a series of basic weights and response functions which can be made available to any engineer without the use of complicated software. In addition, the ANN also helps decision-makers determine the best time economically to replace an old rig with a new one. The ANN model is very effective in estimating and predicting the ORT of a mining drilling rig, since the correlation between the input and output variables is very high and the accuracy is 99%. Moreover, the model’s performance is very consistent with data used for training (seen) and testing (unseen).

4.4 Paper IV

Purpose: This paper presents a practical model to determine the economic replacement time (ERT) of production rigs when also the costs from one redundant rig are considered. The objective is to minimise the total cost of this type of capital equipment, and included in the total cost are acquisition, operating and maintenance costs, and costs related to the rig’s downtime. The costs related to the rig’s downtime are represented by the costs of using a redundant rig.

Findings: The results show that the lowest possible total cost when the redundant rig cost is equal to 1 cu/h can be achieved by replacing the rig at 104 months of its planned lifetime. There is a range between 97 and 109 months when the minimum total cost can still be achieved in practice. Finding the economic replacement range is an important result of our study, as it can help decision makers in their planning. The results also show that the redundant rig cost has the largest impact on the ERT, followed by the acquisition, maintenance and operating costs. The study also finds that increasing redundant rig costs per hour have a negative effect on the ERT, while decreases in other costs have a positive effect. Regression analysis shows a linear relationship between the cost factors and the ERT.

25

5 RESULTS AND DISCUSSIONS

The findings of the conducted research are discussed and presented in this chapter according to the stated research questions.

5.1 Results and discussion related to research question 1

RQ 1: Which critical components make a large contribution to the downtime of the drilling rig? What are the dominant problems influencing the drilling rig downtime, reliability problems and/or maintainability problems?

The first research question of the study is answered in Paper I, whose findings are briefly discussed here.

The downtime visualisation approach proposed by Wijaya (2001) is used in this paper to visualize the downtime of drilling rig components. In this approach, the failure times are modelled with a Weibull distribution and the repair times are modelled with a lognormal distribution, and these distributions are generally valid for this method (Abernethy, 2000; Wiseman, 2001; Rausand and Høyland, 2004; Schroeder and Gibson, 2005; Bovaird and Zagor, 2006).

Figure 5.1 represents the log-log graph used in this paper. The graph shows the log number of failures (the vertical axis) and the log repair time (the horizontal axis). The curves of the constant downtime appear as straight lines with a uniform negative and constant gradient. The downtime confidence interval was used to analyse the downtime of the components of the drilling rig. Three equations were used to establish the downtime confidence log-log plot. The estimation points were the mean (DTM), the lower limit (DTLL) and the upper limit (DTUL) of the downtime. To estimate the interval of the downtime, the three estimated points were connected by a straight line. mM, mUL, mLL, MTTR, TTRUL and TTRLL represent the coordinates of the three previous estimated points. The downtime was calculated for 5,300 hours, which represents the theoretical number of production hours of one year.

In Paper I we made two main types of comparisons based on the downtime of the rigs’ components. The first type was a comparison between the three rigs working in the same mine, which we call mine Y, and the second type was a comparison between two rigs working in different mines (i.e. mine X and mine Y).

Figure 5.2 illustrates the application of the used method for the first type of comparison (for the rest of the results, please consult Paper I). Figure 5.2 indicates that components C2 (the hoses in rig 2), B3 (the feeder in rig 3) and A3 (the rock drill in rig 3) have a higher downtime than all the equivalent components in any other rig used in the same mine. Components F (cables), E (booms) and D (accumulators) have a lower downtime compared with components C, B and A. Figure 5.2 also shows that components C and B have more than 100 failures and a repair time of less than 3 hours. The results show that most of the drilling rig’s components have reliability problems, and therefore design for reliability (DFR) should be adopted to reduce the downtime of the drilling rig.

Figure 5.3 illustrates the application of the used method for the second type of comparison (for the rest of the results, please consult Paper I).

26

Figure 5.1. Log-log plot of downtime confidence interval

Figure 5.2. Confidence log-log plot for the first type of comparison

Figure 5.3 illustrates that components A1 and B1, used in rig 1 in mine X, have less downtime than the corresponding components of drilling rigs used in mine Y. This may be due to the differences in the rock properties between the two mines. The geological strength index (GSI) of mine Y varies between 50 and 80 (Edelbro, 2008), while the GSI of mine X varies between 30 and 50 (Sjöberg, 2003, as cited in Edelbro, 2008).

60mUL

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Figure 5.3. Confidence log-log plot for the second type of comparison

The order of the significant components has been prioritised based on three estimation points of the downtime (see Table 5.1). These estimation points are the mean, the upper limit and the lower limit estimation point of the downtime. This ranking is important to the maintenance decision makers for certain maintenance activities in the mine, for instance planning new operations, making new service schedules and budgeting maintenance. For example, if the maintenance management department determines the highest acceptable amount of rig downtime at the component level, it is essential for the maintenance staff to know which components are likely to exceed the acceptable limit. If is decided that the highest acceptable amount of downtime is 350 hours per year, based on the upper limit of the estimation point of the downtime, they can observe from Figure 5.2 that components C2, B3 and B2 will exceed 350 hours of downtime. In this case, a good strategy may be to convince the manufacturing company to improve the reliability of these components (i.e. the hoses and feeder) in order to reduce their number of failures and increase their lifetime. Another possibility is to increase the preventive maintenance on these particular components.

Paper I also presents some minor suggestions as to how to improve the critical components in order to reduce their downtime. Discussions with maintenance personnel have revealed that most of the failures of the feeder hoses are due to the mine’s environment. For example, during drilling, the feeder hits the wall at different angles, especially when the feeder movement is restricted because of spatial limitations. To overcome this problem, the feeder could be equipped with steel plates on both sides; the plates should be large enough to prevent the hoses from being scraped and scratched and to prevent the nipples at the necks from being broken, see Figures 5.4, 5.5 and 5.6.

Another problem in the feeder is breakage of the pull rope, which can happen for two reasons. Firstly, the pull rope can become slack due to usage and then hang over the edge of the cradle plate when the plate moves back and forward on the slide bar. Secondly, the operator or repair technician may put extreme tension on the pull rope when making an adjustment, see Figures 5.7 and 5.8.


No.

offa

ilu

res

100 B2

B3

B4

20

10 202

80

110

160

B1

A2 A1

A4 A3

30

40

1 1.6

190

100

1.3 7.5Time to repair (hours)

No.

of

fail

ure

s

28

Table 5.1. The order of the drilling rigs’ components based on their downtime

Figure 5.4. Nipples and necks Figure 5.5. Scraped and scratched hoses

Figure 5.6. Suggested plate of steel

Type 1 Mine Y three machines

Type 2 Mine X&Y four machines

Type 3 Mine X&Y three machines

Type 4 Mine X&Y two machines

Scenario Scenario Scenario Scenario Order 1 2 3 Order 1 2 3 Order 1 2 3 Order 1 2 3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

C2 B3 B2 C4 A3 B4 C3 A4 E2 A2 E4 E3 D2 F2 F3 D4 D3 F4

C2 B3 B2 A3 B4 C4 E2 C3 A4 A2 E4 E3 F2 D4 F4 D3 D2 F3

C2 B3 C4 B2 B4 A3 C3 A4 A2 E2 E4 E3 F2 D2 F3 D3 D4 F4

1 2 3 4 5 6 7 8 9

10 11 12

C2 B3 B2 C4 A3 B4 C1 C3 A4 A2 A1 B1

C2 B3 B2 A3 B4 C4 C1 C3 A4 A2 A1 B1

C2 B3 C4 B2 B4 A3 C1 C3 A4 A2 A1 B1

1 2 3 4 5 6

G1 G3 H3 G4 H1 H4

G1 G3 H3 G4 H4 H1

G1 G3 H3 G4 H4 H1

1 2

I2 I1

I2 I1

I2 I1

29

Figure 5.7. Hanging pull rope Figure 5.8. Broken pull rope

To solve this problem, an electric motor with a control circuit should be designed to make automatic adjustments of the pull rope, or a coil spring should be installed, in order to keep the rope at a constant desired tension, as shown in Figure 5.9. Stronger roller bearings are another possibility.

Figure 5.9. Suggestion to prevent pull rope failures

Discussions with maintenance personnel have also revealed that the frequent failures of the rock drill damage the third and fourth cup seals located inside the front head (nose) of this component, as shown in Figure 5.10.

Figure 5.10. Damaged cup seal

A possible cause is the high water pressure inside the nose. Water is used to cool the front head and flush it during the drilling process. However, damaged cup seals will cause water and oil to mix, leading to abnormal wear of the valves used in the hydraulic system. To solve this problem, the water pressure inside the front head should be reduced by increasing the number of holes, especially in the area between the third and the fourth cup seals. Further research is needed to confirm the above explanation for cup seal damage.

Electric Motor Gear

30


RQ 2: How should a model be constructed that can calculate the optimum replacement time of a drilling rig? Moreover, which cost factors have the largest impact on the replacement time?

The second research question of the study is answered in Papers II, III and IV. The drilling rig’s optimal replacement time (ORT) and the cost factors affecting the rig’s ORT are briefly discussed in Paper II. In this paper, a data-driven optimisation model was developed for the operation and maintenance costs, the purchase price and the rig resale value. The paper also presents the values of these costs by using the discount rate.

Figure 5.11 shows that the absolute lowest possible total ownership cost value (TOC value) can be achieved by replacing the rig with an identical new one every 115 months. Figure 5.11 also shows that there is a range of 110-122 months when the minimum TOC value can still be achieved in practice. In this study, we call it the optimum replacement range. Finding the optimum replacement range is an important result of our study, as it can help users in their planning.

A decision to replace the equipment before or after this optimum replacement range will incur greater cost for the company. The use of a lower replacement age (i.e. less than 110 months) will incur higher costs due to the high investment cost. Moreover, if the lifetime of the machine exceeds the upper limit of this range (i.e. more than 122 months), the losses will increase for the following two reasons.

1. The cost of operation and maintenance will increase due to rig degradation when the operating time increases.

2. The rig’s resale value will decrease for each month of operation until the rig reaches its scrap value at the end of its planned lifetime.

Figure 5.11. Optimal replacement time of existing drilling rig

In order to demonstrate the influence of possible options of bathtub curves on the ORT of mining drilling rig, it is interesting to see the effect of the first stage (i.e. 0-25 months) of the curve in Figure 5.12 on the ORT of our case study.

0 25 50 75 100 125 150 175 200 225 2500

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Replacement time (month)

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)

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31

Figure 5.12. Maintenance cost (first model)

However, since the curvature in Figure 5.12 is difficult to present as a continuous function, which is needed for calculations, the function in Figure 5.13 is used instead as an approximate representation of a possible first stage of a bathtub curve in our case study.

Figure 5.13. Maintenance cost (second model)

The function of extrapolation for the expected maintenance cost in Figure 5.13, which was obtained using the Table Curve 2D software, is expressed as

2 3Y a b x x c x (5.1)

where Y represents the expected maintenance cost, a=65.45, b=-0.006, c=0.0006, r2

(adj.)=0.97, and x represents the time (1, 2, 3, 4,…, n months).

Since the maintenance cost (MC) is increasing too much in Figure 5.13, this curve is not realistic in the third stage (i.e. 76-145 months). In this case, the values of the MC for a period of 0 to 120 months are used in ORT calculations. The result for the ORT obtained by using the function in Figure 5.13 (i.e. 0-120 months) is 113 months. This result is close to the result

Maintenance cost

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for the ORT of 115 months which was obtained by using the function in Figure 5.14 for the same interval.

The MC in the first stage of Figure 5.13 is higher than the MC in the same stage of Figure 5.14. This is the reason why the calculated ORT is less than 115 months. Assuming that the first stage in Figure 5.12 can, regarding the influence on the ORT, be approximated by the first stage in Figure 5.13, since the two ORT results (i.e. 113 and 115) obtained using the two functions in Figures 5.13 and 5.14 show only a small difference in their values, it can be concluded that the difference between the ORT calculations using the two functions in Figures 5.12 and 5.14 will be even smaller. In conclusion, the function used in Figure 5.14 is reasonable for calculating the ORT of the drilling rig. This conclusion is also preferred by the Boliden experts, who consider the curve shown in Figure 5.14 to be the most reasonable curve (no recorded data exist for the period before 76 months of operation).

Figure 5.14. Maintenance cost (third model)

The function of extrapolation for the maintenance cost in Figure 5.14, which was obtained by the Table Curve 2D software, is expressed as

arctan2

a x bY

c

(5.2)

where Y represents the expected maintenance cost, a=217.42, b=112.37, c=13.63, r2 (adj.) = 0.97, and x represents the time (1, 2, 3, 4,…, n months).

In order to ascertain which cost factor has the largest impact on the ORT of the drilling rig, sensitivity and regression analyses were performed for the operating and maintenance costs, as well as the rig purchase price. Figure 5.15 illustrates the effect of an increasing purchase price (PP) on the ORT of the drilling rig.

Figure 5.15 shows that the ORT is an increasing step function of the PP (based on percentage increases in the purchase price); the ORT remains constant for a specific range of PP increments, and then increases stepwise. The reason for this stepwise behaviour is that, due to the monthly calculations for the operating cost, the maintenance cost and the rig resale value, the resultant ORT from the optimization model is then computed on a monthly basis.

Maintenance cost

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Figure 5.15. Effect of increasing purchase price

Figure 5.16 illustrates the effect of decreasing the rig operating cost (OC) (based on percentage decreases in the operating cost) on the ORT. It is obvious that when the rig’s operating cost decreases, the ORT will increase. This means that the ORT is not sensitive to a specific range of operating cost reductions and will increase stepwise at specific OC rates of reduction, i.e. 15 and 34%.

Figure 5.16. Effect of decreasing operating cost

Figure 5.17 illustrates the effect of decreasing the rig maintenance costs on the ORT of the drilling rig. When the maintenance cost (MC) decreases, the ORT will increase. In addition, note that the ORT increases at certain reduction percentages of the MC, i.e. 7, 15, 23, 30, 36, 42 and 48%.

Figure 5.17. Effect of decreasing maintenance cost

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Figures 5.15, 5.16 and 5.17 show that, with an increasing purchase price and decreasing operating and maintenance costs, the ORT of a new model of this rig will increase stepwise at specific percentages of these factors. The results also show that these factors exert a significant effect on the total ownership cost at these specific percentages of the IFPP, RFOC and RFMC. The explanation is that a new model of the drilling rig is assumed to be more reliable than the replaced one. This will lead to a decrease in the number of failures in a new model of this rig, which, in turn, will reduce the maintenance cost. A new model of this rig will also be more productive than an old one and thus finish the same job in less time. This will decrease the energy consumption of a new model of the rig, which will lead to a reduction in the operating cost.

Our regression analysis of the ORT results obtained from the previous three cases used the Minitab software and the least squares method. The ORT of a new model of the drilling rig was modelled as a linear function of the IFPP, RFOC and RFMC. The regression analysis results in the following mathematical model:

114 0.133 0.0682 0.164ORT IFPP RFOC RFMC (5.3)

The high R-squared adjusted value obtained from the regression analysis, R2 (adj) = 98.6%, indicates that the ORT of a new model of this rig depends linearly on the IFPP, RFOC and RFMC. Following the results of the sensitivity and regression analyses, the rank of the factors affecting the ORT of a new model of a drilling rig is as follows:

1. reduction in the maintenance cost, 2. increase in the purchase price, 3. reduction in the operating cost.


RQ 3: How should the above model be improved regarding easy and accurate prediction of the economic lifetime of this rig, with a high level of certainty and with a view to enhancing decision making in this regard?

The third research question is answered in Paper III. This paper proposes a new model for easy prediction of the economic replacement time of a drilling rig by using the artificial neural network technique. In this study, three cases, represented by three MATLAB codes for the optimization model, were used. The ORTs resulting from these codes were fed as inputs into an ANN and the results translated into a relatively simple model based on weights and response functions. Ninety percent of the data determined by the MATLAB codes were used in the training of the neural network, see Figure 5.18. The model shown in this figure has very high values for R2 = 0.99. However, the neural network model yields outputs very close to the desired targets with a high level of accuracy.

After the training was completed, the network was tested for its generalization capabilities by investigating its ability to respond to the input sets (unseen data) not included in the training process. Therefore, ten percent of the data determined by the MATLAB codes were used for tests with the obtained network (see Figure 5.19). As is evident in Figure 5.19, the model has very high values for R2 = 0.99 for the ANN. However, the neural network model yields outputs very close to the desired targets with high levels of certainty.

Also studied in Paper III is the relative importance of each factor affecting the rig replacement time. As is evident in Figure 5.20, the most important factor influencing the ORT of the drilling rig is a decreasing maintenance cost (DMC), followed by an increasing purchase price (IPP). A decreasing operating cost (DOC) has the least influence. This result confirms the

35

results presented in Paper II regarding the factors exerting the greatest influence on the rig replacement time.

Figure 5.18. Learning capability Figure 5.19. Generalization capability

Figure 5.20. Relative importance of the factors affecting the ORT of the drilling rig

The main advantage of the proposed neural network model is its ability to produce acceptable results; the correlation between the input and output variables is very high and the accuracy is more than 99%. Moreover, the model’s performance is very consistent for data used for training (seen) and testing (unseen). Therefore, the model is very effective in estimating and predicting the ORT of a mining drilling rig with higher levels of certainty. Further, the ANN gives a series of basic weights and response functions which can be made available to any engineer without the use of complicated software; for more details see Paper III among the appended papers.


RQ 4: How should a model be constructed for estimation of the economic lifetime of mining production rigs when also the costs from one redundant rig are considered?

The fourth research question of the study is answered in Paper IV. This paper aims to present a model to determine the economic replacement time (ERT) of production rigs. The objective

95 100 105 110 11595

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is to minimise the total cost of this type of capital equipment, and included in the total cost are acquisition, operating and maintenance costs, and costs related to the rig’s downtime. In the study, the costs related to the rig’s downtime are represented by the costs of using a redundant rig. We tested the model on a drilling rig used in one underground mine in Sweden. The artificial neural network technique was used to identify the relative importance of factors influencing the drilling rig’s ERT.

In Paper IV we focus on the redundant rig cost as one of the critical factors affecting the rig’s ERT. Mining companies lose a large amount of money each year because of lost production, which, in turn, is due to the production equipment’s downtime. In fact, this may be the most important factor affecting the ERT of production rigs.

In this study, a discussion held with the reference group at the mining company revealed that, after a drilling rig has failed, it is sent to the workshop for maintenance. To continue production without stoppages, the company uses a redundant rig which has the same performance as the existing faulty production rig. Since in the mining industry the downtime in production is almost zero, the compensation cost in this case represents the cost of using a redundant rig. In this study, the experts at the collaborating mine classified the rig’s failures into the following three categories:

1. failures fixed by the maintenance team at the workshop, 2. failures fixed by the maintenance team at the production point (the mining room), 3. failures fixed by the operators at the production point (the mining room).

For more details about the method for calculating the redundant rig cost based on these three failure categories, see Paper IV among the appended papers.

Figure 5.21 shows the optimization curve and the ERT of our case study when the redundant rig is used for a cost equal to 1 cu/h. The results show that the lowest possible total cost can be achieved by replacing the rig at 104 months of its planned lifetime. As Figure 5.21 also shows, there is a range of 97-109 months when the minimum total cost can still be achieved in practice.

Figure 5.21. Economic replacement time of the drilling rig

To show the effect of the redundant rig cost per hour on the ERT of our case study, we changed the values of the redundant rig cost per hour from 1 to 6 cu/h. Figure 5.22 shows the result.

0 20 40 60 80 100 120 140 160 180 200 220 2400

5

10

15

18x 104 Economic replacement time of the drilling rig


Tot

al c

ost (

cu)

Redundant rig cost = 1 (cu/h)

ERT=104 months

37

Figure 5.22. Effect of the redundant rig cost per hour on the ERT of the drilling rig

It is clear from Figure 5.22 that increasing the redundant rig cost per hour has a negative effect on the ERT of the drilling rig.

To determine the effect of other factors on the ERT, we also performed a sensitivity analysis on the rig acquisition, operating and maintenance costs, and the redundant rig costs (cu) using the ANN technique. Four MATLAB codes for six cases of the redundant rig cost (1-6 cu/h) were used to identify the effect of an increased acquisition cost (IAC), a decreased operating cost (DOC), a decreased maintenance cost (DMC) and a decreased redundant rig cost (DRC). The resulting ERT from these four codes was fed as input into the ANN and the results translated into a relatively simple equation for estimating the ERT of the drilling rig. The method of partitioning weights proposed by Garson (1991) and adopted by Goh (1995) was used to determine the relative importance of the various input factors, see Figure 5.23.

Figure 5.23. Relative importance of input factors on the ERT of the drilling rig

It is evident in Figure 5.23 that the most important factor is the redundant rig cost, followed by the acquisition, maintenance and operating costs. As mentioned earlier, four MATLAB

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CRi=1 (cu/h). ERT=104 month CRi=2 (cu/h). ERT 94 month

CRi=3 (cu/h). ERT 87 month CRi=4 (cu/h). ERT 82 month


CRi = Redundant rig cost per

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DMC (cu) 20,4 15,0 17,7 10,1 12,3 6,2

DRC (cu) 32,2 39,8 42,3 45,7 46,6 57,5

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codes were used to identify the effect of IAC, DOC, DMC and DRC on the ERT of the drilling rig. We chose the case where the redundant rig cost is equal to 1 cu/h to demonstrate the effect of these factors on the ERT. Figure 5.24 shows the correlation of DRC and IAC for a given 25% DOC and DMC. Figure 5.25 shows the correlation of DRC and DMC for a given 25% IAC and DOC. Figure 5.26 shows the correlation of DRC and DOC for a given 25% IAC and DMC.

Figure 5.24. Correlation of DRC and IAC for a given 25% DOC and DMC

Figure 5.25. Correlation of DRC and DMC for a given 25% IAC and DOC

Figure 5.26. Correlation of DRC and DOC for a given 25% IAC and DMC

0 5 10 15 20 25 30 35 40 45 50110

112

114

116

118

120

122

124

126

ER

T (

mon

th)

Decreasing redundant rig cost (%)

IAC=10%IAC=20%IAC=30%IAC=40%IAC=50%

DOC=25%DMC=25%

0 5 10 15 20 25 30 35 40 45 50

112

114

116

118

120

122

124

126

ER

T (

mon

th)


DMC=10%DMC=20%DMC=30%DMC=40%DMC=50%

IAC=25%DOC=25%

0 5 10 15 20 25 30 35 40 45 50

114

116

118

120

122

124

ER

T (

mon

th)


DOC=10%DOC=20%DOC=30%DOC=40%DOC=50%

IAC=25%DMC=25%

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As Figures 5.24, 5.25 and 5.26 show, DRC, IAC, DMC and DOC have a positive effect on the ERT of the drilling rig, but it is also evident that DRC has a more positive effect, followed by IAC, DMC and ROC.

The ANN technique is used to construct a formula to calculate the ERT of our case study. The formula is transformed to an Excel spreadsheet to make ERT estimation quick and easy for any engineer to apply. The structure of the optimal ANN model is shown in figure 5.27; its connection weights and threshold levels are summarised in Table 5.2.

Figure 5.27. Optimal structure of artificial neural network (ANN) model

Table 5.2. Weights and threshold levels of proposed ANN

Hidden layer nodes

wij

weights from node i th input layer to node j

th hidden layer

Hidden threshold

(θj) i=1 i=2 i=3 i=4

j=5 0.085 0.089 -0.03 0.108 -8.776 j=6 3.006 0.379 1.441 1.784 -1.120 j=7 1.416 0.452 1.509 1.876 -5.001

Output layer nodes

wij

weights from node i th hidden layer to node j th output layer

Output Threshol

d (θj) i=5 i=6 i=7

j=8 4.679 3.410 5.376 -3.581

The formula length depends on the number of nodes in the hidden layer. Adopting three nodes gives an accuracy of 99%. The small number of connection weights of the neural network enables the ANN model to be translated into a relatively simple formula, in which the predicted ERT can be expressed as follows:

8 5:8 6:8 7:81 2 31 1 1

1 1 1

1

1 expx x x

sw w w

e e e

ERT

(5.4)

where ERTs represents the scaled ERT derived from the ANN model, θj represents the output threshold and wij represents the weight from node i in the hidden layer to node j in the output layer. Hence,

51 5:1 5:2 5:3 5:4x w IAC w DOC w DMC w DRC (5.5)

2 6 6:1 6:2 6:3 6:4x w IAC w DOC w DMC w DRC (5.6)

73 7:1 7:2 7:3 7:4x w IAC w DOC w DMC w DRC (5.7)

IAC (%)

DOC (%)

DRC (%)

DMC (%)Output(ERT)

Inpu

t fac

tors

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To obtain the actual value of ERT, the predicted ERTs must be re-un-scaled using the following formula:

max min max minmax0.9

0.8 0.8s

ERT ERT ERT ERTERT ERT ERT

(5.8)

where ERTmax and ERTmin represent the maximum and minimum values of ERT respectively derived from the optimisation model.

Since the accuracy of ANN model is 99% for tested data set, the connection weights and threshold levels are valid for this particular case study. The ANN model can be used for ERT prediction of another production rigs by using new connection weights and new threshold levels which can be extracted from the ANN based on new cost data for these production rigs.

A discussion held with the reference group at the collaborating mining company revealed that the overhaul service cost for the redundant rig during its life is 300 cu. The group also stated that the cost of using the redundant rig is about equal to the maintenance cost of the existing rig during its lifetime. Based on that, the cost of using the redundant rig per hour could be calculated. Dividing the sum of the overhaul service cost and the maintenance cost of the production rig by the number of usage hours of the redundant rig gives 1.5 cu/h. Based on this new redundant rig cost (i.e. 1.5 cu/h), the ERT of the drilling rig was calculated and found to be 96 months (i.e. 8 years).

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6 CONCLUSIONS

The following conclusions can be made on the basis of this thesis.

There are notable differences in the downtime of most of the investigated components of all the drilling rigs used in two different mines. For the rigs used in the same mine, 3 out of 6 components show significant differences. For rigs used in different mines, 5 out of 6 components exhibit significant differences.

The rigs’ components have been ranked based on three estimation points of the downtime (i.e. the mean, the upper limit and the lower limit). This ranking will help the maintenance decision makers in redesigning the rigs’ preventive maintenance schedule and in prioritizing the components that have the highest downtime.

The downtime (DTUL • 200 hours) of components C (the hoses), B (the feeder), A (the rock drill), E (the boom) and G (the steering system) stem from reliability problems. It is concluded that DFR should be implemented to decrease their downtime. Overall, no maintainability problems were detected for the rigs’ significant components, and therefore, a design for maintainability strategy is not required.

The harsh working environment of mining drilling rigs has a strong effect on the occurrence of failures of the feeder hoses. In this case, the installation of steel plates on both sides of the feeder can reasonably be assumed to reduce the number of failures.

The breakage of the feeder pull rope can be caused by the rope becoming slack due to usage or being subjected to excessive tension; this can possibly be remedied and reduced by installing a coil spring or installing an electric motor with a control circuit to keep the pull rope at a constant desired tension.

Increasing the number of holes between the third and the fourth cup seals inside the nose of the rock drill could possibly solve the problem of cup seal damage.

There is an absolute ORT of the drilling rig. However, the ORT also has a range of months during which the total ownership cost remains almost constant. Therefore, the company has the flexibility of being able to make replacements within the optimum replacement age range.

The results of the regression analysis show that a reduction in the maintenance cost has the largest impact on the ORT, followed by an increase in the purchase price and a reduction in the operating cost. Therefore, the manufacturer must make a greater effort to improve the reliability and maintainability of the drilling rig to reduce the costs associated with maintenance and to increase the ORT.

The decision makers at the user company can easily use the optimization model to estimate the ORT of a new rig and see the behaviour of its ORT at different IFPPs, RFOCs and RFMCs. These factors will provide a clear view of the ORT of the new rig. Therefore, this will help the user company determine when to buy a new rig and assist them in any negotiations with the manufacturer concerning the purchase price.

The main advantage of the proposed neural network model is its ability to produce acceptable results; the correlation between the input and output variables is very high and the accuracy is more than 99%. Moreover, the model’s performance is very consistent for data used for training (seen) and testing (unseen). Therefore, the model is very effective in estimating and predicting the ORT of a mining drilling rig. Further,

42

because the ANN model uses a series of basic weights and response functions, it helps engineers in estimating the ORT of drilling rigs without using complicated software.

Although the problem of the equipment replacement time has been solved previously by other researchers using different models, our ERT model examines the relationship between the factors affecting the ERT of production rigs, especially the cost of using a redundant rig. The model can also be extended to other capital production assets in other industries.

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7 SCIENTIFIC & INDUSTRIAL CONTRIBUTIONS

The scientific contribution of this thesis is that it expands the existing body of knowledge about the reliability and maintainability analysis of drilling rigs and the problems affecting their downtime, as well as methods for modelling the optimal replacement time of production equipment. The knowledge created will have useful applications in the future.

The scientific contribution of this thesis can be summarized as follows:

deeper insight into how the drilling rig behaves regarding its downtime and related problems (Paper I),

models that can be used to estimate the economic replacement time of a drilling rig (Papers II-IV),

identification and explanation of the factors that have the largest impact on the rig’s ERT (Papers II-IV).

The industrial contribution of this thesis is the provision of a method which can be used in mining companies for estimation of the economic replacement time of production mining rigs. This estimation will support decision makers in their planning and in their improvement of components and machinery.

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8 SCOPE OF FURTHER RESEARCH

Based on the conducted research, the following areas are recommended for future research.

This thesis has dealt with the reliability and maintainability analysis of drilling rigs and future research should focus on greater use of RAMS analysis (availability due to maintenance supportability) for such rigs.

More research is needed on calculation of the cost of improving the reliability and maintainability of drilling rig components and on estimation of the level of improvement which has to be attained in order to obtain the optimum reliability of drilling rigs in a cost-effective way.

An extension of the ORT study is needed which will include profit maximization by also using the rig revenue.

Due to competition, the manufacturing company may need to reduce the price of its drilling rigs. As a consequence, the reliability of its subsystems will eventually be downgraded. More research is needed to determine which subsystems can be selected for reliability reduction and to what extent this should be done to achieve a maximum price reduction and a maximum system ORT.

More research is needed to estimate the optimal preventive maintenance replacement intervals of the drilling rig components.

The proposed ORT model can be improved so that it can be used to determine the optimum replacement interval for other systems by modifying the model parameters based on industry specifications.

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APPENDED PAPERS

PAPER I

Downtime analysis of drilling machines and suggestions for improvements

Al-Chalabi, H., Lundberg, J., Wijaya, A. and Ghodrati, B., 2014. Downtime analysis of drilling machines and suggestions for improvements. Published in the Journal of Quality in Maintenance Engineering, 20(4), 306-332. http://dx.doi.org/10.1108/JQME-11-2012-0038

Downtime analysis of drillingmachines and suggestions for

improvementsHussan S. Al-Chalabi

Division of Operation,Maintenance and Acoustics, Lulea University of Technology,Lulea, Sweden and Mechanical Engineering Department, College of Engineering,

Mosul University, Mosul, Iraq, and

Jan Lundberg, Andi Wijaya and Behzad GhodratiDivision of Operation, Maintenance and Acoustics,Lulea University of Technology, Lulea, Sweden

Abstract

Purpose – The purpose of this paper is to analyse and compare the downtime of four drillingmachines used in two underground mines in Sweden. The downtime of these machines was comparedto show what problems affect downtime and which strategies should be applied to reduce it.Design/methodology/approach – The study collects failure data from a two-year period for fourdrilling machines and performs reliability analysis. It also performs downtime analysis utilising a log-log diagram with a confidence interval.Findings – There are notable differences in the downtime of most of the studied components for allmachines. The hoses and feeder have relatively high downtime. Depending on their downtime, thesignificant components can be ranked in three groups. The downtime of the studied components is dueto reliability problems. The study suggests the need to improve the reliability of critical components toreduce the downtime of drilling machines.Originality/value – The method of analysing the downtime, identifying dominant factors and theinterval estimation for the downtime, has never been studied on drilling machines. The researchproposed in this paper provides a general method to link downtime analysis with potential componentimprovement. To increase the statistical accuracy; four case studies was performed in two differentmines with completely different working environment and ore properties. Using the above methodshowed which components need to be improved and suggestions for improvement was proposed andwill be implemented accordingly.

Keywords Reliability analysis, Confidence interval, Downtime analysis, Drilling machine

Paper type Research paper

1. IntroductionUnderground mines are a main source of minerals. Growing demand for metals as aresult of modern lifestyles and the industrial development of recent decades has

The current issue and full text archive of this journal is available atwww.emeraldinsight.com/1355-2511.htm

Received 20 November 2012Revised 23 October 2013Accepted 11 January 2014

Journal of Quality in MaintenanceEngineeringVol. 20 No. 4, 2014pp. 306-332Emerald Group Publishing Limited1355-2511DOI 10.1108/JQME-11-2012-0038

r Hussan S. Al-Chalabi, Jan Lundberg, Andi Wijaya and Behzad Ghodrati. Boliden AB isgratefully acknowledged for their financial support. Published by Emerald Group PublishingLimited. This paper is published under the Creative Commons Attribution (CC BY 3.0) licence.Anyone may reproduce, distribute, translate and create derivative works of this paper (for bothcommercial and non-commercial purposes), subject to full attribution to the original publicationand authors. The full terms of this licence may be seen at http://creativecommons.org/licences/by/3.0/legalcode

Boliden AB is gratefully acknowledged for their financial support. The maintenancepersonnel and maintenance management system employees at Boliden AB who helped theauthors in this research are also thanked for their support.

306

JQME20,4

focused our attention on the factors affecting the extraction of minerals. One ofthe most important factors is unscheduled downtime of the machines used in theextraction of ore. Lost production due to downtime will obviously increase theproduction costs (Roman and Daneshmend, 2000). A mine production system consists ofmany subsystems. To make the system both profitable and practical, the optimisation ofeach subsystem in relation with other subsystems should be considered (Barabady andKumar, 2008). To achieve this aim, reliability and maintainability analysis for eachsubsystem in mine production system should be performed. Since the mid-1980s,reliability analysis techniques have been essential tools in automatic mining systems(Blischke and Murthy, 2003; Barabady and Kumar, 2008).

A drilling machine is very important to the extraction process. Drilling is theprocess of making holes in the mining room face. From an economic viewpoint, thedrilling machine dominates a mine’s production rate, since drilling is the first processof a typical mining cycle. Economic competition has pushed mining companies toachieve higher production rates by enhancing techniques of drilling and blasting andincreasing mechanisation and automation. A significant cost issue is the maintenanceof underground mobile machines: 30-65 per cent of a mine’s total operation coststypically come frommaintenance (Cutifani et al., 1996; Gustafson et al., 2013). Maintenancecosts include the cost of planned and unplanned maintenance.

Historical data over the period of one year from an underground mine in Swedenshow that more than 15 per cent of unplanned downtime of mobile machines is relatedto the drilling machine. Since the drilling machine is key to production, it is importantto find solutions for machine problems and reduce downtime.

This study performs downtime analysis of drilling machine to identify whichcomponents and what type of problems (maintainability problems and/or reliabilityproblems) contribute to downtime, and to determine which strategies, designs formaintainability and/or designs for reliability should be applied to reduce it. To betterunderstand the downtime of the drilling machine, we conducted an analysis of thehistorical data for three machines of the same model used in one Swedish mine and forone machine used in another mine, using jack-knife diagrams with confidenceintervals. The results of a study of downtime with or without confidence intervals foronly one machine used in only one mine may not give a clear picture of the overallbehaviour of the machine’s components. Thus, it will prevent the designers to givegood suggestions to improve the reliability and/or maintainability of the machine. Toovercome this shortcoming, a comparison study and an analysis of the downtime byusing jack-knife diagrams with confidence intervals for one machine used in mine Xand three machines same model used in mine Y was conducted during this study. Thereason of using data for one machine, which used in mine X, is that this mine has onlyone machine of the same model of the machines that used in mine Y. This diagram wasused in order to overcome the shortcomings of using Pareto diagrams in maintenanceengineering applications (Knights, 2001).

A jack-knife diagram has one shortcoming; it presents downtime as a single value(point estimated), and because of involved uncertainties it has been considered insufficient(Altman et al., 2000; Curran-Everett and Benos, 2004; Wijaya et al., 2012). Systemdesigners and users have a tendency to be risk-averse regarding downtime. They prefer adesign with a slightly higher estimated downtime (lower reliability) if the estimated valueis known to be accurate (as characterised by the upper limit of a confidence interval of thedowntime) rather than a design with possible inaccuracies in point estimation; therefore,it is important to consider a confidence interval for system downtime (Colt, 1997).

307

Downtimeanalysis of

drilling machines

1.1 Literature reviewMany researchers studied the reliability and maintainability of mining equipmentand its failure behaviour. For example, Kumar et al. (1989) analysed the operationalreliability of a fleet of diesel operated load-haul-dump (LHD) machines in Kirunamine in Sweden. Kumar et al. (1992) performed reliability analysis on the powertransmission cables of electric mine loaders in Sweden. Kumar and Klefsjo (1992)analysed the maintenance data of one subsystem (hydraulic system) of a fleet of sixLHD machines divided into three independent groups at Kiruna mine.

Reliability assessment of mining equipment was performed by Vagenas and Nuziale(2001); using genetic algorithms, they developed and tested mobile mining equipmentreliability assessment models. Vayenas and Xiangxi (2009) studied the availabilityof 13 LHD machines in an underground mine. They were interested in the influence ofmachine downtime on productivity and operation costs and used a reliability-basedapproach and a basic maintenance approach to determine the machine’s availability.Wijaya et al. (2012) developed a method for visualising downtime by using a jack-knifediagram; they applied the method on a scaling machine at a mine in Sweden. Gustafsonet al. (2013) used a fault tree analysis to analyse the idle times of automated LHDmachines at a Swedish underground mine. Hoseinie et al. (2012) performed reliabilitymodelling of the drum Shearer machine used at Taba’s coal mine in the central desert ofIran. They analysed the failure rate of the machine’s subsystems.

As the literature review shows, there are many reliability and maintainabilitystudies of underground mining equipment but none of these has looked at drillingmachines. Given the importance of underground mining mobile equipment for production,as well as the complexity of the equipment and the harsh mining environment, reliabilityanalysis of the drilling machine must meet rigorous requirements. This study is basedon data from several drilling machines working in different mines. In these mines theworking environment, ore properties and operators are different.

The aims of this study are as follows:

(1) to analyse the reliability and downtime of several drilling machines todetermine what kind of problems affect their downtime;

(2) to specify which strategies, design for maintainability and/or design for reliability(DFR) should be applied to reduce the drilling machines downtime; and

(3) to suggest improvement for the components that most contribute to themachines downtime.

2. Drilling machine and data collectionAll drilling machines for mining applications are composed of similar operationaldesign units, such as cabin, boom, rock drill, feeder, service platform, front jacks,hydraulic pump, rear jack, electric cabinet, hose reeling unit, cable reeling unit, dieselengine, hydraulic oil reservoir, operator panel and water tank. A typical example ofa drilling machine and its components are presented in Figure 1.

Drilling machines manufactured by different companies have different technicalcharacteristics, e.g. capacity and power. Based on the operation manuals, fieldobservations and maintenance reports from the collaborating mines, in this study thedrilling machine is considered a system divided into several components andconnected in series configuration; if any component fails, the operator will stop themachine to maintain it. Thus, all machine components work simultaneously to achieve

308

JQME20,4

the desired function. Table I shows the critical components for each machine mentionedin this study.

The dimensions of the drilling machine are: length 14.5-16.6m; width 2.5m; width ofrig with side platforms 2.9m; height of rig with cabin 3.15m; weight 26-33 tonnes.It has four retractable stabilizer legs and an articulated four-wheel drive chassis. It canbe operated by a water cooled turbocharged diesel engine with 120 kW at 2,300 rpm orby electric power with a capacity of 158 kW.

3. Reliability and downtime analysisThe failure data used in this study were collected over two years for four drillingmachines operated in two different underground mines in Sweden. The Maximocomputerised maintenance management system (CMMS) is the main source of the failuredata. In CMMS, the failure data are recorded based on calendar time. Since drilling isnot a continuous process, the time between failures is estimated by considering theutilisation of each machine. In this study, we test and validate the failure and repair dataafter collection. We test for trends using the Laplace trend test; we also test for serialcorrelation (Ansell and Phillips, 1994). When these tests are used, depending on theresults, classical statistical techniques for reliability modelling may be appropriate(Ascher and Feingold, 1984; Kumar and Klefsjo, 1992; Modarres, 2006; Birolini, 2007;Louit et al., 2009; Ghosh and Majumdar, 2011). The Kolmogorov-Smirnov (K-S) test is

1 Cabin 6 Front jacks 11 Cable reeling unit2 Boom 7 Hydraulic pump 12 Diesel engine3 Rock drill 8 Rear Jack 13 Hydraulic oil reservoir4 Feeder 9 Electric cabinet 14 Operator panel5 Service platform 10 Hose reeling unit

14

10 1211 13

1 2

3

4

5

6789

Figure 1.A typical example of

a drilling machine

Mine X Mine YMachine 1 Machine 2 Machine 3 Machine 4

Component Sym. Component Sym. Component Sym. Component Sym.

Rock drill A1 Rock drill A2 Rock drill A3 Rock drill A4Feeder B1 Feeder B2 Feeder B3 Feeder B4Hoses C1 Hoses C2 Hoses C3 Hoses C4

Accumulators D2 Accumulators D3 Accumulators D4Boom E2 Boom E3 Boom E4Cables F2 Cables F3 Cables F4

Steering system G1 Steering system G3 Steering system G4Cylinders H1 Cylinders H3 Cylinders H4

Table I.Critical components

for each machine

309

Downtimeanalysis of

drilling machines

classically used for the selection and validation of the probability distribution models (forfurther information, refer to Louit et al., 2009). In this study, we conduct all componentanalysis based on the black box approach.

To estimate the interval of downtimes, we assume that the failure times havea Weibull distribution and the repair times have a lognormal distribution. In additionto its flexibility, the Weibull distribution gives a reasonably accurate failure analysiseven with a small sample size (Masters et al., 1992; Abernethy, 2000). The shape andscale parameters of the Weibull distribution are determined by using the maximumlikelihood estimation method. Lognormal distribution is generally used to model repairtimes (Rausand and Hoyland, 2004; Schroeder and Gibson, 2010). The long tail to theright of lognormal distribution provides the best fitting representation of the repairsituation. Most repairs are accomplished in a small period of time, but in certaincases, repairs can take a much longer time (Wijaya et al., 2012). The Weibulldistribution has a probability density function given by:

g yð Þ ¼ bZ

y

Z

� �b�1

exp � y

Z

� �b" #

; y40 ð1Þ

where b and Z are the shape and the scale parameters of the Weibull distribution,respectively. The expected mean time between failures (MTBF) is given as:

MTBF ¼ my ¼ ZG1

bþ 1

� �ð2Þ

Lognormal distribution has a probability density function given by:

f xð Þ ¼ 1

xsffiffiffiffiffi2p

p exp � 1

2

ln xð Þ � ms

� �2" #

; x40 ð3Þ

where s and m are the standard deviation and the mean of the variable’s naturallogarithm, respectively. The expected mean time to repair (MTTR) is given as:

MTTR ¼ mx ¼ exp mþ s2

2

� �ð4Þ

The confidence interval of the downtime is determined according to the followingequations:

MTTR ¼ DT

mð5Þ

MTBF ¼ UT

mð6Þ

DT

UT¼ MTTR

MTBFð7Þ

310

JQME20,4

where DT is the downtime,m is the number of failures and UT is the uptime. Thus, thedowntime can be formulated as (Wijaya et al., 2012):

DT ¼ mxmy

UT ð8Þ

The confidence interval of the estimated downtime can be solved by findinga confidence interval for mx/my. In this study, the exact method (Masters et al., 1992) isimplemented to estimate the confidence interval of mx/my (for more clarification of themethod to estimate the interval of the downtime, see Wijaya et al., 2012). All tests areconducted using the Minitab, Matlab and Easy Fit software; the significance levela used in all tests is 0.05.

4. MethodologyA simple yet important graphical method to visualise downtime is the jack-knifediagram (Knights, 2001). In this diagram, the failure data are presented as a log-loggraph. The graph shows log number of failures (vertical axis) and log repair time(horizontal axis). The curves of constant downtime appear as straight lines witha uniform and constant gradient (Knights, 2001). This study uses the jack-knifediagram with the downtime confidence interval to analyse the downtime of thecomponents of the drilling machine. Three equations are used to establish theconfidence log-log plot. The estimation points are the mean, lower limit and upperlimit of the downtime. The value of these points can be estimated from the followingequations (Wijaya et al., 2012):

DTM ¼exp mþ s2

2

� �ZG 1

b þ 1� �

24

35�UT ð9Þ

DTLL ¼ a�exp s2

2

� �G

G 1b þ 1

� �2Z1�b

Pmi¼1 y

bi

24

35�UT ð10Þ

DTUL ¼ b�exp s2

2

� �G

G 1b þ 1

� �2Z1�b

Pmi¼1 y

bi

24

35�UT ð11Þ

where DTM is mean downtime, DTLL is a lower limit of the downtime, a is a constantfor the lower limit, G is a geometric mean of the lognormal distribution, y is timebetween failures, DTUL is an upper limit of the downtime and b is a constant for theupper limit.

311

Downtimeanalysis of

drilling machines

The next step is the determination of coordinates of the three previous estimatedpoints. For the DTM, the abscissa is the MTTR, and the ordinate is determined as:

mM ¼ UT

MTBFð12Þ

For the lower and upper limit of the downtime, the abscissa and the ordinate aredetermined as:

TTRL ¼ 10 logffiffiffiffiffiffiffiDTL

p�log

ffiffiffiffiffiffiffiffiDTM

pþlog MTTRð Þ

� �ð13Þ

mL ¼ DTL

TTRLð14Þ

where TTRL is time to repair of the limit (upper or lower); DTL is the downtime of thelimit (upper or lower);MTTR is mean time to repair;mL is the number of failures of thelimit (upper or lower). For more information on derivation of the abscissa, the lowerand upper limits of downtime refer to Wijaya et al. (2012).

To estimate the interval of the downtime, the three estimated points are connectedby a straight line (Figure 2).

5. Results and discussionThe present study only considers corrective maintenance. It assumes that thefailure times follow a Weibull distribution and the repair times follow a lognormaldistribution; therefore, the iid assumption is validated before analysis. The maximumlikelihood estimation method is used to estimate the corresponding parametersusing Minitab software. K-S test is used to validate the distributions using EasyFit software.

60mUL

10

90

2

7TTRUL

3

20

4

30

10

50 80 13011

5

Time to repair

70

mMmLL

MTTR

TTRLL

DTUL

DTLLDTM

No.

of f

ailu

res

1020

40

100

Downt

ime

200

1,00

0

Figure 2.Log-log plot of downtimeconfidence interval

312

JQME20,4

Parameters of the distributions are determined the lower bound, mean and upperbound for a confidence interval of 95 per cent. For the failure data, blow and bupp arethe estimates of the lower and upper limits, respectively, of the maximum likelihoodestimate of shape parameter b, denoted by best. Zlow and Zupp are the estimates of thelower and upper limits, respectively, of the maximum likelihood estimate of scaleparameter Z, denoted by Zest. MTBFlow and MTBFupp are the estimates of the lowerand upper limits, respectively, of the maximum likelihood estimate of the MTBF,denoted by MTBFest. For the repair data, mlow and mupp are the estimates of thelower and upper limits, respectively, of the maximum likelihood estimate of the meanparameter m of the lognormal distribution, denoted by mest. slow and supp are theestimates of the lower and upper limits, respectively, of the maximum likelihoodestimate of the standard deviation parameter s of the lognormal distribution, denotedby sest. MTTRlow and MTTRupp are the estimates of the lower and upper limits,respectively, of the maximum likelihood estimate of the MTTR, denoted by MTTRest.

Tables II-V show the data analysis of the critical components of four drillingmachines working in two different mines in Sweden.

We compare the machines’ downtime using a jack-knife diagram with a confidenceinterval. Using Equations (9-11), we determine three downtime estimation points,DTM, DTLL and DTUL. The study uses theoretical production hours for one year asuptime. When the data were collected for this study, each mine averaged about 16.5working hours per day, or approximately 115 hours per week. By fitting lognormaldistribution for preventive maintenance (PM) data (service data) to all machines, wefind that mean time to service averages 6.7 hours. Since PM is scheduled for everyweek, the theoretical service time for 49 working weeks for one year is calculated asapproximately 330 hours. Consequently, the stoppage for PM is three weeks per year;hence, each mine is worked for 46 weeks per year. We can conclude that each mine hasapproximately 5,300 production hours per year. The coordinates of the three downtimeestimation points are determined by using Equations (4), (12-14). Tables VI-IX showsthe values of the three estimation points and their coordinates.

We make four types of comparisons of the downtime of the machines’ components.Type 1 is a comparison of six components on three machines used only in mine Y. Type2 is a comparison of three components on four machines (1, 2, 3 and 4) used in bothmines. Type 3 is a comparison of two components on three machines (1, 3 and 4) usedin both mines. Type 4 compares one component on two machines (1 and 2) used in bothmines. Figures 3-9 are visualisations of these four types of comparisons.

Since the number of failures and repair time are noted manually, we expect thesedata have some errors. Based on interviews with several maintenance personswho work in the mines collaborating in this study, we conclude that 80 per cent of thedata does not include documentation errors. With this in mind, we define a ratio R,whereby R¼maximum mean downtime/minimum mean downtime, and determinethe following limits:

(1) no significant differences; 1pRp1.2;

(2) indicated differences; 1.2oRp1.4; and

(3) significant differences; R41.4.

Figure 3 shows for a given uptime of 5,300 hours, there is a significant differencebetween E2, E3 and E4 (boom), as R¼ 3.5. Also there is a significant differencebetween A2, A3 and A4 (rock drill), as R¼ 1.7. But there is no significant

313

Downtimeanalysis of

drilling machines

Tim

eto

failure

(95%

normal

CI)

Weibullparam

eters

Com

pon

ent

mb l

ow

b est

b upp

Z low

Z est

Z upp

MTBFlow

MTBFest

MTBFupp

(a)Failure

data

a

A1

Rockdrill

210.68

0.94

1.3

62.8

102.6

167.6

66.2

105.1

166.8

B1

Feeder

70.76

1.47

2.85

186.5

330.8

586.7

172.4

299.3

519.6

C1

Hoses

610.68

0.82

0.99

23.9

33.3

46.4

27.1

37.0

50.6

G1

Steeringsystem

260.71

0.95

1.29

54.5

84.0

129.5

56.9

85.6

128.8

H1

Cylinders

51.48

3.78

9.62

262.8

343.3

448.4

233.4

310.2

412.2

I1Hydraulics

50.74

1.55

3.23

186.0

363.5

710.5

170.9

326.8

624.8

J1Fuelsystem

50.61

1.29

2.71

138.4

309.7

692.8

132.9

286.3

616.5

Tim

eto

repair(95%

normal

CI)

Lognormal

param

eters

Com

pon

ent

ms l

ow

s est

s upp

m low

m est

m upp

MTTRlow

MTTRest

MTTRupp

(b)Repairdata

b

A1

Rockdrill

210.42

0.57

0.77

0.09

0.33

0.58

1.2

1.6

2.1

B1

Feeder

70.44

0.74

1.2

0.17

0.72

1.27

1.4

2.7

5.0

C1

Hoses

610.41

0.49

0.59

0.13

0.25

0.38

1.2

1.4

1.6

G1

Steeringsystem

260.59

0.78

1.02

0.44

0.74

1.04

2.0

2.8

4.0

H1

Cylinders

50.19

0.36

0.67

0.20

0.52

0.83

1.2

1.7

2.4

I1Hydraulics

50.38

0.72

1.34

0.55

0.08

0.71

0.6

1.4

2.8

J1Fuelsystem

50.14

0.27

0.51

0.10

0.13

0.38

0.9

1.1

1.5

Notes:m

isthenumber

offailures.

aZandMTBFaregiven

inunitsof

hours;bMTTRisgiven

inunitsof

hours

Table II.Summary formachine 1, mine X

314

JQME20,4

Tim

eto

failure

(95%

normal

CI)

Weibullparam

eters

Com

pon

ent

mb low

b est

b upp

Z low

Z est

Z upp

MTBFlow

MTBFest

MTBFupp

(a)Failure

data

a

A2

Rockdrill

390.77

0.97

1.24

47.7

69.0

99.9

49.1

69.7

98.7

B2

Feeder

370.65

0.83

1.07

36.0

55.4

85.4

40.5

60.9

91.6

C2

Hoses

124

0.80

0.92

1.06

16.7

20.7

25.6

17.6

21.5

26.3

D2

Accumulators

100.70

1.22

2.13

156.1

272.7

476.3

149.6

254.9

434.4

E2

Boom

190.70

1.04

1.54

87.5

146.2

244.5

88.5

143.8

233.8

F2

Cables

70.79

1.50

2.83

298.1

555.1

1033.8

275.0

501.0

912.7

I2Hydraulics

50.73

1.51

3.12

143.8

286.6

571.1

132.9

258.4

502.6

J2Control

panel

190.86

1.30

1.95

87.5

131.8

198.7

82.3

121.7

180.1

K2

Water

cooler

80.45

0.84

1.54

121.6

332.2

907.6

140.4

363.1

938.6

L2

Valves

a23

0.67

0.93

1.3

67.9

109.9

178.0

71.7

113.2

178.5

M2

Manual

valves

160.78

1.18

1.79

113.5

180.9

288.1

109.5

170.5

265.4

N2

Movem

entdevice

60.61

1.28

2.65

211.2

434.6

893.9

202.3

402.6

801.2

Tim

eto

repair(95%

normal

CI)

Lognormal

param

eters

Com

pon

ent

ms low

s est

s upp

m low

m est

m upp

MTTRlow

MTTRest

MTTRupp

(b)Repairdata

b

A2

Rockdrill

390.41

0.52

0.65

0.27

0.44

0.60

1.5

1.7

2.1

B2

Feeder

370.46

0.58

0.73

0.72

0.91

1.10

2.4

2.9

3.6

C2

Hoses

124

0.56

0.64

0.72

0.48

0.59

0.70

1.9

2.2

2.5

D2

Accumulators

100.29

0.45

0.71

0.13

0.15

0.43

0.9

1.2

1.7

E2

Boom

190.51

0.71

0.97

0.75

1.07

1.39

2.6

3.7

5.4

F2

Cables

70.36

0.62

1.05

0.24

0.70

1.17

1.4

2.4

4.0

I2Hydraulics

50.23

0.43

0.81

0.16

0.21

0.60

0.9

1.3

2.0

J2Control

panel

190.37

0.51

0.71

0.10

0.34

0.57

1.2

1.6

2.0

K2

Water

cooler

80.52

0.85

1.39

0.007

0.58

1.17

1.2

2.5

5.1

L2

Valves

230.51

0.68

0.91

0.17

0.45

0.73

1.4

1.9

2.7

M2

Manual

valves

160.42

0.60

0.85

0.07

0.36

0.66

1.2

1.7

2.4

N2

Movem

entdevice

60.37

0.66

1.17

0.36

0.89

1.42

1.6

3.0

5.5

Notes:m

isthenumber

offailures.

aZandMTBFaregiven

inunitsof

hours;bMTTRisgiven

inunitsof

hours

Table III.Summary for

machine 2, mine Y

315

Downtimeanalysis of

drilling machines

Tim

eto

failure

(95%

normal

CI)

Weibullparam

eters

Com

ponent

mb low

b est

b upp

Z low

Z est

Z upp

MTBFlow

MTBFest

MTBFupp

(a)Failure

data

a

A3

Rockdrill

380.62

0.78

0.99

32.1

50.0

77.7

37.8

57.3

87.0

B3

Feeder

540.66

0.81

1.01

29.7

42.4

60.7

33.6

47.3

66.4

C3

Hoses

450.83

1.05

1.33

43.2

58.1

78.0

42.9

56.8

75.2

D3

Accumulators

60.66

1.39

2.94

169.4

325.5

625.5

157.9

296.7

557.5

E3

Boom

81.14

1.93

3.28

266.7

400.9

602.5

237.7

355.5

531.9

F3

Cables

70.57

1.08

2.04

182.9

399.6

873.0

146.2

387.6

811.9

G3

Steeringsystem

240.91

1.28

1.79

85.0

120.8

171.8

80.0

111.9

156.7

H3

Cylinders

140.56

0.86

1.33

90.2

180.0

359.0

100.7

193.2

370.6

Tim

eto

repair(95%

normal

CI)

Lognormal

param

eters

Com

ponent

ms low

s est

s upp

m low

m est

m upp

MTTRlow

MTTRest

MTTRupp

(b)Repairdata

b

A3

Rockdrill

380.63

0.79

0.99

0.36

0.62

0.87

1.9

2.5

3.4

B3

Feeder

540.56

0.68

0.82

0.61

0.79

0.97

2.2

2.7

3.4

C3

Hoses

450.48

0.60

0.73

0.31

0.49

0.66

1.6

1.9

2.3

D3

Accumulators

60.27

0.47

0.83

0.26

0.11

0.49

0.8

1.2

1.8

E3

Boom

80.38

0.62

1.02

0.33

0.77

1.20

1.6

2.6

4.2

F3

Cables

70.24

0.41

0.70

0.14

0.45

0.76

1.2

1.7

2.3

G3

Steeringsystem

240.45

0.60

0.79

0.37

0.61

0.85

1.7

2.2

2.8

H3

Cylinders

140.28

0.42

0.62

0.41

0.64

0.87

1.6

2.0

2.6

Notes:m

isthenumber

offailures.

aZandMTBFaregiven

inunitsof

hou

rs;bMTTRisgiven

inunitsof

hours

Table IV.Summary for machine 3,mine Y

316

JQME20,4

Tim

eto

failure

(95%

normal

CI)

Weibullparam

eters

Com

pon

ent

mb low

b est

b upp

Z low

Z est

Z upp

MTBFlow

MTBFest

MTBFupp

(a)Failure

data

a

A4

Rockdrill

460.83

1.05

1.33

45.0

60.6

81.7

44.7

59.4

78.9

B4

Feeder

490.88

1.10

1.38

43.9

57.9

76.3

42.9

55.8

72.5

C4

Hoses

780.81

0.96

1.15

28.0

35.9

46.0

28.8

36.4

46.0

D4

Accumulators

60.68

1.48

3.19

270.1

502.0

933.1

249.6

453.8

825.0

E4

Boom

150.62

0.93

1.41

100.6

181.7

328.1

107.0

187.0

326.7

F4

Cables

50.58

1.27

2.79

305.7

685.8

1,538.4

293.8

635.5

1,374.6

G4

Steeringsystem

150.90

1.34

2.00

135.2

203.8

307.2

126.1

187.0

277.1

H4

Cylinders

60.84

1.81

3.88

255.5

452.8

802.4

229.5

402.5

705.9

J4Generator

60.41

0.99

2.40

108.0

299.8

831.8

112.0

299.9

802.8

K4

Pumps

50.69

1.54

3.41

259.2

507.3

992.9

238.6

456.6

873.7

Tim

eto

repair(95%

normal

CI)

Lognormal

param

eters

Com

pon

ent

ms low

s est

s upp

m low

m est

m upp

MTTRlow

MTTRest

MTTRupp

(b)Repairdata

b

A4

Rockdrill

460.49

0.60

0.74

0.28

0.45

0.63

1.5

1.8

2.2

B4

Feeder

490.60

0.73

0.89

0.42

0.62

0.83

1.9

2.4

3.0

C4

Hoses

780.45

0.53

0.62

0.29

0.41

0.52

1.5

1.7

1.9

D4

Accumulators

60.40

0.71

1.25

0.15

0.41

0.98

1.0

1.9

3.7

E4

Boom

150.51

0.74

1.06

0.28

0.66

1.04

0.5

2.5

3.9

F4

Cables

50.33

0.62

1.16

0.13

0.68

1.22

1.3

2.4

4.3

G4

Steeringsystem

150.31

0.44

0.63

0.19

0.42

0.65

1.3

1.6

2.1

H4

Cylinders

60.27

0.47

0.83

0.19

0.57

0.95

1.3

1.9

2.9

J4Generator

60.44

0.78

1.38

0.08

0.71

1.34

1.3

2.7

5.6

K4

Pumps

50.35

0.66

1.23

0.36

0.94

1.52

1.6

3.2

6.1

Notes:m

isthenumber

offailures.

aZandMTBFaregiven

inunitsof

hours;bMTTRisgiven

inunitsof

hours

Table V.Summary for machine 4,

mine Y

317

Downtimeanalysis of

drilling machines

difference between D2, D3 and D4 (accumulators), as R¼ 1.2 in this particular case.Moreover, component A3 in machine 3 has more downtime than the similar componentused in machines 2 and 4. Similarly, component E2 in machine 2 has more downtimethan components E3 and E4. Figure 3 shows there are notable differences in thedowntime of most of the studied components for all machines used in mine Y.

Downtime Repair time/failure No. of failuresComponent DTLL DTM DTUL TTRLL MTTR TTRUL mLL mM mUL

A1 Rock drill 55.5 83.0 127.8 1.3 1.6 2.0 41.2 50.4 62.5B1 Feeder 23.0 48.2 111.4 1.8 2.7 4.1 12.2 17.7 26.9C1 Hoses 171.7 209.2 274.8 1.3 1.4 1.6 129.5 142.9 163.8G1 Steering system 120.3 179.2 273.0 2.3 2.8 3.5 50.7 61.9 76.4H1 Cylinders 14.5 30.7 74.3 1.2 1.7 2.7 11.7 17.0 26.5I1 Hydraulics 9.7 22.8 62.1 0.9 1.4 2.3 10.5 16.2 26.7J1 Fuel system 10.6 22.0 52.1 0.8 1.1 1.8 12.8 18.5 28.4

Notes: DTM, DTLL, DTUL, MTTR, TTRLL and TTRUL are given in units of hours

Table VI.Three estimation pointsof the downtime andtheir coordinates formachine 1, mine X


A2 Rock drill 117.0 136.0 213.4 1.6 1.7 2.2 70.5 76.0 95.2B2 Feeder 208.3 259.4 390.5 2.6 2.9 3.6 77.9 86.9 106.6C2 Hoses 510.6 547.9 726.3 2.1 2.2 2.5 237.6 246.2 283.5D2 Accumulators 15.4 26.8 49.5 0.9 1.2 1.7 15.7 20.7 28.2E2 Boom 106.8 139.5 271.8 3.3 3.7 5.2 32.2 36.8 51.4F2 Cables 15.6 26.1 70.3 1.9 2.4 4.0 8.1 10.5 17.3I2 Hydraulics 13.1 28.1 69.6 0.9 1.3 2.1 14.0 20.5 32.2J2 Control panal 55.6 69.9 131.6 1.4 1.6 2.2 38.7 43.5 59.6K2 Water cooler 21.2 37.7 101.7 1.9 2.5 4.2 10.9 14.5 23.9L2 Valves 65.4 93.6 151.5 1.6 1.9 2.5 39.1 46.8 59.5M2 Manual valves 36.3 53.9 95.9 1.4 1.7 2.3 25.4 31.0 41.4N2 Movement device 18.7 40.2 98.0 2.0 3.0 4.7 8.9 13.1 20.5


Table VII.Three estimation pointsof the downtime andtheir coordinates formachine 2, mine Y


A3 Rock drill 174.1 236.5 345.5 2.1 2.5 3.0 79.2 92.3 111.6B3 Feeder 254.2 312.8 437.5 2.5 2.7 3.3 100.9 111.9 132.4C3 Hoses 137.9 182.5 245.0 1.7 1.9 2.2 80.9 93.1 107.9D3 Accumulators 11.0 22.4 51.2 0.8 1.2 1.8 12.5 17.8 26.9E3 Boom 20.3 39.2 81.6 1.8 2.6 3.7 10.7 14.9 21.5F3 Cables 12.3 23.4 48.9 1.2 1.7 2.4 9.8 13.6 19.7G3 Steering system 78.5 105.0 172.9 1.9 2.2 2.8 40.9 47.3 60.7H3 Cylinders 44.7 67.3 123.8 2.0 2.4 3.3 22.3 27.4 37.1


Table VIII.Three estimation pointsof the downtime andtheir coordinates formachine 3, mine Y

318

JQME20,4

When we interpret Figures 4-9 in the same way, we conclude the results of the ratio Rfor all machine components, as shown in Table X.

Table X it shows notable differences in the downtime of most investigatedcomponents of all machines used in both mines. For the machines used in the samemine, three out of six components have significant differences. For the machines usedin different mines, five out of six components have significant differences.

Figure 4 indicates that the components C2 and B3 have higher downtime than theequivalent components in another machine used in the same mine.

Figure 5 and 6 illustrate that the components A1 and B1 used in machine 1 in mineX have less downtime than the same components used in the machines in mine Y.This may be due to the differences of the rock properties between the two mines.The geological strength index (GSI) of mine Y varies between 50 and 80

No.

of f

ailu

res


A3

A2

A4

D3

D4

10

100

1,00

0

Downt

ime

(Hou

rs)E4

E2

E3

D2

0.7 1.1

14.2

100

616.6

10

57

10

135

24

Figure 3.Confidence log-log plot

comparison between threemachines used in mine Y


A4 Rock drill 134.0 169.1 237.2 1.6 1.8 2.2 79.3 89.1 105.5B4 Feeder 183.8 234.4 330.1 2.1 2.4 2.9 84.1 94.9 112.7C4 Hoses 213.9 253.1 326.9 1.5 1.7 1.9 133.7 145.4 165.3D4 Accumulators 10.4 22.8 56.8 1.3 1.9 3.0 7.8 11.6 18.4E4 Boom 43.5 72.5 126.5 1.9 2.5 3.3 21.9 28.3 37.4F4 Cables 8.8 20.0 53.3 1.5 2.4 3.9 5.5 8.3 13.6G4 Steering system 30.4 47.8 77.9 1.3 1.6 2.1 22.6 28.3 36.1H4 Cylinders 16.1 26.2 74.9 1.5 1.9 3.3 10.3 13.1 22.2J4 Generator 27.3 49.0 157.3 2.0 2.7 4.9 13.1 17.6 31.6K4 Pumps 16.1 37.2 101.0 2.1 3.2 5.2 7.6 11.6 19.1


Table IX.Three estimation points

of the downtime andtheir coordinates formachine 4, mine Y

319

Downtimeanalysis of

drilling machines

Notes: A1 (rock drill) and B1 (feeder) are components usedin machine 1 in mine X, while A2, A3 and A4 (rock drill),B2, B3, and B4 (feeder) are components used in machines 2,3 and 4 in mine Y

A2

A1

60

100

Downt

ime

(Hou

rs)

500

A4A3

30

40

1 1.6

190

100

1.3 7.5Time to repair (hours)

No.

of f

ailu

res

Figure 5.Confidence log-logplot comparisonbetween four machinesused in both mines

No.

of f

ailu

res


C2

C3

C4

B3

B2

B4

F4

F3

10

100

1,00

0

Downt

ime

(Hou

rs)

F2

2 40

100

705

1

200

300

10

Figure 4.Confidence log-log plotcomparison between threemachines used in mine Y

320

JQME20,4

(Edelbro, 2008) while the GSI of mine X varies between 30 and 50 (Sjoberg, 2003 ascited in Edelbro, 2008).

Figure 7 compares the downtime of component hoses C in four machines in differentmines. Component C2 (hoses) has more downtime than the same components, C1, C3and C4, used in the rest of the machines. A possible explanation is the difference inhow the various machines were handling. However, further research is needed toconfirm this explanation. Figures 5-7 clearly show that components B2 and C4 haveapproximately the same downtime (259 h and 253 h, respectively). Similarly,components A3 and B4 have approximately the same downtime (236 h and 234 h,respectively). In addition, at the upper limit of the downtime interval, componentsB4 and C4 have approximately the same downtime. The figures also show that at thelower limit of the downtime interval, components C4 and B2 have approximatelythe same downtime, as do components A3 and C1 and components C3 and A4.

Figure 8 compares two components used in machines 1, 3 and 4 in two differentmines. The components G4 (steering system), H4 and H1 (cylinders) haveapproximately the same downtime at the upper limit of the downtime interval.

For comparison type four, Figure 9 shows no significant difference in the downtime ofthe component I (hydraulics) used in machines 1 and 2, as R¼ 1.2 in this particular case.

The order of the significant components has been prioritised by Wijaya et al. (2012),based on three scenarios: the mean estimation point of the downtime (the high-likelihoodscenario), the upper limit estimation point of the downtime (the worst-case scenario)and the lower limit estimation point of the downtime (the best-case scenario).


No.

of f

ailu

res

100 B2

B3

B4

20

10 202

80

110

160

B1

20

100

1,00

0

Downt

ime

(Hou

rs)

Note: A1 (rock drill) and B1 (feeder) are components used inmachine 1 in mine X, while A2, A3 and A4 (rock drill), B2,B3, and B4 (feeder) are components used in machines 2, 3and 4 in mine Y

Figure 6.Confidence log-log plotcomparison betweenfour machines used

in both mines

321

Downtimeanalysis of

drilling machines

These three scenarios are important to decisions about certain activities in the mine,for instance, planning new operations and budgeting maintenance. Table XI illustratesthe order of the significant components from the prioritisation of maintenance actionpoint of view. During smooth operations, the component B4 (feeder) has a downtimeof about 330 h more than component C4 (hoses) which has a downtime about 327 h.In the worst-case scenario of comparison type 1, component C4 should be givenpriority because it has a high number of breakdowns, combined with breakdowns ofshort duration; in comparison, component B4 has fewer breakdowns, combined withbreakdowns of long duration; refer to Figure 4 and Table IX. This is important becausea high frequency of breakdowns leads to a lower production rate as the machine needsmore time to reach normal performance after each breakdown.

To cite another example, if the maintenance management department determinesthe highest acceptable amount of machine downtime at the component level, it isessential for the maintenance staff to know which components are likely to go beyondthe acceptable limit. For example, if they decide that the highest acceptable amount ofdowntime is 350 hours per year for one component, in the worst-case scenario, we canobserve in Figure 4 that components C2 (hoses on machine 2), B3 (feeder on machine 3)and B2 (feeder on machine 2) will exceed 350 hours of downtime. In this case, a goodstrategy may be to convince the manufacturing company to improve the lifetime of thecomponents; another possibility is to increase the PM on these particular components.However, more research is needed on the topic.

Notes: C1 (hoses) is a component used in machine 1 in mine X,while C2, C3 and C4 (hoses), are components used inmachines 2, 3, and 4 in mine Y. G1 (steering system) andH1 (cylinders) are components used in machine 1 in mine X;G3 and G4 (steering system), H3 and H4 (cylinders) arecomponents used in machines 3 and 4 in mine Y

No.

of f

ailu

res


C3

100

300

1,00

0

Downt

ime

(Hou

rs)

C4

1.5 8

C1

C2

6.6

80

60

300

100

400

1.11 5

Figure 7.Confidence log-log plotcomparison betweenfour machines usedin both mines

322

JQME20,4

5.1 Link between analysis and improvementsThe following general method is suggested regarding the link between analysis andcritical components improvement:

(1) collecting of maintenance and repair data;

(2) using confidence log-log diagram with reliability vs maintainability;

(3) identifying the most critical components (largest downtime);

(4) identifying the contribution of influencing factors (reliability and\ormaintainability) for each of the critical components; and

(5) redesigning of the critical components with respect to the finding.

Using confidence log-log plots, we pinpoint reliability/maintainability problems inFigures 3-8. The plots show that at the upper limit of downtime (DTULX200 hours)per year, components C (hoses), B (feeder), A (rock drill), E (boom) and G (steeringsystem) have reliability problems, with a high number of failures and low levels ofrepair time. Thus, DFR strategy should be adopted to reduce their downtime.

5.2 Suggestions for critical components improvementIt has been concluded that the most common problem for all critical componentsis reliability problems. Therefore, this section will focus on suggestions on how toredesign the critical components to improve the reliability and reduce the machine’s


No.

of f

ailu

res

8070

60

8

G1

G3G4

10

H4

H3

H1

1030

100

Downt

ime

(Hou

rs)

200

300

121 1.25 7.5 10

50

Note: C1 (hoses) is a component used in machine 1 in mine X,while C2, C3 and C4 (hoses), are components used inmachines 2, 3 and 4 in mine Y. G1 (steering system) andH1 (cylinders) are components used in machine 1 in mine X;G3 and G4 (steering system), H3 and H4 (cylinders) arecomponents used in machines 3 and 4 in mine Y

Figure 8.Confidence log-log plotcomparison betweenthree machines used

in both mines

323

Downtimeanalysis of

drilling machines

downtime. Discussions with maintenance personal reveal that the most of the failuresin the feeder hoses are due to the mine’s environment. For example, during drilling, thefeeder hits the wall at different angles, especially when the feeder movement isrestricted because of spatial limitations. To overcome this problem, the feeder could beequipped with an iron plate on both sides; the plate should be large enough to preventhoses from being scratched and to prevent nipples at the necks from being broken(Plates 1-2 and Figure 10).

Another problem in the feeder is the pull rope breaking. This happens for tworeasons. First, the pull rope relaxes with usage; it then hangs over the edge of the cradleplate when the plate moves forward and back on the slide bar (see Plates 3 and 4).

Component Symbol Mine Machine Figure R Status

Rock drill A2, A3, A4 Y 2, 3, 4 3 1.7 Significant differencesBoom E2, E3, E4 Y 2, 3, 4 3 3.5 Significant differencesAccumulators D2, D3, D4 Y 2, 3, 4 3 1.2 No significant differencesHoses C2, C3, C4 Y 2, 3, 4 4 3 Significant differencesFeeder B2, B3, B4 Y 2, 3, 4 4 1.3 Indicated differencesCables F2, F3, F4 Y 2, 3, 4 4 1.3 Indicated differencesRock drill A1, A2, A3, A4 X, Y 1, 2, 3, 4 5 2.8 Significant differencesFeeder B1, B2, B3, B4 X, Y 1, 2, 3, 4 6 6.5 Significant differencesHoses C1, C2, C3, C4 X, Y 1, 2, 3, 4 7 3 Significant differencesSteering system G1, G3, G4 X, Y 1, 3, 4 8 3.7 Significant differencesCylinders H1, H3, H4 X, Y 1, 3, 4 8 2.5 Significant differencesHydraulics I1, I2 X, Y 1, 2 9 1.2 No significant differences

Table X.R ratio for machinescomponents

Notes: I1 (hydraulics) is a component of machine 1 used in mineX; I2 (hydraulics) is a component in machine 2 in mine Y


No.

of f

ailu

res

I2

1020

30Dow

ntim

e

(Hou

rs)

70

100

I1

12.5

4

37.5

10

44

11.2

30.8 10.9Figure 9.Confidence log-log plotcomparison betweentwo machines usedin both mines

324

JQME20,4

Second, the operator or repair person may put extreme tension on the pull ropewhen making an adjustment. This excessive tension leads to two undesirableoccurrences: first, a reduction in the lifetime of the pull rope; second, a high load on thepulley wheel leading to a reduction of the lifetime of the roller bearing inside it (seePlate 5).

To solve this problem, an electrical motor with control circuit should be designed tomake automatic adjustments for the pull rope, keeping it at a constant desired tension,as shown in Figure 11. Stronger roller bearings are another possibility.

Type 1, mineY three machines

Type 2, mine X andY four machines

Type 3, mine X andY three machines

Type 4, mine X andY two machines

Scenario Scenario Scenario ScenarioOrder 1 2 3 Order 1 2 3 Order 1 2 3 Order 1 2 3

1 C2 C2 C2 1 C2 C2 C2 1 G1 G1 G1 1 I2 I2 I22 B3 B3 B3 2 B3 B3 B3 2 G3 G3 G3 2 I1 I1 I13 B2 B2 C4 3 B2 B2 C4 3 H3 H3 H34 C4 A3 B2 4 C4 A3 B2 4 G4 G4 G45 A3 B4 B4 5 A3 B4 B4 5 H1 H4 H46 B4 C4 A3 6 B4 C4 A3 6 H4 H1 H17 C3 E2 C3 7 C1 C1 C18 A4 C3 A4 8 C3 C3 C39 E2 A4 A2 9 A4 A4 A410 A2 A2 E2 10 A2 A2 A211 E4 E4 E4 11 A1 A1 A112 E3 E3 E3 12 B1 B1 B113 D2 F2 F214 F2 D4 D215 F3 F4 F316 D4 D3 D317 D3 D2 D418 F4 F3 F4

Table XI.The order of the

significant component

Plate 1.Scratched hoses

325

Downtimeanalysis of

drilling machines

Discussions with maintenance personal also reveal that the frequent failures in rockdrill are damaging the third and fourth cup seals located inside front head (nose) of thiscomponent, as shown in Plates 6-7 and Figure 12.

A possible cause is the high water pressure inside the nose. Water is used to cool thefront head and flush it during the drilling process. However, damaging the cup sealswill cause water and oil to mix, leading to the adhesion of the valves used in thehydraulic system. To solve this problem, the water pressure inside the front headshould be reduced by increasing the number of holes, especially in the area between thethird and the forth cups seals, as shown in Plate 8. Further research is needed toconfirm this explanation.

It is worth to mention that all suggestions for improvement were discussed andagreed up on together with the maintenance experts and product development team ofthe manufacturing company. The product development team also decided to take thesuggestions on and implement them in the future.

IronPlate

Figure 10.Suggested plate of iron

Plate 2.Nipples and necks

326

JQME20,4

6. ConclusionsThe downtime analysis of drilling machines shows a significant difference betweenthe three machines used in same mine (mine Y) in the downtime of components A(rock drill), C (hoses) and E (boom). There is no significant difference between thesemachines in the downtime of component D (accumulators). The analysis also findsdifferences in the downtime of components B (feeder) and F (cables). Components Aand B used in mine X have less downtime than the same components used in themachines of mine Y, most probably as a result of the differences in the rock propertiesbetween the two mines. Further research is required to explain the differences in thedowntime between the same models of the drilling machine. There is a significantdifference in the downtime of component G (steering system) found in machines usedwithin a single mine and across mines. In contrast, there is no significant difference inthe downtime of component I (hydraulics) found in machines 1 and 2 used in differentmines. In general, there are notable differences in the downtime of most investigated

Plate 4.Hung pull rope

Plate 3.Broken pull rope

327

Downtimeanalysis of

drilling machines

components of all machines used in both mines. For the machines used in thesame mine, three out of six components have significant differences. For machines usedin both mines, five out of six components have significant differences.

The downtime analysis of drilling machines also shows that the machines’components can be ranked on their downtime, using three different scenarios (the highlikelihood, the worst-case, and the best-case scenarios) based on three estimation

Electrical MotorGearFigure 11.Suggested electrical motor

Plate 6.Damaged cup seal

Plate 5.Roller bearing with pulley

328

JQME20,4

Plate 7.Cup seals

Cup seals

Figure 12.Cup seals

Plate 8.Front head (nose)

of rock drill

329

Downtimeanalysis of

drilling machines

points of downtime. The components C2 (hoses on machine 2), B3 (feeder on machine 3)and B2 (feeder on machine 2) have more downtime (DTULX350) hours per year.The downtime (DTULX200) hours per year of components C (hoses), B (feeder), A (rockdrill), E (boom) and G (steering system) stem from reliability problems. Because theyhave a high number of failures and short repair times, as shown in Figures 3-8, a DFRshould be created to decrease their downtime. Overall, no maintainability problemswere detected for the machines’ significant components; therefore, a design for amaintainability strategy is not required. The failures of the feeder hoses are likely dueto the harsh work environment during drilling. In this case, putting iron plates on bothsides of the feeder may reduce the number of failures. The breakage of the feeder pullrope is due to usage and excessive tension; this can be treated and reduced byinstalling an electrical motor with a control circuit to keep the pull rope at a constantdesired tension. Finally, increasing the number of holes between the third and thefourth cup seals inside the nose of the rock drill could solve the problem of cupseal damage.

In summary, the suggested “DFR” solution is found to be applicable. In order tojudge for cost effectiveness, one should perform life cycle cost analysis to identify, if thesolution is also economically viable.

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About the authors

Hussan S. Al-Chalabi received BEng Degree in Mechanical Engineering from the MosulUniversity, Iraq in 1994 and MSc Degree in Mechanical Engineering in Thermal Power from theMosul University, Iraq in 2008. Then he joined the Department of Mechanical Engineering at theMosul University as a Lecturer. In 2011 he joined the Division of Operation, Maintenance and

331

Downtimeanalysis of

drilling machines

Acoustics at the LTU as a Doctoral Student. Hussan S. Al-Chalabi is the corresponding authorand can be contacted at: [email protected]

Jan Lundberg is a Professor of Machine Elements at the Lulea University of Technologyand also in Operation &Maintenance with focus on product development. During the years 1983-2000, his research concerned mainly about engineering design in the field of machine elements inindustrial environments. During the years 2000-2006, his research concerned mainly aboutindustrial design, ergonomic and related problems as cultural aspects of design and modern toolsfor effective industrial design in industrial environments. From 2006 and forward, his research iscompletely focused on maintenance issues like methods for measuring failure sources, how to dodesign out maintenance and how to design for easy maintenance.

Dr Andi Wijaya received BEng Degree in Mechanical Engineering from the Gadjah MadaUniversity (GMU), Indonesia in 1998 and MSc Degree in Industrial Ergonomics and LicentiateDegree in Sound and Vibration from the Lulea University of Technology (LTU), Sweden in 2001and 2003, respectively. Then he joined to the Department of Mechanical and IndustrialEngineering at the GMU as a Lecturer. Since 2009, he received PhD Degree from the Division ofOperation, Maintenance and Acoustics, Lulea University of Technology, Sweden in 2012.

Behzad Ghodrati is an Associate Professor of Maintenance and Reliability Engineeringat the Lulea University of Technology. He obtained his PhD Degree on “Reliability based spareparts planning” from the Lulea University of Technology and he was awarded the PostdoctoralResearch Fellowship from the University of Toronto in 2008.

To purchase reprints of this article please e-mail: [email protected] visit our web site for further details: www.emeraldinsight.com/reprints

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PAPER II

Case Study: Model for Economic Lifetime of Drilling Machines in the Swedish Mining Industry

Al-Chalabi, H., Lundberg, J., Jonsson, A., Ahmadi, A., 2014. Case Study: Model for Economic Lifetime of Drilling Machines in the Swedish Mining Industry. Published in the Engineering Economist. http://dx.doi.org/10.1080/0013791X.2014.952466

The Engineering Economist, 00:1–17, 2014Published with license by Taylor & Francis Group, LLCISSN: 0013-791X print/1547-2701 onlineDOI: 10.1080/0013791X.2014.952466

Case Study: Model for Economic Lifetime of Drilling Machines in the Swedish Mining Industry

HUSSAN AL-CHALABI,1 JAN LUNDBERG,2

ALIREZA AHMADI,2 AND ADAM JONSSON3

1Division of Operation, Maintenance and Acoustics, Lulea University of Technology, Lulea, Sweden and Mechanical Engineering Department, College of Engineering, University of Mosul, Mosul Iraq 2Division of Operation, Maintenance and Acoustics, Lulea University of Technology, Lulea, Sweden 3Division of Mathematic Science, Lulea University of Technology, Lulea, Sweden

The purpose of this article is to develop a practical economic replacement decision model to identify the economic lifetime of a mining drilling machine. A data-driven optimization model was developed for operating and maintenance costs, purchase price, and machine resale value. Equivalent present value of these costs by using discount rate was considered. The proposed model shows that the absolute optimal replacement time (ORT) of a drilling machine used in one underground mine in Sweden is 115 months. Sensitivity and regression analysis show that the maintenance cost has the largest impact on the ORT of this machine. The proposed decision-making model is applicable and useful and can be implemented within the mining industry.

Introduction Economic globalization increases competition among mining companies, pushing them to achieve higher production rates by increasing automation and mechanization and using new and more effective equipment. This forces companies to use more reliable capital equipment with higher performance capabilities; naturally, these are more expensive. The equipment used in underground mining industries is subject to degradation throughout its operating life. This increases the operating and maintenance costs and reduces production rates, causing a negative economic effect. In addition, the equipment used in underground mining is subject to a harsh working environment, and this accelerates degradation. Given all of these factors, key questions for the mining industry include the following. When should the company replace the equipment to minimize cost? How can the maintenance manager

C© Hussan Al-Chalabi, Jan Lundberg, Adam Jonsson, and Alireza Ahmadi This is an Open Access article. Non-commercial re-use, distribution, and reproduction in any

medium, provided the original work is properly attributed, cited, and is not altered, transformed, or built upon in any way, is permitted. The moral rights of the named author(s) have been asserted.

Address correspondence to Hussan Al-Chalabi, Division of Operation, Maintenance and Acous- tics, Lulea University of Technology, Lulea 97187, Sweden; E-mail: [email protected]

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2 H. Al-Chalabi et al.

convince finance and production managers to replace capital equipment at a specified time in its life cycle? To answer these questions, life cycle cost analysis should be done in advance of an equipment replacement decision.

The optimum replacement age of equipment is defined as the time at which the total cost is at its minimum value (Jardine and Tsang 2006). In the mining industry, the costs associated with owning equipment can be grouped into categories: initial purchase, installation, direct downtime, maintenance and operating, financing, and cost recovery on disposal. The sum of these costs represents the total cost required to own the mining equipment (Hall 2007). Life cycle cost analysis helps decision makers justify equipment replacement on the basis of the total costs over the equipment’s useful life. It allows the maintenance manager to specify the optimal replacement time at the time of the equipment’s purchase.

Cost function models can be allocated to the various categories to allow easy estimation of the total cost. Such models can be generally classified as detailed models, analogous models, and parametric models. A detailed model uses estimates of material quantities and prices, labor time, and rates to estimate the direct costs of equipment. Analogous models identify similar equipment and adjust costs to account for differences between it and the target equipment. Cost estimation with a parametric model is based on predicting the equipment’s total cost by using regression analysis based on technical information and historical cost (Asiedu 1998). Life cycle cost (LCC) analysis should not be seen as a method for defining the total cost of the equipment but as a help in decision making; thus, LCC analysis should be restricted to costs that can be controlled. In general, LCC is determined by summing up all of the potential costs associated with equipment over its lifetime. It is well known that the value of expenditure today costs more than the same value of expenditure next year because of the “time value of money.” A discount rate is used to take into consideration the time value of money. To compare costs incurred at different times we must shift expenditure to a reference point in time. Thus, in this article, we are interested in estimating the equivalent present value of earlier or future costs.

Literature Survey Standard models for economic replacement time decision contain an estimation of the discounted costs by minimizing the LCC of the equipment. The assumption of these models is that equipment will be replaced at the end of its economic lifetime by a continuous sequence of identical equipment (Hartman and Tan 2014). Recently, a number of researchers have studied the economic lifetime of capital equipment. Some consider the optimal lifetime of capital equipment using economic theories and vintage capital models, represented mathematically by nonlinear Volterra integral equations with unknown limits of integration (Boucekkine et al. 1997; Cooley et al. 1997; Hritonenko 2005; Hritonenko and Yatsenko 2003; Yatsenko 2005). Others use the theory of dynamic programming considering technological changes under finite and infinite horizons (Bellman 1955; Bethuyne 1998; Elton and Gruber 1976; Hartman 2005; Hritonenko and Yatsenko 2008; Mardin and Arai 2012). Yatsenko and Hritonenko (2005) studied the lifetime optimization of capital equipment using integral models. The study designs a general investigation framework for optimal control of the models. Hritonenko and Yatsenko (2007) studied optimal equipment replacement without paradoxes. Using an integral model to calculate the economic lifetime of equipment and considering technological changes (TCs), they showed that the economic lifetime of equipment is shorter when the embodied TC is more intense. Hartman and Murphy (2006) offered a dynamic programming approach to the finite-horizon equipment

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Model for Economic Lifetime of Drilling Machines 3

replacement problem with stationary cost. Their model studies the relationship between the infinite-horizon solution (continuous replacement of equipment at the end of its economic lifetime) and the finite-horizon solution. Hritonenko and Yatsenko (2009) constructed a computational algorithm to solve a nonlinear integral equation. The solution is important for finding the optimal policy of equipment replacement under technological advances. Karri (2007) considered the optimal replacement time of an old machine, using an optimization model that minimizes the machine cost. The model is built to handle capacity expansion and replacement situations. Using real costs without inflation, Karri (2007) modeled the costs of the old machine with simple linear functions. He also used an optimization model that maximizes profit. Scarf and Bouamra (1999) addressed the capital replacement problem using a discounted cost criterion over a finite time horizon. They presented a robust approach to solving the fleet replacement problem in which the fleet size is allowed to vary at replacement. A survey of multiple and single asset solution techniques under a variety of settings, including tax, variable utilization, various uncertainties, and technological change, was addressed by Hartman and Tan (2014). They also illustrated a number of open problems that are worthy of future research. Generally speaking, these studies focus on estimating the economic lifetime of equipment, considering technological changes and using integral models, theories of dynamic programming, vintage capital models, and algorithms to solve nonlinear integral equations.

Despite the available information, it can be difficult for users to implement complex models to calculate the optimal replacement time of equipment. Moreover, these models sometimes require specific types of data that, as in our case study, are not available. These can include data on production output, technological labor/output coefficient, revenue, profit, etc. Thus, the aim of this study is to identify the replacement age of a mining drilling machine from an economic point of view, using available data from a mining company, specifically, the operating and maintenance costs, purchase price, and machine resale value. In this study, equivalent present value of these costs was considered by using a discount rate.

Description of Drilling Machine The drilling machines typically used in mines are manufactured by different companies and have different technical characteristics; for example, capacity and power. An example of a drilling machine and its components is presented in Figure 1.

The drilling machine is divided into several subsystems connected in series configuration (see Atlas Copco Rock Drills AB 2010). If any subsystem fails, the operator will stop the machine to fix it. Thus, all machine subsystems work simultaneously to achieve the desired function.

Data Collection The cost data used in this study were collected over 4 years in the Maximo computerized maintenance management system (CMMS). The cost data contain corrective maintenance costs, preventive maintenance costs, and repair time. The corrective and preventive maintenance costs contain spare parts and labor (repair person) costs. In CMMS, the cost data are recorded based on calendar time. Because drilling is not a continuous process, the operating cost is estimated by considering the utilization of the machines. It is important here to mention that all cost data used in this study are real costs without inflation. Due to the company regulations, all cost data are encoded and expressed as currency unit (cu) for this study. Samples of cost data can be seen in Table 1.

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Figure 1. Drilling machine. Source: Andreas Nordbrandt, Vice President Service Operations, Atlas Copco Rock Drills AB (2010). © Atlas Copco Rock Drills AB. Reproduced by permission of Atlas Copco Rock Drills AB. Permission to reuse must be obtained from the rightsholder.

Methodology and Model Development In this study the following assumptions are made for the optimization model:

• The cost of capital is given by the mining company involved in this study. • Acquisition cost of the machine remains constant at each replacement. • There is no installation cost for the machine. • The optimization model is used for a finite time horizon. • Production losses due to lead time during machine replacement are not considered. • The machine will be used as a redundant machine after it reaches to its scrap value.

The taxes are included in the purchase price and operating and maintenance costs; for that reason, taxes are not included as an independent parameter in the optimization model.

The study develops a practical optimization model based on the total cost. Associated operating and maintenance costs, as well as purchase price and machine resale value, are considered. The maintenance costs (MC) for each month of operation consist of corrective maintenance (CM) and preventive maintenance (PM) costs:

MC = CM + PM. (1)

The corrective and preventive maintenance costs are given by

CM = SPc + LCc (2)

PM = SPp + LCp. (3)

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Table 1Sample of Cost Data

Workdescription

Actualworkingtime (h)

Actualmateri-als cost

(cu)

Totalreal cost

(cu)

Actuallabor(cu)

Actualservice

cost (cu)

Actualstartdate

Inventorydescrip-

tionWorktype

Extension Extender 2 bolts of V-feeder

1 28.148 28.598 0.45 0 20xx- 03-15 13:23

Feeder PM

FU1 Atlas L2C/2

5 9.836 14.018 0 4.182 20xx- 03-15 13:24

PM

Mount the sensor cables

6 0 2.7 2.7 0 20xx- 03-15 22:41

Steering system

CM

Atlas Copco L2C

16 0 7.2 7.2 0 20xx- 03-16 13:17

Electrical system

CM

Replacing the hose feeding shift

0.5 0 0.225 0.225 0 20xx- 03-19 07:30

Hoses CM

Because drilling is not a continuous process in the collaborating mine, operating cost (energy cost and steel rod cost) is calculated for each month based on the utilization of the drilling machine. The company plans to use the machine for 120 months. Therefore, extrapolation for the operating and maintenance cost data was done. Figures 2 and 3 illustrate the maintenance and operating costs determined by the data extrapolation.

In Figures 2 and 3, the dots represent the real historical data for maintenance and operating costs. Curve fitting was done using Table Curve 2D (Alfasoft AB, Goteborg, Sweden) software to show the behavior of these costs before and after the time when data were collected. Note that the fitting would be better if more data were available for a time period of more than 4 years. This software uses the least squares method to find a robust (maximum likelihood) optimization for nonlinear fitting. It is worth mentioning that the drilling machine in this case study has no multilevel preventive maintenance programme. In addition, it was new at the start of utilization. This is the main reason why the maintenance cost is quite low in earlier months. The history shows that when the maintenance costs started growing, the user company began to keep track of cost data by using CMMS.

The Lorentzian cumulative equation of extrapolation for expected maintenance cost obtained by the software is expressed as

Y = a

π

[arctan

(x − b

c

)+ π

2

], (4)

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Figure 2. Maintenance cost.

where Y represents the expected maintenance cost, a = 217.42, b = 112.37, c = 13.63, r2 (adj.) = 0.97, and X represents the time (1, 2, 3, 4, . . . , n months). Similarly, the Lorentzian cumulative equation of extrapolation for expected operating cost is expressed as

Y = a

π

[arctan

(x − b

c

)+ π

2

], (5)

Figure 3. Operating cost.

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where Y represents the expected operating cost, a = 79.89, b = 109.2, c = 13.85, r2 (adj.) = 0.91, and X represents the time (1, 2, 3, 4, . . . , n months).

As the figures show, the operating and maintenance costs increase over time. In fact, the number of failures increases with time and/or the machine consumes more energy due to machine degradation.

A declining balance depreciation model is used to estimate the resale value of the machine after each month of operation. The machine’s resale value is its value if the company wants to sell it at any time during its planned lifetime. The resale value of the machine, denoted S(i), is assumed to be given by the following formula (Eschenbach 2010; Luderer et al. 2010):

S (i) = BV1 × (1 − Dr)i , (6)

where i represents time (month), i = 1, 2, 3, . . . , 120, and BV1 is the machine’s value at the first day of operation. In addition,

BV1 = PP × a, (7)

where a represents the percentage that multiplied by the machine purchase price to represent the machine value at the first day of use. During discussions with us, company experts agreed that the machine’s purchase price decreases by 10% on the first day of use (i.e., a = 0.9). In this study, the machine purchase price is 6,000 cu. Hence, the machine’s value on the first day of use is 5,400 cu.

The depreciation rate that allows for full depreciation by the end of the planned lifetime of the machine is modeled by the following formula (Luderer et al. 2010):

Dr = 1 −(

SV

BV1

) 1 T

, (8)

where T represents the planned lifetime of the machine, 120 months in the case study. The machine was assumed to reach scrap value after 10 years. The machine’s resale value is given by

S (i) = (PP × a) × (1 − Dr)i . (9)

The declining balance depreciation model is suitable in this case because it assumes that more depreciation occurs at the beginning of the equipment’s planned lifetime and less at the end. It also considers that the equipment is more productive when it is new and its productivity declines continuously due to equipment degradation. Therefore, in the early years of its planned lifetime, a machine will generate more revenue than in later years. In accountancy, depreciation refers to two aspects of the same concept. The first is the decrease in the equipment’s value. The second is the allocation of the cost of the equipment to periods in which it is used. The scrap value is an estimate of the value of the equipment at the time it is disposed of. In this case study, 50 cu is assumed to be the scrap value of the machine at end of its planned lifetime, a figure given to us by experts at the company. Figure 4 shows the drilling machine’s resale values using the declining balance depreciation model.

It is clear from Figure 4 that the machine’s resale values decrease with time until it reaches scrap value at the end of its planned lifetime.

The next step in the calculations is to calculate the total ownership cost over each operating month. In this study, the economic lifetime of the drilling machine is defined as

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Figure 4. Machine resale value.

the machine age that minimizes the machine total ownership cost. The total ownership cost over period i is denoted by TOCi, i = 1, 2, 3, . . . , n, where n is the number of operating months. By definition,

TOCi = PP +[

RT∑i=1

(MCi + OCi)

]− S (i) , (10)

where MCi and OCi is the maintenance and operating costs for the ith month. The reason for using total ownership cost is that the machine’s PP, OC, and MC

represent costs, whereas the resale value represents income for the company when it is willing to sell the machine.

The objective is to determine the optimal replacement time that minimizes the total ownership cost over the machine’s planned horizon. We assume that the replacement machines (i.e., the new machines) have the same performance and cost as the existing machine (i.e., identical machines). The number of replacement cycles during the planned horizon is modeled as

M =[

Planned lifetime Replacement time

]=

[T

RT

]. (11)

Figure 5 illustrates the expected total ownership cost of the machine over the planned horizon.

As Figure 5 shows, the total ownership cost increases with time for two reasons: first, operating and maintenance costs increase over time; second, the machine’s resale value decreases over time until reaches its scrap value.

The optimal replacement time is the value of RT that minimizes the total ownership cost value, as shown in Eq. (12). A discount rate of 10% was used to consider the time value of money as mentioned by the collaborating mining company.

TOCvalue =⎡⎣

⎧⎨⎩

⎛⎝PP +

⎡⎣RT∑

i=1

MCi + OCi

⎤⎦ − S (i)

⎞⎠ × 1

(1 + r) i

12

⎫⎬⎭ × M

⎤⎦ . (12)

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Figure 5. Expected total ownership cost.

Results and Discussion Figure 6 shows the results when MATLAB (MathWorks, Natick, MA) software is used to enable a variation of the parameter RT of Eq. (12) for a planned horizon of 120 months. This is done to identify the optimal replacement time (ORT) of a drilling machine that minimizes TOCvalue. The figure shows the TOCvalue versus a different replacement time RT.

To show the behavior of the optimization curve for a period more than the planned horizon, we assume that the optimization is used for a new finite time horizon of 240 months; see Figure 7. The total ownership cost for each operating month of the new planned horizon (i.e., i = 1, 2, 3, . . . , 240) is computed by using the total ownership cost

Figure 6. Total ownership cost versus replacement time of existing drilling machine.

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Figure 7. Optimal replacement time of existing drilling machine.

function obtained from Figure 5. This function is the fit of the calculated total ownership cost over the machine’s old planned horizon (i.e., 120 months).

As is evident, the absolute lowest possible TOCvalue can be achieved by replacing the machine with an identical new one every 115 months. However, it must be noted that RT = 115 months generates the absolute minimum cost. As Figures 6 and 7 also show, within that, there is a range (e.g., 110–122 months) when the minimum TOCvalue can still be achieved in practice. In this study, we call it the optimum replacement range. Finding the optimum replacement range is an important result of our study because it can help users in their planning. A decision to replace equipment before or after this optimum replacement range incurs greater cost for the company. The use of a lower replacement age (i.e., less than 110 months) incurs higher costs due to the high investment cost. Meanwhile, if the lifetime of the machine exceeds the upper limit of this range (i.e., more than 122 months), losses will increase for two reasons:

1. The cost of operation and maintenance increases when the operating time increases due to machine degradation.

2. The machine’s resale value will decrease each month of operation until it reaches its scrap value at the end of its planned lifetime.

Sensitivity Analysis We next perform a sensitivity analysis to identify the effect of purchase price and operating and maintenance costs on the ORT of the drilling machine. However, because most of the factors may be interrelated, we use a multisensitivity analysis to identify the effect of multiple changes of cost factors.

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Figure 8. Effect of increasing purchase price.

Single-Variable Sensitivity Analysis

A single-variable sensitivity analysis varies one factor and keeps the others constant. The factors considered in our sensitivity analysis include machine purchase price, as well as operating and maintenance costs. Figure 8 illustrates the effect of an increasing purchase price on the ORT of the drilling machine.

Figure 8 shows that the ORT is an increasing step function of PP (based on the percentage of purchase price); the ORT remains constant for a specific range of PP increments and then increases stepwise. As an example, if the purchase price increases from 1 to 4%, the ORT is constant. This means that the ORT increases stepwise at specific PP percentage increments; that is, 5, 12, 19, 26, 34, and 42%.

Figure 9 illustrates the effect of decreasing machine operating cost (based on the percentage of operating cost) on the ORT. It is obvious that when the machine’s operating cost decreases, the ORT will increase stepwise, although it remains constant within a specific range of decreasing OC. This means that the ORT is not sensitive to a specific range of operating cost reductions and will increase stepwise at a specific OC rate of reduction; that is, 15 and 34%.

Figure 10 illustrates the effect of decreasing machine maintenance costs on the ORT of the drilling machine. When the maintenance cost decreases, the ORT will increase as a step function of MC reduction. In addition, note that the ORT increases at reduction steps of MC—that is, 7, 15, 23, 30, 36, 42, and 48%—and remains constant within these steps.

Figures 8, 9, and 10 show that with increasing purchase price and decreasing operating and maintenance costs, the ORT of a new model of this machine will increase stepwise at a

Figure 9. Effect of decreasing operating cost.

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Figure 10. Effect of decreasing maintenance cost.

specific percentage of these factors. This may occur because there is a significant effect of these factors on the total ownership cost at these specific percentages of increasing factor of purchase price (IFPP), reduction factor of operating cost (RFOC), and reduction factor of maintenance cost (RFMC).

Multivariable Sensitivity Analysis

To increase our understanding of the correlation of input and output variables in the optimization model, a multisensitivity analysis was performed considering three different cases. MATLAB software was used to enable a variation of the three factors, IFPP, RFMC and RFOC, to show their effects on the ORT of the drilling machine. In all three cases, the purchase price increases while the operating and maintenance costs decrease. Case 1 represents the effect of decreasing machine maintenance costs while increasing purchase price and decreasing operating costs at different percentages at the same time. Figure 11 shows the correlation between decreasing machine maintenance cost and increasing purchase price for a given 15% reduction in the cost of operation. As the figure shows, decreasing maintenance cost while increasing purchase price has a positive effect on increasing the machine’s optimal replacement time.

Case 2 studies the effect of increasing machine purchase price while simultaneously decreasing the maintenance cost at a given percentage of operating cost reduction. Case 3 considers the effect of decreasing the machine’s operating cost while decreasing maintenance cost at a given percentage of increasing purchase price.

Figure 11. Effect of RFMC and IFPP for a given 15% RFOC.

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From the results of the three cases (Figure 11), it is clear that the ORT of a new model of this machine will increase as a result of increasing its purchase price, decreasing the maintenance cost, and decreasing the cost of operation at different percentages. The explanation is that a new model of this machine is assumed to be more reliable than the old ones. This will lead to a decreased failure rate in a new model of this machine, which, in turn, reduces the maintenance cost. In addition, a new model of this machine is more productive than an old one; thus, it will finish the same job in less time. This will decrease the energy consumption of a new model of this machine, which leads to a reduction in the operating cost of it.

Regression Analysis Our regression analysis of the ORT results obtained from the previous three cases uses Minitab (Minitlab Inc., State College, PA) software and the least squares method. The ORT of a new model of drilling machine is modeled as a linear function of IFPP, RFOC, and RFMC. IFPP is defined as the percentage increment on the machine’s purchase price. RFOC is the percentage reduction in the machine’s operating cost, and RFMC is the percentage reduction in the machine’s maintenance cost. The regression analysis results in the following mathematical model:

ORT = 114 + 0.133 × IFPP + 0.0682 × RFOC + 0.164 × RFMC, (13)

where IFPP = 5%, RFOC = 6%, and RFMC = 12%. The ORT resulting from the regression model is calculated as follows:

ORT = 114 + 0.133 × 5 + 0.0682 × 6 + 0.164 × 12 = 117 (month).

The ORT obtained from the regression model is compatible with the values shown in Figure 11. The other values of IFPP, RFOC, and RFMC can be calculated and checked as well.

The high R2 adjusted value obtained from regression analysis, R2 (adj.) = 98.6%, indicates that the ORT of a new model of this machine depends linearly on the IFPP, RFOC, and RFMC. Following the results of the sensitivity and regression analyses, the rank of the factors affecting the ORT of a new vintage model of a drilling machine is as follows:

1. The reduction in maintenance cost. 2. The increase in purchase price. 3. The reduction in operating cost.

Many studies have considered reliability, maintainability, and optimum replacement decisions; readers are referred to, for example, Ahmadi and Kumar (2011), Wijaya et al. (2012) and Dandotiya and Lundberg (2012) for further studies in the recent literature.

Graphical User Interface

During the study, we noticed that the user company is not always able to go through the process introduced here. Therefore, to facilitate the decision-making process and to enhance the company’s ability to make the right decision at the right time, we developed a graphical user interface (GUI) to compute the ORT. The proposed GUI is designed to enable checking of the effect of changing any of the factors; that is, IFPP, RFOC, or RFMC. Figure 12 represents the GUI for case 1.

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Figure 12. Graphical user interface.

The selected input factors appear on the left side of Figure 12; the program calculates the ORT of the machine according to the selected input. The generated fields shown on the right of the figure represent the ORT values, calculated after applying the proposed optimization model. A plot representing the ORT trend appears in the figure’s central column. From this, decision makers can determine the best time economically to buy a new machine. They can choose one of three factors: purchase price, operating cost, or maintenance cost. They can determine its effect on the ORT by observing the plot on the interface. This method also provides decision makers with useful information if they are negotiating with manufacturers over the purchase price of a new model of this machine.

Concluding Remarks This article presents a comprehensive and practical approach that can be used to provide the optimal replacement time of an underground mining drilling machine. The following conclusions can be derived from this study:

1. Although many other models require reliability and failure data to identify the optimum replacement age, the approach presented herein is based on financial data on the purchase price, operating and maintenance costs, and the machine’s resale value. This makes it very practical for industries.

2. According to the results obtained from the optimization curve, the absolute ORT of the drilling machine at the case study’s mine is 115 months of operation. However, the ORT has a practical range of 110 to 122 months, during which the total ownership cost remains almost constant. This means that the company has the flexibility to make replacements within the optimum replacement age range; that is, 12 months. Therefore, there is no fixed date or age at which the TOCvalue is minimum. In general, a range of months provides the minimum TOCvalue.

3. The results of the sensitivity analysis indicate that increasing the purchase price and decreasing the operating and maintenance costs have a positive effect on increasing the ORT.

4. The results of the regression analysis show that the ORT of the new machine depends linearly on its IFPP, RFOC, and RFMC. These results confirm the computation and the results of the sensitivity analysis.

5. The results of regression analysis show that the reduction in maintenance cost has the largest impact on the ORT, followed by the increase of purchase price and

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reduction of operating cost. Hence, the manufacturer must make a greater effort to improve the reliability and maintainability of the drilling machine to reduce the costs associated with maintenance and to increase the ORT. However, a detailed RAMS analysis is required to identify the weakest points of the machine from reliability, maintainability and supportability points of views.

6. Economists at the user company can easily use the GUI to estimate the ORT of a new machine and see the behavior of its ORT at IFPP, RFOC, and RFMC. These factors will provide a clear view of the ORT of the new machine. Knowing this will help the user company determine when to buy a new machine and assist them in any negotiations with the manufacturer over the purchase price.

Acknowledgments The people at Boliden AB and Atlas Copco who helped in this research are gratefully acknowledged. The authors also thank Behzad Ghodrati for his help. My sincerest gratitude is extended to the reviewers and the editor of this journal for the valuable comments that I received from them, which helped to improve this article.

Funding The authors thank Atlas Copco for their financial support.

Nomenclature a Purchase price percentage at first day of operation (%) BV1 Machine’s value at first day of operation (cu) LCc Labor cost for corrective maintenance (cu) LCp Labor cost for preventive maintenance (cu) M Number of replacement cycles S(i) Resale value (cu) SPc Spare part cost for corrective maintenance (cu) SPp Spear part cost for preventive maintenance (cu) T Planned lifetime (month) TOCvalue Total ownership cost multiplied by number of replacement cycles (cu)

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tions, 38(5), 409–419. Hartman, J. C. and Tan, C. H. (2014) Equipment replacement analysis: a literature review and

directions for future research. The Engineering Economist, 59(2), 136–153. Hritonenko, N. (2005) Optimization analysis of a nonlinear integral model with applications to

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Journal of Operations Research Letters, 36(5), 565–568. Hritonenko, N. and Yatsenko, Y. (2009) Integral equation of optimal replacement: analysis and

algorithms. Journal of Applied Mathematical Modelling, 33(6), 2737–2747. Jardine, A. and Tsang, A. (2006) Maintenance, replacement, and reliability theory and application.

Taylor & Francis Group, New York. Karri, T. (2007) Timing of capacity change: models for capital intensive industry. Lappeenranta

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Biographical Sketches Hussan Al-Chalabi received a B.Sc.Eng. degree in mechanical engineering from Mosul University, Iraq, in 1994 and an M.Sc degree in mechanical engineering in thermal power from Mosul University, Iraq, in 2008. Then he joined the Department of Mechanical Engineering at Mosul University as a lecturer. In 2011, he joined the Division of Operation, Maintenance and Acoustics at Lulea University of Technology as a doctoral student.

Jan Lundberg is Professor of Machine Elements at Lulea University of Technology and also Professor in Operation & Maintenance with a focus on product development. During 1983–2000, his research concerned engineering design in the field of machine elements in industrial environments.

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During 2000–2006, his research concerned industrial design, ergonomics, and related problems as cultural aspects of design and modern tools for effective industrial design in industrial environments. Since 2006 his research is completely focused on maintenance issues including methods for measuring failure sources, how to design out maintenance, and how to design for easy maintenance.

Alireza Ahmadi is an assistant professor in the Division of Operation and Maintenance Engineering, Lulea University of Technology (LTU), Sweden. He received his Ph.D. degree in operation and maintenance engineering in 2010. Alireza has more than 10 years of experience in civil aviation maintenance as a licensed engineer and production planning manager. His research topic is related to the application of RAMS and maintenance optimization.

Adam Jonsson is a senior lecturer in the Department of Engineering Sciences and Mathematics, Lulea University of Technology, Sweden. He received his Ph.D. in statistics in 2008. Jonsson’s research is in applied probability and social welfare economics.

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PAPER III

Economic lifetime prediction of a mining drilling machine using an artificial neural network

Al-Chalabi, H., Ahmadzadeh, F., Lundberg, J., Ghodrati, B., 2014. Economic lifetime prediction of a mining drilling machine using an artificial neural network. Published in the International Journal of Mining, Reclamation and Environment, 28(5), 311-322. http://dx.doi.org/10.1080/17480930.2014.942519

Economic lifetime prediction of a mining drilling machine using anartificial neural network

Hussan Al-Chalabia,b*, Farzaneh Ahmadzadehc, Jan Lundberga and Behzad Ghodratia

aDivision of Operation, Maintenance and Acoustics, Luleå University of Technology, Luleå,Sweden; bMechanical Engineering Department, College of Engineering, University of Mosul,Mosul, Iraq; cDivision of Product Realization, Mälardalen University, Eskilstuna, Sweden

(Received 15 June 2014; accepted 4 July 2014)

This study develops models for predicting the economic lifetime of drillingmachines used in mining. It uses three cases, each represented by a MATLAB code,to develop an optimisation model. The resulting ORT is fed as input to an artificialneural network (ANN) and the results translated into a relatively simple equation.The study finds that increasing the purchase price and decreasing the operating andmaintenance costs will increase a machine’s ORT linearly. Decreased maintenancecost has the largest impact on ORT, followed by increased purchase price anddecreased operating cost. The ANN method gives a series of basic weight andresponse functions which can be made available to any engineer without the use ofcomplicated software. It also helps decision-makers determine the best time econom-ically to replace an old machine with a new one; thus, it can be extended to moregeneral applications in the mining industry.

Keywords: artificial neural network; decision support system; mining drillingmachine; optimisation model; replacement time

1. Introduction

Mining is a large, integrated, automated and complex industry; having safe, reliableand cost-effective production is a strategic necessity if a company is to meet customerrequirements and gain a competitive advantage globally. Mining industries are underconstant pressure to improve their production performance at minimum cost. On theone hand, they need more reliable capital equipment with higher performance capabili-ties; on the other hand, these are more expensive.

Drilling machines are a key element of mining production, especially in the mineralextracting process (see Figure 1). These machines are subject to degradation throughouttheir operating life; this reduces production rates, with a resulting negative economiceffect. In addition, because drilling machines are used in underground mines, they aresubjected to a harsh working environment, thereby accelerating degradation. A keyquestion for mining companies is when to replace the drilling machines to minimisecost and maximise profit.

As operating and maintenance costs are the main contributing factors to the totalcost, researchers concerned with cost optimisation are especially interested in the opti-mum replacement time of production and repairable equipment, defined as the time at

*Corresponding author. Email: [email protected]

© 2014 The Author(s). Published by Taylor & Francis.This is an Open Access article. Non-commercial re-use, distribution, and reproduction in any medium, provided the originalwork is properly attributed, cited, and is not altered, transformed, or built upon in any way, is permitted. The moral rights ofthe named author(s) have been asserted.

International Journal of Mining, Reclamation and Environment, 2014Vol. 28, No. 5, 311–322, http://dx.doi.org/10.1080/17480930.2014.942519

which the total cost is minimised [1]. For example, Ahmadi and Kumar [2] developeda cost rate function to identify the optimum interval and frequency of inspection andrestoration of an aircraft’s repairable but ageing components whose failures are hidden.Wijaya et al. [3] proposed a robust-optimum multi-attribute age-based replacement pol-icy. A model for estimating the lifetime of mill liners was developed by Dandotiya andLundberg [4] based on the properties of the ore used. Their proposed lifetime model iscombined with a replacement interval model to determine the optimum replacementinterval for the mill liners; it considers process parameters of multiple ore types.

Some researchers have considered the optimal lifetime of capital equipment usingeconomic theories and vintage capital models, represented mathematically by non-linearVolterra integral equations with unknown limits of integration [5–8]. Others have usedthe theory of dynamic programming to consider technological changes under finite andinfinite time horizons [9–12]. For instance, Yatsenko and Hritonenko [13] studied thelifetime optimisation of capital equipment using integral models; they designed a gen-eral investigation framework for optimal control of the models. Hartman and Murphy[14] suggested a dynamic programming approach to the finite time-horizon equipmentreplacement problem with stationary cost. Their model considers the relationshipbetween the infinite time-horizon solution (continuous replacement of equipment at theend of its economic lifetime) and the finite time-horizon solution. Hritonenko andYatsenko [15] constructed a computational algorithm to solve a nonlinear integral equa-tion; the solution helps determine the optimal policy of equipment replacement giventhe technological advances. Finally, Kärri [16] considered the optimal replacement timeof an old machine by modelling the costs of the old machine with simple linear func-tions. The resulting optimisation model minimises the machine cost and maximises theprofit. It can handle capacity expansion and replacement situations.

The artificial neural network (ANN) has been widely touted as solving many fore-casting and maintenance decision modelling problems. For example, Gebraeel et al.[17] proposed a set of neural network models using exponential approximations to esti-mate the remaining life of thrust ball bearings in real time. Later, Wu et al. [18] devel-oped an integrated neural network-based decision support system for predictivemaintenance of rotational equipment. The integrated system is platform-independent

Figure 1. Drilling machine.


and is aimed at minimising the expected cost per unit operational time. Jafar et al. [19]used an application of ANN to model the failure rate and estimate the optimal replace-ment time for individual pipes in an urban water distribution system.

Other researchers have studied the remaining life predictions of various componentsusing ANN [20–22]. For example, Ahmadzadeh and Lundberg [23] developed a methodwhich predicts the remaining useful life of grinding mill liners. Using this method,there is no need to stop the mill, enter it and measure the liners’ wear to make appro-priate maintenance decisions, leading to enormous monetary savings.

Although many studies have estimated the optimal lifetime of equipment consider-ing the possibility of technological change, more practical methods of ORT predictionare required. It is well known that ANNs are able to model easily any type of paramet-ric or non-parametric process and automatically transform the input data into optimaland accurate outputs, in this case, the ORT of a drilling machine. In addition, using aneural network gives a clear picture of the relative importance of the input variablesand suggests how variations in inputs will affect the ORT. Finally, because the neuralnetwork can be represented by a series of basic weight and response functions, theresults can be made available to any engineer without the need for complicatedsoftware.

The present study develops an ANN-based optimisation model using available costdata to estimate the ORT of a drilling machine. The available cost data are the machinepurchase price, maintenance costs and operating costs. The production loss cost ofmachine downtime is not considered due to the availability of a spare drilling machinein the case study. The overall goal of model development is to minimise costs in themining industry.

2. Data collection

Four years of cost data were collected in a Maximo computerised maintenance manage-ment system. Since drilling is not a continuous process, the operating cost can be esti-mated by considering the utilisation of the machine. Data include correctivemaintenance costs (CM), preventive maintenance costs (PM) and repair time. The cor-rective and preventive maintenance costs comprise spare parts costs (SP) and labourcosts (LC), calculated as real costs without inflation.

3. Optimal replacement time prediction using ANN

ANNs can perform nonlinear modelling without prior information and are able to learncomplex relationships between inputs and outputs; the process is also fast. One of thefirst successful applications of ANNs in forecasting was reported by Zhang et al. [24];these researchers designed a feedforward ANN to accurately simulate a chaotic series.In general, feedforward ANNs trained with the back propagation algorithm have beenfound to perform better than classical autoregressive models for trend prediction in anonlinear time series [25,26].

In this study, ANN is applied to find nonlinear or linear relationships between inputs(costs) and outputs (ORT) for a drilling machine. The proposed ANN model combinesmulti-layer perceptions with the back-propagation Levenberg-Marquardt algorithm. Infunction approximation problems, this algorithm is considered to have the fastestconvergence and is one of the most powerful learning algorithms [25,27].

International Journal of Mining, Reclamation and Environment 313

The analyses are based on three cases, increasing purchase price (IPP), decreasingoperating cost (DOC) and decreasing maintenance cost (DMC), each represented by aMATLAB code. The resulting ORT is fed as input to ANN and the results translatedinto a relatively simple equation. The equation is transformed to an Excel spreadsheetto make ORT estimation quick and easy for any engineer to apply.

As noted above, the proposed model has three inputs: the increased purchase price(IPP (%)), decreased operating cost (DOC (%)) and decreased maintenance cost (DMC(%)). A hidden layer with three neurons and a nonlinear transfer function allows thenetwork to learn nonlinear and linear relationships between input and output variables.The number of neurons in the output layer is constrained to one, as the output onlyrequires one parameter, in this case, the ORT of the drilling machine.

The number and size of layers between network inputs and the output layer aredetermined by testing several combinations of numbers of layers and various numbersof neurons in each layer. Each of the selected combinations is tested with several differ-ent initial conditions to guarantee the proposed model is the best solution. The structureof the optimal ANN model is shown in Figure 2.

4. Calculation of the ANN inputs

The optimal value for costs is required to obtain the ORT using ANN, so the followingoptimisation model is developed to find the replacement time (RT) that minimises thetotal cost value (TCvalue), as shown in Equation (6). The term ‘total cost value’ isdefined as the summation of the machine purchase price (PP), operating cost (OC),maintenance cost (MC) and resale value S (t) over a long period, with replacementsoccurring at intervals of n periods. Therefore,

MC ¼ CM þ PM (1)

CM ¼ SPc þ LCc (2)

PM ¼ SPp þ LCp (3)

S tð Þ ¼ PP � a� 1� Drð Þt t ¼ 1; 2; 3; . . .; 120 ðmonthÞ (4)

Figure 2. Optimal structure of ANN model.


where a represents the percentage that is multiplied by the machine purchase price torepresent the machine’s value on the first day of use. During discussions, a group ofexperts agreed the machine’s purchase price decreases by 10% at this time. The depre-ciation rate that allows for full depreciation by the end of the planned lifetime of themachine is modelled by Equation (5) [28]:

Dr ¼ 1� SV

BV1

� �1L

(5)

TCvalue ¼ PP þXRTk¼1

MCk þ OCk

" #� S tð Þ

( )� N

" #(6)

where

N ¼ T

RT(7)

MATLABTMTM software is used to enable a variation of the parameter RT of Equation(6) for the optimisation time horizon in order to identify the ORT of a drilling machinethat minimisesTCvalue. The results show that the lowest possible TCvaluecan be achievedby replacing the machine every 96 months.

When MATLAB codes are used to identify the effect of IPP, DOC and DMC onthe optimal age of replacement, in all cases, the purchase price increases while theoperating and maintenance costs decrease (e.g. Figure 3). Case one represents the effectof IPP from (1–50)% with DOC and DMC at different percentages. Case two repre-sents the effect of DOC from (1–50)% with DMC and IPP at different percentages.Case three represents the effect of DMC from (1–50)%, with IPP and DOC at differentpercentages. For greater clarity, part of case three is selected (Figure 3) to show thesimultaneous production of (1–50)% DMC and 7% DOC and IPP at different percent-ages. For this case alone, 400 different input data for ANN are considered. The proce-dure is repeated for all cases, producing 6150 data-sets.

The produced data-sets (6150 data) from these codes are treated as inputs for theproposed ANN model to predict the ORT of the drilling machine at any percentage ofIPP or DMC and DOC.

Figure 3. Producing 400 input data for ANN as part of case three.


5. Training and testing the proposed ANN model

Pre-processing data by scaling improves the training of the neural network. To avoid aslow rate of learning, specifically near the end points of the output range (due to theproperty of the sigmoid function, which is asymptotic to values 0 and 1), the input andoutput data are scaled between the interval 0.1 and 0.9 [29]. It should be noted thatany new input data should be scaled before being presented to the network and the cor-responding predicted values should be un-scaled before use [30]. The linear scalingequation is expressed by:

Xs ¼ 0:8

D

� �X þ 0:9� 0:8Xmax

D

� �(8)

where Xs represents the scaled value of input variables and X represents the un-scaledvalue of input variables. The input variables are IPP, DOC and DMC. Equation (8) isused here for an IPP, DOC and DMC between minimum increasing or decreasing percent-age 1% (Xmin) and maximum increasing or decreasing percentage 50% (Xmax), such that

D ¼ Xmax � Xmin (9)

From the 6150 scaled data, 90% are used in the training of the neural network; seeFigure 4. The model shown in Figure 4 has very high values of R2 = 0.9962 for ANN.However, as also shown in the figure, the neural network model yields outputs veryclose to the desired targets with high accuracy.

After the training is completed, the network is tested for its learning and generalisationcapabilities. Its learning ability is tested by examining its ability to produce outputs forthe set of inputs (seen data) used in the training phase. Its generalisation ability is testedby investigating its ability to respond to the input sets (unseen data) not included in thetraining process; thus, 10% are used for tests with the obtained network (Figure 5). Asevident in Figure 5, the model has very high values of R2 = 0.99653 for ANN. However,the neural network model also yields outputs very close to the desired targets with highlevels of certainty.

Figure 4. Learning capability: Output of the proposed ANN for seen data.


6. Results and discussion

The proposed ANN model is used to design a formula to calculate the ORT of a drillingmachine. The structure of the optimal ANN model is shown in Figure 2; its connectionweights and threshold levels are summarised in Table 1.

The equation length depends on the number of nodes in the hidden layer. Adoptingthree nodes gives an accuracy of 99%. The small number of connection weights of theneural network enables the ANN model to be translated into a relatively simple formula,in which the predicted ORT can be expressed as follows:

ORTs ¼ 1

1þ e� h7þ w4:7

11þe�x1ð Þþ w5:7

11þe�x2ð Þþ w6:7

11þe�x3ð Þ

n o (10)

where ORTs represents the scaled ORT derived from the ANN model, θj represents theoutput threshold and wij represents the weight from node i in the hidden layer to node jin the output layer. Hence,

x1 ¼ h4 þ w4:1 � IPP þ w4:2 � DOC þ w4:3 � DMC (11)



Note that before using Equations (10–13), all input variables need to be scaled between0.1 and 0.9 using Equation (8). It should also be noted that the predicted ORTsobtained from Equation (10) is scaled between 0.1 and 0.9; however, in order to obtainthe actual value of ORT, it must be re-unscaled using the following formula:

Figure 5. Generalisation capability: Output of the proposed ANN for unseen data.


X ¼ XsD0:8

� �� 0:9

D0:8

� �þ Xmax (14)

Equation (14) is obtained by solving Equation (8), considering the input variable (X) asunknown and the output variable (Xs) as known. An Excel spreadsheet can be used asa substitute for fast and accurate calculation of the ORT. Equation 15 is applied to esti-mate the actual value of the ORT of the drilling machine as follows:

ORT ¼ ORTsORTmax � ORTmin

0:8

� �� 0:9

ORTmax � ORTmin

0:8

� �þ ORTmax (15)

where ORTmax and ORTmin represent the maximum and minimum values of ORTderived from the optimisation model.

6.1. Study of relative importance of input parameters

The method of partitioning weights, proposed by Garson [31] and adopted by Goh[32], is now used to determine the relative importance of the various input parameters;see Figure 6.

As evident in Figure 6, the most important parameter influencing the ORT of thedrilling machine is the DMC, followed by the IPP. The DOC has the least influence.The design for reliability and maintainability should be adapted to reduce the mainte-nance cost, thus increasing the ORT of the drilling machine.

Table 1. Weights and threshold levels for the proposed ANN.

Hidden layer nodes

wii weights from node ith input layer tonode jth hidden layer

Hidden threshold (θj)i = 1 i = 2 i = 3

j=4 −0.0648 −0.03030 −0.1297 10.4780j=5 −2.6814 −0.78166 −2.1337 0.18142j=6 −1.2496 −0.8258 −2.3112 5.023854Output layer nodes wij weights from node ith hidden layer to

node jth output layerOutput threshold (θj)

i = 4 i = 5 i = 6j=7 7.795 −5.3591 −10.801 2.919081

Figure 6. Relative importance of the variables affecting the ORT of the drilling machine.


6.2. Study of variables influencing the ORT of the drilling machine

With applying Equation 15, the ORT of drilling machine is calculated for differentvariables, including IPP, DOC and DMC, to see the influence of these variables. TheDMC is the most important factor, as shown in Figure 6. Generally, the ORT increaseswith a decrease in maintenance cost, compatible with the results shown in Figures 7 and 8.

6.3. Effect of increasing machine purchase price

As Figure 6 shows, the second most influential variable on the ORT is the machine’sIPP. The correlation of IPP and DMC when the cost of operating is reduced by 25% isshown in Figure 7. As is evident, both IPP and DMC have a positive effect on increas-ing the ORT.

Figure 7. Effect of IPP and DMC for 25% OC decrease.

Figure 8. Effect of DOC and DMC for 25% PP increase.


6.4. Effect of decreasing machine operating cost

Figure 8 shows the correlation of DOC and DMC for a given 25% increase in PP.Clearly, both DOC and DMC have a positive effect on increasing the ORT.

7. Conclusions

The main advantage of the proposed neural network model is its ability to produceacceptable results: the correlation between input and output variables is very high andthe accuracy is more than 99%. Moreover, the model’s performance is very consistentfor data used for training (seen) and testing (unseen). Therefore, it is very effective inestimating and predicting the ORT of a mining drilling machine. Further, because theANN model uses a series of basic weight and response functions, it does not requireexpensive and sophisticated equipment for data recording and analysis.

The predicted ORT from the ANN model indicates that increasing the purchase priceand decreasing the operating and maintenance costs will increase the ORT of the dril-ling machine. Results also show that the maintenance cost has the largest impact on theORT, followed by the purchase price and operating cost. Hence, the manufacturer mustmake a greater effort to improve the reliability and maintainability of the drillingmachine to reduce the costs associated with maintenance and increase the ORT.

This study presents a comprehensive and very practical approach using ANN whichcan provide the economic replacement time of a drilling machine with higher levels ofcertainty. It helps engineers and decision-makers determine when it is best to economi-cally replace an old machine with a new one without using complicated software.Because of its effectiveness and simplicity, the model can be extended to more generalapplications in the mining industry. The dynamic nature of the proposed methodologyopens up future studies of economic lifetime prediction for different categories ofmining equipment.

Notations

ORT optimal replacement time (months)ANN artificial neural networkCM corrective maintenance cost (CU)CU currency unitPM preventive maintenance cost (CU)IPP increase purchase price (%)DOC decrease operating cost (%)DMC decrease maintenance cost (%)RT replacement time (months)TCvalue total cost value (CU)PP purchase price (CU)OC operating cost (CU)MC maintenance cost (CU)S(t) resale value (CU)SPc spare part cost for corrective maintenance (CU)LCc labour cost for corrective maintenance (CU)SPp spare part cost for preventive maintenance (CU)LCp labour cost for preventive maintenance (CU)


Dr depreciation ratet machine lifetime (months)SV scrap value (CU)BV1 booking value on first day of operation (CU)L planned lifetime (month)N number of machine replacementsT optimisation time horizon (120 months)Xs scaled value of input variablesΔ difference between maximum and minimum values of input variablesX unscaled value of input variablesXmax maximum value of input variablesXmin minimum value of input variablesθj output thresholdwij weight from node i in the hidden layer to node j in the output layer

AcknowledgementThe authors would like to thank Boliden AB, Atlas Copco for supporting this research. Specialappreciation is extended to the operating and maintenance engineers at Boliden AB for sharingtheir valuable knowledge, experience and data to improve this study. The authors would also liketo thank Majid Al-Gburi, Alireza Ahmadi for their help.

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PAPER IV

Model for economic replacement time of mining production rigs including redundant rig costs

Al-Chalabi, H., Lundberg, J., Al-Gburi, M., Ahmadi, A., Ghodrati, B., 2014. Model for economic replacement time of mining production rigs including redundant rig costs. Submitted for publication in the Journal of Quality in Maintenance Engineering.

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Model for economic replacement time of mining production rigs including redundant rig costs

Hussan Al-Chalabia,b, Jan Lundberga, Majid Al-Gburic, Alireza Ahmadia and Behzad Ghodratia

a Division of Operation, Maintenance and Acoustics. Luleå University of Technology. Luleå, Sweden. b Mechanical Engineering Department, College of Engineering, University of Mosul, Mosul, Iraq.

c Division of Structural Engineering and Production. Luleå University of Technology. Luleå, Sweden.

Abstract Purpose - This paper presents a practical model to determine the economic replacement time (ERT) of production machines. The objective is to minimise the total cost of capital equipment, where total cost includes acquisition, operating, maintenance costs and costs related to the machine’s downtime. The costs related to the machine’s downtime are represented by the costs of using a redundant machine. Design/methodology/approach - Four years of cost data are collected. Data is analysed, practical optimisation model is developed and regression analysis is done to estimate the drilling rigs ERT. The artificial neural network (ANN) technique is used to identify the effect of factors influencing the ERT of the drilling rigs. Findings - The results show that the redundant rig cost has the largest impact on ERT, followed by acquisition, maintenance and operating costs. The study also finds that increasing redundant costs per hour have a negative effect on ERT, while decreases in other costs have a positive effect. Regression analysis shows a linear relationship between the cost factors and ERT. Practical implications - The proposed approach can be used by the decision maker in determining the economic replacement time of production machines which used in mining industry. Originality/value - The research proposed in this paper provides and develops an optimisation model for economic replacement time of mining machines. This research also identifies and explains the factors that have the largest impact on the production machine’s ERT. This model for estimating the ERT has never been studied on mining drilling rigs. Keywords Decision support model, Life cycle cost, Optimisation, Replacement time Paper type Research paper

Abbreviations ERT Economical replacement

time (month) CiLC Labour cost for corrective maintenance (cu)

ANN Artificial neural network ViSP Spare part value (cu)

IAC Increasing acquisition cost (%)

LiSP Spare part logistic cost (cu)

DOC Decreasing operating cost (%)

rt Repair time (h)

DMC Decreasing maintenance cost (%)

ln Number of labours

DRC Decreasing redundant rig cost (%)

lc Man hour cost (cu /h)

RT Replacement time (month) PiSP Spare part cost for preventive maintenance

(cu) ERTs Scaled economical

replacement time PiLC Labour cost for preventive maintenance (cu)

TC Total cost (cu) iRC Redundant rig cost (cu)

2

cu Currency unit TiP Using time of redundant rig (h)

AC Acquisition cost (cu) RiC Redundant rig cost per hour (cu/h)

i Time period (month) RiT Logistic time for redundant rig (h)

iMC Maintenance cost (cu)

FiT Restoring time of faulty rig to operation (h)

iOC Operating cost (cu)

1iT Moving time of redundant rig from its location to production point (h)

iCO Compensation cost (cu)

2iT Moving time of redundant rig from production point to its original location (h)

iS Resale value (cu)

MiT Moving time of faulty rig from production point to workshop (h)

r Discount rate (%) WiT Time in workshop of faulty rig (h)

N Number of replacement cycles

LiT Moving time of repaired rig from workshop to production point (h)

iCM Corrective maintenance cost

(cu) dit Delay time in workshop of faulty rig before

repair (h)

iPM Preventive maintenance cost (cu)

rit Actual repair time of faulty rig (h)

CiSP Spare part cost for corrective maintenance (cu)

Iit Idle time in workshop of faulty rig after repair (h)

1. Introduction Industrial companies, or more speci cally, mining companies put huge funds, often millions of dollars into their annual budgets to purchase heavy mobile equipment (HME) such as drilling rigs, scaling rigs, wheel dozers, wheel loaders, dump trucks, etc. Given the enormous costs of acquiring, operating, and maintaining their HME, it is important for companies to optimise their replacement and procurement strategies (Richardson et al., 2013). As the HME operating hour’s rise, so too do the maintenance and operating costs. At some point in the equipment’s life span, these costs will be too high; it will no longer be economically viable to continue using the old equipment, so it should be replaced (Verheyen, 1979). An essential economic consideration in industrial companies is to find a model that can discriminate this point (i.e. the point at which the equipment replacement time is expected to yield minimal life-cycle cost). Obviously, for mining companies, one of the most important decisions is determining the ERT of capital equipment; this can be done with the help of life-cycle cost (LCC) analysis. The main reason for the increasing use of the life cycle costing concept for HME is that at some point the operating and maintenance costs will exceed their acquisition costs.

In general, LCC is determined by summing up all potential costs associated with equipment over its life time (i.e. the total of ownership and acquisition costs). It is well known that the value of expenditure today costs more than the same expenditure next year because of the decreasing “time value of money”. In this study we use a discount rate to account for the time value of money. To compare costs incurred at different times, we must shift expenditure to a reference point in time. Thus, we calculate the present equivalent value of the costs by considering the discount rate factor. 1.1 Literature review Standard models for ERT decisions contain an estimation of the discounted costs by minimising the total cost of the equipment. The assumption of these models is that equipment will be replaced at the end of its economic lifetime by a continuous sequence of identical equipment (Hartman and Tan, 2014). Bellman (1955) developed the first optimal asset replacement model for variable lifetime of assets. Wagner (1975) offered dynamic

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programming formulation for the equipment replacement problem in which the state of the system is the time period and the decision at each period is to keep the equipment for N periods. His formulation has been extended by researchers to deal with realities of technological changes, for example, see (Oakford et al., 1984; Bean et al., 1985; Hartman and Rogers, 2006; Hritonenko and Yatsenko, 2008). These authors assumed a finite horizon in their approaches to the problem of equipment replacement under non-stationary costs. In 1976, Elton and Gruber showed that an equal life policy was optimal on an infinite horizon under technological changes. In contrast, Hartman and Murphy (2006) studied an asset replacement problem for a stationary finite horizon; they illustrated how a bound on the number of times an asset is retained at its economic life can be obtained, thus suggesting it is optimal to replace the asset at its economic lifetime.

Dynamic programming models have been utilised in real cases of calculating equipment replacement time because of the important uncertainties associated with life cycle costs (Richardson et al., 2013). The net present value of all life cycle costs associated with an in nite sequence of equipment life cycles has also been used to make equipment replacement decisions (Bethuyne, 1998; Scarf and Bouamra, 1999; Hartman, 2005; Yatsenko and Hritonenko, 2005). Other researchers have used different equipment replacement models to analyse a variety of equipment, such as forklifts, buses, and aircraft (Eilon et al., 1966; Keles and Hartman, 2004; Bazargan and Hartman, 2012). Although Tanchoco and Leung (1987) found replacement decisions could be influenced by capacity considerations, others have noted that technological changes can encourage decision makers to utilise equipment beyond its economic life (Cheevaprawatdomrong and Smith, 2003). Still other researchers have considered reliability, maintainability and optimum replacement decisions; readers are referred to, e.g., Wijaya et al. (2012); Dandotiya and Lundberg, (2012), Golmakani and Pouresmaeeli, (2014) and Al-Chalabi et al. (2014) for further discussion of the recent literature. 1.2 Aim of the study Blanchard et al., 1995 mentioned that the costs associated with equipment support, operation and maintenance can account for more than 75% of the equipment LCC. Thus, careful consideration must be given to estimating the capital equipment ownership costs. Given the importance of operating and maintenance (O&M) costs and in order to assure a specific level of availability, industries must consider using redundant equipment to overcome production loss when a failure occurs. Another way to ensure production performance is to make a pooling agreement with other companies, renting commonly owned equipment to ensure that failed equipment will be replaced by serviceable machines. But any of these compensation strategies cost money for the operator. In the assessment of equipment replacement time, the compensation cost (i.e. redundant rig cost in this case study) associated with a machine should be taken into account. Thus, the aim of this paper is to develop a model to determine the economic replacement time of production equipment, in this case, a drilling rig, considering redundant rig cost. In this paper, we also consider the relative importance of other cost factors on the rig’s ERT; these factors are the equipment acquisition, operating, maintenance and redundant rig costs. Finally, in the model, we consider the time value of money by using a discount rate.

2. Case study In this study, our model of ERT for production machines is implemented in a case study of a drilling rig used in mining industry. Our case study was selected from the mining sector, as maintenance costs in this sector account for 20-30% of the total cost of production (Kumar, 1994). Kumar (1994) also maintained that to achieve optimal performance from the capital intensive mining equipment and systems, mine operators must ensure world-class maintenance in line with other advanced industries. The drilling rig is selected as a case study for several

4

reasons: drilling is the first step in a typical mining cycle and thus is extremely important (see figure 1); the drilling rigs are heavily loaded; the rigs’ acquisition and maintenance costs are high; finally, drilling represents a critical bottleneck for production.

Figure 1. Typical underground mining cycle

3. Model formulation The ERT of capital equipment is the age that minimises its total cost. In this study, the total cost is represented by acquisition (initial or investment) cost and ownership cost. The ownership cost includes operating and maintenance costs and compensation cost. All repairable systems wear over time; consequently, the ownership cost increases and the resale value decreases.

In this study, the ERT is defined as the value of the replacement time (RT) which minimises the total discounted cost, calculated on a monthly basis as follows:

1 12

1

1

RT

i i i i ii

Min TC Min AC MC OC CO S Nr

(1)

The objective of the proposed model (i.e. Eq. 1) is to determine the ERT which minimises the total discounted cost over the rig’s planned lifetime. We assume the replacement rig (i.e. the new rig) has the same performance and cost as the existing rig (i.e. identical rigs). The number of replacement cycles during the planned lifetime is represented as:

TN

RT (2)

where T and RT represent the planned lifetime and the replacement time (in months) respectively.

3.1 Maintenance cost Maintenance can be defined as any work used to keep something in an appropriate condition. Maintenance can corrective or preventive. Corrective maintenance refers to actions which take place after an unscheduled breakdown to return an item to a specified condition. Preventive maintenance refers to regularly scheduled actions planned to keep an item in the desired condition. The maintenance cost can be labelled as a summation of the materials and labour expense required to keep an item in suitable working condition. In this study, due to the company’s regulations, all costs data are encoded and expressed as currency unit (cu). The maintenance cost is represented as follows:

i i iMC CM PM (3)

where iCM and iPM represent corrective and preventive maintenance cost (cu) respectively.

1. Drilling

2. Charging

3. Blasting

4. Loading

5. Scaling

6. Bolting

5

i Ci CiCM SP LC (4)

where CiSP and CiLC represent spare part and labour costs for corrective maintenance (cu) respectively.

Vi LiCiSP SP SP (5)

where ViSP and LiSP are spare part value and spare part logistic costs (cu) respectively.

Ci l lLC rt n c (6)

where rt represents repair time (h), ln is number of repairs and lc is man hour cost (cu /h).

i Pi PiPM SP LC (7)

where PiSP and PiLC represent spare part and labour costs for preventive maintenance (cu) respectively.

Pi Vi LiSP SP SP (8)

Pi l lLC rt n c (9)

3.2 Operating cost Data on O&M costs were collected over four years and stored in the MAXIMO computerised maintenance management system (CMMS). Operating cost can be defined as recurring costs for efficiently operating the equipment, in our case study, a drilling rig. The operating costs include administration, energy, fuel, indirect overhead costs, consumables like steel rods, operator’s salary, a figure given to us by experts at the collaborating company. In CMMS, the cost data are recorded based on calendar time. Since drilling is not a continuous process, the operating cost is estimated by considering the utilisation of the drilling rig. The company plans to use the machine for 120 months. Therefore, extrapolation for the operating and maintenance cost data was done. Figures 2 and 3 illustrate the maintenance and operating costs determined by the data extrapolation.

Figure 2. Maintenance cost Figure 3. Operating cost

In Figures 2 and 3, the dots represent the real historical data for maintenance and operating costs. Curve fitting is done by using Table curve 2D software to show the behaviour of these costs before and after the time when data were collected. Note that the fitting would be better if more data were available for a time period of more than four years. This software uses the least squares method to find a robust (maximum likelihood) optimisation for nonlinear fitting. It is worth mentioning that the drilling machine in this case study has no multi-level preventive maintenance programme. In addition, it was new at the start of utilisation. This is the main reason why the maintenance cost is quite low in earlier months. The history shows that when the maintenance costs started growing, the user company began to keep track of cost data by using CMMS. The equation “Lorentzian Cumulative” of extrapolation for expected maintenance cost obtained by the software is expressed as

6

arctan2

a x bY

c (10)

where Y represents the expected maintenance cost, a=217.42, b=112.37, c=13.63, r2 (adj.) = 0.97 and X represents the time (1, 2, 3, 4,…, n months). Similarly, the equation “Lorentzian Cumulative” of extrapolation for expected operating cost is expressed as

arctan2

a x bY

c (11)

where Y represents the expected operating cost, a=79.89, b=109.2, c=13.85, r2 (adj.) = 0.91 and X represents the time (1, 2, 3, 4,…, n months).

As the figures show, the operating and maintenance costs increase over time. In fact, the number of failures increases with time and/or the machine consumes more energy due to machine degradation.

3.3 Compensation cost In the present study, we focus on the compensation cost by using a redundant rig cost as one of the critical factors affecting the ERT. Mining companies, for example, lose a large amount of money each year from lost production which, in turn, is due to the production equipment’s downtime. In fact, this may be the most important factor affecting the ERT of production machines. In this study, we assume when a drilling rig fails and is sent to the workshop for maintenance, to continue production without stops, the company uses a redundant rig which has the same performance as the existing faulty rig. Since in the mining industry, downtime in production is almost zero, the compensation cost in this case represents the cost of using a redundant rig. In this study, the experts at the collaborating mine classified the rig’s failures in three categories as follows:

1. Failures fixed by maintenance team at the workshop. 2. Failures fixed by maintenance team at the production point (mining room). 3. Failures fixed by operators at the production point (mining room).

Note: we obtained information on the drilling process and maintenance of drilling rigs by talking with experts at the user company (U) and manufacturing company (M). Detailed information, such as experience in years and work position of the experts, appears in table 1.

Table 1. Description of expertise of the experts used in the present study

Current position at companies (U) and (M) Expert field and experience (# years) Maintenance Engineer for open pit and underground mines (U)

Maintenance of mobile and fixed equipment’s (23)

Mine production Foreman (U) Underground drill machines (30) Mine production Manager (U) Mine drilling and production (15) Mine production Planner (U) Mine production planning (22) Maintenance Supervisor (U) Maintenance of mobile equipment’s (30) Maintenance Manager (U) Maintenance of mobile equipment’s (26) Mine production Manager (U) Mine drilling and production (32) Maintenance Foreman (U) Maintenance of mobile equipment’s (25) Maintenance Engineer for fixed equipment (U) Maintenance of fixed equipment’s (10) Global Service Operations Manager (M) Maintenance of equipment (20) Design Engineer–Underground Drill Rigs (M) Designing underground equipment (10) Global Fleet Manager Marketing and business management (8) Vice President Service Operations (M) Parts and Service Business management and

Maintenance of mobile equipment (18) Regional business-Europe and product line manager-Rental (M)

Project management and business management (10)

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The compensation cost based on a category one failure of the rig is modelled as follows:

i iCO RC (12)

where iRC represents redundant rig cost (cu).

i Ti RiRC P C (13)

where TiP and RiC represent the used time of the redundant rig (h) and redundant rig cost per hour (cu/h) respectively.

Ti Ri FiP T T (14)

where RiT and FiT represent the logistic time of the redundant rig (h) and the time to restore the faulty rig to operation (h) respectively.

1 2Ri i iT T T (15)

where 1iT and 2iT represent the time to move the redundant rig from its location to the production point and the return time from the production point to its original location (h) respectively.

Fi Mi Wi LiT T T T (16)

where MiT , WiT and LiT represent for the time to move the faulty rig from the production point to the workshop (h), time in workshop (h) and return time after repair (from workshop to production point) (h) respectively.

riWi IidiT t t t (17)

where dit , rit and Iit represent delay time in workshop before repair (h), actual repair time

(h) and idle time in workshop after repair (h) respectively. Figure 4 illustrates the time the redundant rig is used due to a category one failure in the existing rig:

Figure 4. Time the redundant rig is used due to a category one rig failure

Table 2 represents the clarifications of symbols A, B, C, D, E and G of Figure 2.

Table 2. Clarifications of symbols A, B, C, D, E and G of Figure 2

Symbol Clarification A Production stops and a redundant rig starts moving from its location B Production starts with a redundant rig and a faulty rig starts moving to the workshop C Faulty rig enters the workshop D Faulty rig exits the workshop E Faulty rig starts work after repair and redundant rig starts moving to its original location G Redundant rig arrives at the original location

C

1iT

MiT di

trit

Iit

D

LiT

WiT

FiT

TiP

A B

2iT

E

G

E

G

Time

8

Since the moving speed inside the underground mine is limited to low speed, we assume the moving time of the maintenance team from the workshop to the production point is almost equal to the moving time of the faulty rig from a production point to the same workshop. Thus, the using time a redundant rig is used after a category two rig failure is modelled as follows:

riTi Ri MiP T T t (18)

Note: as the failures fixed by operators are classified as small failures and take only a short time, the mining company does not use a redundant rig in the third category of failures. Table 3 illustrates the minimum and maximum time values given by the maintenance expert in the collaborating mine; these are used in the model.

Table 3. Minimum and maximum time values (minute) used in the model

Time Minimum Maximum Moving time of faulty rig from production point to workshop ( MiT ) 30 60

Delay time in workshop before repair ( dit ) 30 90

Idle time in workshop after repair ( Iit ) 30 60

We assume the moving time of the redundant rig 1iT is equal to the moving time of the faulty

rig MiT . It is worth mentioning that the time values dit , Iit , MiT , LiT , 1iT and 2iT are

randomly generated by using MATLAB code, since this type of data is not available from the collaborating mine. We use a discount rate of 10% to consider the “time value of money” following the suggestions of the collaborating mining company.

3.4 Resale value A Matheson formula (declining balance depreciation model) was used to estimate the resale value of the rig after each month of operation. In this method, a fixed percentage of the book value at the beginning of the month represents the monthly depreciation of the rig. The rig resale value is its value if/when the firm wants to sell it at any time during its lifetime. The resale value denoted by iS is calculated by using the following model (Luderer et al., 2010; Eschenbach, 2010; Dhillon, 2010):

1 (1 )iiS BV Dr (19)

where “i” represents a time (number of months), i=1, 2, 3, …120 planed lifetime, 1BV and

Dr represent the rig value on the first day of operation and depreciation rate respectively. In addition,

1BV AC A (20)

where “A” represents the percentage of decrease multiplied by the rig acquisition cost to represent the rig value on the first day of use. During discussions with us, company experts agreed that the rig acquisition cost decreases by 10% on the first day of use (i.e. A=0.9). In this study, the rig acquisition cost is 6000 (cu). Hence, the rig value on the first day of use is 5400 (cu).

The depreciation rate that allows for full depreciation by the end of the planned lifetime of the rig is modelled by the following formula (Luderer et al., 2010, Dhillon, 2010):

1

1

1TSVDr

BV (21)

9

where T and SV represent the planned lifetime of the rig, 120 months, and rig scrap value respectively. The rig is assumed to reach scrap value after 10 years. The rig resale value is calculated by:

(1 )iiS AC A Dr (22)

The declining balance depreciation model is suitable in our case study because this model writes off the cost of the rig early in its lifespan at an accelerated rate and at correspondingly lower monthly charges close to the end of its lifespan. It also considers the rig to be more productive when it is new, and its productivity declines continuously due to rig aging. Therefore, in the early years of its lifespan, a rig will generate more revenue than in later years. In accountancy, depreciation refers to two aspects of the same concept. The first is the decrease in the rig value. The second is the systematic allocation of the capital cost of the rig over its lifespan. The scrap value is an estimate of the value of the equipment at the time it is sold or disposed of. In our case study, 50 (cu) is assumed to be the scrap value of the rig at the end of its planned lifetime, a figure given to us by company experts.

4. Results and discussion We tested the model for ERT on a case study of a drilling rig. This rig is manufactured by Atlas Copco Company and used by Boliden mineral AB Company in Sweden. MATLABTM software is used to enable a variation of the replacement time (RT) of Eq. (1) which minimises the total cost.

Figure 5 shows the optimisation curve and the ERT of our case study at a redundant rig cost per hour equal to 1 (cu/h).

Figure 5. Economic replacement time of the drilling rig

The results show the lowest possible total cost can be achieved by replacing the rig at 104 months of its planned lifetime. A decision to replace the rig before or after its ERT incurs greater costs for the user company. The use of a lower replacement age (i.e. less than 104 months) incurs higher costs due to the high investment cost. Meanwhile, if the lifetime of the rig exceeds its ERT (i.e. more than 104 months), losses will increase for two reasons:

1. The O&M and redundant rig costs increase when the operating hours increase due to rig degradation.

2. The rig resale value will decrease for each month of operation until it reaches its scrap value by the end of its planned lifetime.

As Figure 5 also shows, there is a range 97-109 (months) when the minimum total cost can be still achieved in practice. In this study, we call it the economic replacement range. Finding the

0 20 40 60 80 100 120 140 160 180 200 220 2400

5

10

15

18x 104 Economic replacement time of a drilling rig

Replacement time RT (month)

Tot

al c

ost (

cu)

Redundant rig cost = 1 (cu/h)

ERT=104 months

10

economic replacement range is an important result of our study, as it can help decision makers in their planning. To show the effect of the redundant rig cost per hour ( RiC ) in the ERT of our case study, we change the values of the redundant rig cost per hour from 1 to 6 (cu/h). Figure 6 shows the result.

Figure 6. Effect of the redundant rig cost per hour on the ERT of the drilling rig

It is clear from figure 6 that increasing the RiC (cu/h) has a negative effect on the ERT of the drilling rig. To determine the effect of other factors on the ERT, we perform a sensitivity analysis on rig acquisition, operating, maintenance and redundant rig costs (cu) using the ANN technique. Four MATLAB codes for six cases of RiC (1-6 cu/h) are used to identify the effect of increased acquisition cost (IAC), decreased operating cost (DOC), decreased maintenance cost (DMC) and decreased redundant rig cost (DRC). The resulting ERT from these four codes is fed as input to the ANN and the results translated into a relatively simple equation to estimate the ERT of the drilling rig. The method of partitioning weights, proposed by (Garson, 1991) and adopted by (Goh, 1995), is used to determine the relative importance of the various input factors; see figure 7.

Figure 7. Relative importance of input factors on ERT of drilling rig

0

30000

60000

90000

120000

150000

180000

0 20 40 60 80 100 120 140 160 180 200 220 240

Tot

al c

ost

(cu

)


Effect of redundant cost per hour

CRi=1 (cu/h). ERT=104 month CRi=2 (cu/h). ERT 94 month



CRi = Redundant rig cost per hour

0

10

20

30

40

50

60

1 2 3 4 5 6IAC (cu) 33,1 33,1 31,7 34,6 30,5 32,8DOC (cu) 14,1 11,9 8,0 9,4 10,3 3,2DMC (cu) 20,4 15,0 17,7 10,1 12,3 6,2DRC (cu) 32,2 39,8 42,3 45,7 46,6 57,5

Rel

ativ

e 1m

por

tan

ce (

%)

11

As evident in figure 7, the most important factor is the redundant rig cost, followed by the acquisition, maintenance and operating costs. Therefore, a design for reliability and maintainability should be adapted to reduce the downtime and maintenance costs of the drilling rig. As mentioned earlier, four MATLAB codes are used to identify the effect of IAC, DOC, DMC and DRC on the ERT of drilling rig. We choose the case where RiC = 1 (cu/h) to demonstrate the effect of these factors on the ERT. Figure 8 shows the correlation of DRC and IAC for a given 25% DOC and DMC. Figure 9 shows the correlation of DRC and DMC for a given 25% IAC and DOC. Figure 10 shows the correlation of DRC and DOC for a given 25% IAC and DMC.

Figure 8. Correlation of DRC and IAC for a given 25% DOC and DMC

Figure 9. Correlation of DRC and DMC for a given 25% IAC and DOC

Figure 10. Correlation of DRC and DOC for a given 25% IAC and DMC

As figures 8-10 show, DRC, IAC, DMC and DOC have a positive effect on the ERT of the drilling rig, but it is also evident that DRC has a more positive effect, followed by IAC, DMC and ROC.

0 5 10 15 20 25 30 35 40 45 50110

112

114

116

118

120

122

124

126

ER

T (

mon

th)


IAC=10%IAC=20%IAC=30%IAC=40%IAC=50%

DOC=25%DMC=25%

0 5 10 15 20 25 30 35 40 45 50

112

114

116

118

120

122

124

126

ER

T (

mon

th)


DMC=10%DMC=20%DMC=30%DMC=40%DMC=50%

IAC=25%DOC=25%

0 5 10 15 20 25 30 35 40 45 50

114

116

118

120

122

124

ER

T (

mon

th)


DOC=10%DOC=20%DOC=30%DOC=40%DOC=50%

IAC=25%DMC=25%

12

4.1 Training and testing the proposed ANN model Artificial neural networks can perform nonlinear modelling without prior information and are able to learn complex relationships between inputs and outputs; the process is also fast (Ahmadzadeh and Lundberg, 2013). Our ANN analyses are based on the results obtained from the four cases represented by four MATLAB codes, as explained above. The resulting ERTs from these codes are fed as inputs to ANN and the results translated into a relatively simple equation which can be used to estimate the overall ERT of the drilling rig. The equation is transformed to an Excel spread-sheet to make ERT estimation quick and easy for any engineer to apply. As mentioned earlier, the proposed model has four inputs: IAC, DOC, DMC and DRC. A hidden layer with three neurons and a nonlinear transfer function allows the network to learn nonlinear and linear relationships between input and output variables. The number of neurons in the output layer is constrained to one, as the output only requires one parameter, in this case, the ERT of the drilling rig. 90 % of the data are used in training and 10 % in testing the neural network; see figures 11 and 12. The model shown in figures 11 and 12 have very high values of R = 99 % for ANN. However, as also shown in the figures, the neural network model yields outputs very close to the desired targets with a high level of accuracy.

Figure 11. Training capability Figure 12. Testing capability

The proposed ANN model is used to construct a formula to calculate the ERT of our case study. The formula is transformed to an Excel spreadsheet to make ERT estimation quick and easy for any engineer to apply. The structure of the optimal ANN model is shown in figure 13; its connection weights and threshold levels are summarised in Table 4.

Figure 13. Optimal structure of artificial neural network (ANN) model

105 110 115 120 125 130 135105

110

115

120

125

130

135

Targets T

Outp

uts

Y, L

inea

r Fit: Y

=(1

)T+

(-0.

44)



105 110 115 120 125 130 135105

110

115

120

125

130

135

Targets T

Outp

uts

Y, L

inea

r Fit: Y

=(1

)T+

(-0.

81)



IAC (%)

DOC (%)

DRC (%)

DMC (%)Output(ERT)

Inpu

t fac

tors

13

Table 4. Weights and threshold levels of proposed ANN

Hidden layer nodes

wij

weights from node i th input layer to node j

th hidden layer

Hidden threshold

( j) i=1 i=2 i=3 i=4

j=5 0.085 0.089 -0.03 0.108 -8.776 j=6 3.006 0.379 1.441 1.784 -1.120 j=7 1.416 0.452 1.509 1.876 -5.001

Output layer nodes

wij weights from node i th hidden layer

to node j th output layer

Output Threshold

( j) i=5 i=6 i=7

j=8 4.679 3.410 5.376 -3.581

Pre-processing data by scaling improves the training of the neural network. To avoid a slow rate of learning, specifically near the end points of the output range (due to the property of the sigmoid function, which is asymptotic to values 0 and 1), the input and output data are scaled in the interval between 0.1 and 0.9 (Oreta, 2004). It should be noted that any new input data should be scaled before being presented to the network and the corresponding predicted values should be un-scaled before use (Yousif, 2007). The linear scaling equation is expressed by:

max0.80.8 0.9sXX X (23)

where Xs represents the scaled value of input factors and X represents the un-scaled value of input factors. As it used in MATLAB code for neural networks, Eq. (23) is used here for an IAC, DOC, DMC and DRC between a minimum increasing or decreasing percentage of 1% (Xmin) and a maximum increasing or decreasing percentage of 50% (Xmax). This results in:

max minX X (24)

The equation length depends on the number of nodes in the hidden layer. Adopting three nodes gives an accuracy of 99%. The small number of connection weights of the neural network enables the ANN model to be translated into a relatively simple formula, in which the predicted ERT can be expressed as follows:

8 5:8 6:8 7:81 2 31 1 1

1 1 1

1

1 expx x x

sw w w

e e e

ERT (25)

where ERTs represents the scaled ERT derived from the ANN model, j represents the output threshold and wij represents the weight from node i in the hidden layer to node j in the output layer. Hence,

51 5:1 5:2 5:3 5:4x w IAC w DOC w DMC w DRC (26)

2 6 6:1 6:2 6:3 6:4x w IAC w DOC w DMC w DRC (27)

73 7:1 7:2 7:3 7:4x w IAC w DOC w DMC w DRC (28)

To obtain the actual value of ERT, the predicted ERTs must be re-un-scaled using the following formula:

14

max0.90.8 0.8sX X X (29)

Equation (29) is obtained by solving Equation (23), considering the input variable (X) as unknown and the output variable (Xs) as known. An Excel spread-sheet can be used as a substitute for fast and accurate calculation of the ERT of the drilling rig. Eq. 30 is applied to estimate the actual value of the ERT of the drilling rig as follows:

max min max minmax0.9

0.8 0.8s

ERT ERT ERT ERTERT ERT ERT (30)

where ERTmax and ERTmin represent the maximum and minimum values of ERT respectively derived from the optimisation model.

In this paper, it is worth to mention that the artificial neural network techniques were used for the following two main reasons.

One aim was to help the engineers and decision makers in the user company to estimate the ERT of new drilling rigs without needing to use complicated software. Another aim was to determine the relative importance of factors which were used in the optimization model and which would affect the ERT of new drilling rigs. The factors which have the highest impact on the ERT of new rigs should be prioritized in the development process of new drilling rigs.

4.2 Regression analysis The regression analysis of the results obtained from the above four MATLAB codes uses Minitab software and the least squares method. ERT is modelled as a linear function of IAC, DOC, DMC and DRC. The regression analysis results in the following mathematical model:

104 0.19 0.04 0.14 0.17ERT IAC DOC DMC DRC (31)

It is evident from the regression analysis for this particular case (i.e. RiC = 1 cu/h) that the IAC has the greatest effect on the ERT of the drilling rig, followed by DRC, DMC and DOC, but at the same time, RiC (cu/h) increases from 2 to 6 for other cases. Ultimately, the DRC has the largest effect on ERT in our case study; see figure 7. The R-squared value obtained from the regression analysis, R2 (adj) = 99 %, indicates that the ERT of the drilling rig depends linearly on the factors of IAC, DOC, DMC and DRC, supporting the results obtained in the sensitivity analysis.

5. Conclusions This paper presents a model for the economical replacement time of production machines. Although the problem has been solved previously by other researchers using different models, our model can more readily examine the relationship between the factors affecting the ERT of production machines, especially the cost of using a redundant rig. The model is found to be a good choice for estimating the ERT in a case study of the drilling rig used in underground mines in Sweden, and it can be extended to other production capital assets in other industries. In our case study, the results of the sensitivity analysis show that the redundant equipment cost has the highest impact on the ERT followed by equipment acquisition, maintenance and operating costs. The results of the sensitivity analysis also indicate that decreasing the operating, maintenance and redundant rig costs have a positive effect on increasing the ERT. The results obtained from the optimisation curves show that increasing the redundant rig cost per hour has a negative effect on the ERT. Therefore, improving the reliability and maintainability of production equipment is essential to reduce their downtime and maintenance costs.The

15

absolute ERT of the drilling rig when RiC = 1 cu/h is 104 months. However, the ERT has a range of 97 to 109 months, during which period the total cost remains almost constant. This means the user company has the flexibility of making replacements within the optimum replacement age range (12 months). The results of the regression analysis show that the ERT of the new equipment depends linearly on its acquisition, operating, maintenance and redundant rig costs. These results confirm the results of the sensitivity analysis. In summation, this study presents a comprehensive and very practical approach which can determine the ERT of any mobile equipment with higher levels of certainty by using ANN analysis.

Acknowledgment The authors would like to thank Atlas Copco and Boliden mineral AB, for supporting this research. Special appreciation is extended to the experts at Boliden mineral AB and Atlas Copco for sharing their valuable knowledge and experience. The authors would like also to thank Arne Vesterberg at Boliden mineral AB and Andreas Nordbrandt at Atlas Copco for them supports. The authors would like also to thank for the support of CAMM (Centre of Advanced Mining & Metallurgy) project in this research work. My sincerest gratitude is extended to the reviewers and the editor of this journal for the valuable comments that we received from them, which helped to improve this article.

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