annual reliability and ma

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Cost-Optimized Scheduled Maintenance Interval for Reliability-Centered Maintenance

William R. Wessels MEVATEC Corporation Huntsville

Key Words: Reliability-centered maintenance, Scheduled maintenance interval, Predictive maintenance, Reliability,Maintainability, Availability

SUMMARY AND CONCLUSIONS

Implementation of a reliability-centered maintenance programis based on performance of proactive maintenance actions thatserves to preserve system functionality. Predictivemaintenance is a recognized proactive maintenance action thathas been underutilized due to quantitative complexity and tothe lack of a constraint that defined an optimum scheduledmaintenance interval. A cost-optimized scheduledmaintenance interval is proposed that uses costs as theconstraint and overcomes quantitative complexity by use of current computer and software technology. Combined withcondition-based monitoring the cost-optimized scheduledmaintenance interval enables an organization that owns andoperates fleets of assets to implement a comprehensivereliability-centered maintenance program.

NOTATION

A..................System availabilityt ...................The independent variable time................... The scheduled maintenance interval in time units

R SMI(t) ......... System reliability with a scheduled maintenanceintervalR SYS( )System reliability at time equals the scheduledmaintenance intervalk ..................The number of scheduled maintenance intervalsthat have occurred since the implementation of an RCM

programR SYS(t-k ) .... System reliability at time greater than the kthscheduled maintenance interval .................. The mean-time-between-failure, MTBF/mean-time-between-replacement, MTBR MMT P .........The predicted mean maintenance time for thesystemFCP ...............The predicted corrective maintenance actions per

thousand hours for the systemMCPT ............The mean predicted corrective maintenance timefor the systemFPP ...............The predicted predictive maintenance actions per thousand hours for the systemMPPT ............The mean predicted predictive maintenance timefor the systemCMP ..............The predicted total maintenance costCCP ...............The predicted mean corrective maintenance cost

CPP ...............The predicted mean predictive maintenance cost

INTRODUCTION

In 1975 mine maintenance foremen wondered why machineryand equipment corrective repairs could not be scheduled rather than occur randomly, often at the worst possible time, or in theworst possible situations. This was certainly not the first

occasion that those responsible for maintaining machinery andequipment pondered on the concept of predictive maintenanceas a panacea to the disruptions in operations resulting fromunplanned corrective maintenance actions. There is a stronglikelihood that a predictive maintenance concept wasarticulated in the earliest days of the industrial revolution asthe advent of mechanical and electrical machinery andequipment replaced manual labor, hand tools and simpleanimal drawn vehicles as the primary mechanisms for

production of goods and services. Therefore we can observethat the predictive maintenance concept is not new. Yet

predictive maintenance has remained an elusive concept toimplement.

RCM Theory

In their books on reliability-centered maintenanceSmith and Moubray identified proactive maintenance as a keycomponent of a reliability-centered maintenance program, toinclude predictive maintenance, condition-based maintenance,and scheduled inspections. Both authors emphasize thatreliability-centered maintenance is the analysis, design, andimplementation of proactive maintenance procedures thatserve to preserve system functionality [1][2].

System functionality can be measured in terms of system dependability, which is, in turn, characterized bysystem availability and system reliability. The availability of a system is the probability that a system is in an operable state

when its functionality is required or scheduled. The reliabilityof a system is the probability that a system will function to its

performance specifications during the time that it is expectedto operate. The dependability of a system is the product of theavailability and reliability. The parameter of reliability is thefailure rate, or its inverse, the mean-time-between-failure/mean-time-between-replacement, MTBF/MTBR. The

parameters of availability are the mean-time-between-maintenance-actions, MTBMA, and maintenance time. The

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MTBMA is a function of MTBF so it can be said that bothreliability and availability are dependent upon the failure rate[3].

The term failure rate begs the question, failure of what? When a system is not capable of functioning when itsis scheduled to function, or ceases functioning during itsscheduled operation, the system experiences a downing eventresulting from the failure of a Lowest Replaceable Unit, LRU.This point needs to be emphasized; systems do not fail, LRUsfail and only LRUs. An LRU is defined by the organization.An LRU is that design level of the system that is removed toeither be replaced or repaired. Replaced and discarded partsare logically identified as an LRU. An example includes ahydraulic hose on a mine haul truck, or an electronic circuit

board in a radar cabinet. Parts that are removed and repaired,or repaired in place, often are sources of identity confusion.Where a part is removed for repair, and the repair consists of removal and replacement of internal parts, the part removedfrom the system is still identified as an LRU, and the partsremoved and replaced within it are identified as shopReplaceable Units, SRU. But if the same part is repaired in

place the parts removed and replaced are the LRUs. Anexample is a hydraulic pump. An organization that respondsto the failure of a hydraulic pump on the system by removingand replacing it will identify the hydraulic pump as an LRU.Then removing and replacing internal parts, SRUs, repairs thefailed hydraulic pump. But an organization that responds tothe failure of a hydraulic pump on the system by removingand replacing a failed internal part, or parts, leaving thehydraulic pump in place during the maintenance procedureswill not identify the hydraulic pump as an LRU. The internal

parts would be identified as LRUs [4][5].The conclusion is drawn that predictive maintenance

must be applied to those LRUs that have failure modes, effectsand consequences that result in a system downing event.Smith and Moubray appear to differ on the practicality of

predictive maintenance. Smith suggests that the quantitativeanalysis is too difficult. Moubray provides a theoreticaldiscussion of the quantitative analysis with a brief coverage of mean-time-between-failure, MTBF, or mean-time-between-replacement, MTBR. It is indeed fitting that a book onreliability-centered maintenance would acknowledge theimportance of a parameter of system reliability as one of itscriteria. Moubray introduces the concept of the P-F curve asan analytical approach to the design of a reliability-centeredmaintenance program (Fig 1 P-F Curve) [2].

t

P

F

f(t)

Figure 1 - P - F Curve

Moubray shows that an LRU has an output function,as for any process point, that has an expected value over timeuntil failure of the LRU is imminent. At some point in timefollowing the initiation of degradation towards failure the

prediction of failure can be determined, P, on the P-F curve.The time after the prediction time, P, when the LRU outputfunction drops below an acceptable level and a failure stateoccurs, is the failure point, F. Moubray observes that

proactive maintenance by inspection or condition-basedmonitoring will preserve system functionality when the P-Fduration is long enough to detect the degradation and repair the LRU prior to an unscheduled LRU failure. An example of condition-based monitoring that identifies the prediction point,P, prior to the failure point, F, is the water temperature gaugeon an automobile. As the gauge shows increases the operator is alerted to the potential for overheating in adequate time toavert loss of system functionality of the car.

Moubray agrees that predictive maintenance isrequired to preserve system functionality when the P-Fduration is too brief to allow proactive maintenance to preventthe LRU failure. In such cases condition-based monitoringand inspection are not effective. Consider again theautomobile. Most models include tachometers that show theengine RPM as one is driving. One can suggest that thisgauge is a condition-based monitor for the engine, but shouldthe tachometer show the RPM drop to zero as the car is beingdriven the operator is not provided sufficient time to preservesystem functionality. In this example preservation of systemfunctionality can only be achieved through predictivemaintenance.

SMI Theory

Predictive maintenance is defined as the calculationof the duration that an LRU can be expected to operate absentcommon causes of failure and the replacement of the LRU ator prior to that duration of use. This maintenance action goesagainst the nature of maintenance managers and practitioners

because it calls for the replacement of an LRU that has not yetfailed; often an LRU that shows no evidence of degradation.This is the quantitative approach Smith eschewed andMoubray avoided; not so Dr. Alessandro Birolini. Dr. Birolinideveloped the quantitative approach to describe the impact of the scheduled maintenance interval, SMI, on the reliability,MTBF, and availability of an LRU and the system. Theexpression for the system reliability using Dr. Birolinis SMIis presented in equation 1 [6].

( ) ( ) k t R Rt R SYS k SYS SMI =)( (1)

The scheduled maintenance interval, , is theduration between repair or replacement maintenance actions.The number of intervals expected over the life of the system,k, is an integer value. The time since the last scheduledmaintenance interval is the independent variable, time, t,minus the cumulative time preceding the last scheduledmaintenance interval, k . The comparison between thereliability function and MTBF for a system without a

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scheduled maintenance interval and the reliability functionand MTBF for a system with a scheduled maintenance intervalis shown in Figure 2 Reliability and MTBF [5].

0

1.0

t

RSYS (t)

RSYS ( )kRSYS (t-k )

( ) ( )dt k t R R SYS k

SYS SMI =

( )= dt t RSYS RTF

2 3 4 5 6 7 8 9

R(t)

Figure 2 - Reliability and MTBF

It is graphically evident that the reliability for asystem that implements a scheduled maintenance interval inwhich LRUs are replaced and repaired prior to failure issignificantly improved over the reliability for a system that isallowed to run to failure. Since the MTBF, , is the indefiniteintegral of the reliability function it is also evident that theMTBF for a system that implements a scheduled maintenanceinterval is significantly improved over the MTBF for a systemwhich is allowed to run to failure. But the calculation of theMTBF for a system that implements a scheduled maintenanceinterval is impeded by the discontinuity of the reliabilityexpression. Indeed solving for the MTBF tends to support

Smiths contention that the quantitative approach to predictivemaintenance is too difficult for practical application. But theadvent of software programs that perform integral operationsallows the calculation of the MTBF.

The comparison between the availability function for a system without a scheduled maintenance interval and theavailability function for a system with a scheduledmaintenance interval is shown in Figure 3 Availability [5].

0

1.0

t 2 3 4 5 6 7 8 9

Ao

Figure 3 Availability

Theoretically the availability of a system with a scheduledmaintenance interval declines in a small magnitude from onescheduled maintenance activity to the next and as the systemis repeatedly restored the availability returns to unity. Thesmall magnitude of the decreases in availability over time

between scheduled maintenance intervals is justified by theassumption that the decrease for any interval is comparable tothe decrease from the condition of the system when new. Theavailability over time for a system that does not implement ascheduled maintenance interval shows a gradual decline inoverall availability of the system. The increases in availabilityfollowing each maintenance action does not reach unity

because the system is not restored by the maintenance action.Therefore only the LRU that failed is removed and replacedwhile othe LRUs that are in a near failure state remain in

place.

Limitations

Birolini did not show the approach to calculate theappropriate scheduled maintenance interval for a system.Instead Birolini allows the calculation of the impact on asystem for a specified scheduled maintenance interval. Butthe question that demands an answer is, what is the optimumscheduled maintenance interval for a system? The reliability,maintainability and availability engineering and analysisdisciplines of reliability-centered maintenance cannot alone

provide the answer. The reason is that the reliability,maintainability and availability engineering and analysis for asystem is not constrained. This fact is illustrated by anexample. Assume a system is run to failure and LRUs areremoved and replaced when each causes a downing event. Letthat system have a mean-time-between-failure of 200 hours.If one introduces a scheduled maintenance interval at 160hours the theory shows that the reliability will improve,resulting in an improvement in the system MTBF andavailability. But if the scheduled maintenance interval wasimplemented at 120 hours the resulting system reliability,MTBF and availability would be more improved than for 160hours. So too would a scheduled maintenance interval of 80hours be more improved than for 120 hours. One couldextend this iterative approach until the scheduled maintenanceinterval is 0 hours, that is, maintenance is performedcontinuously. The reliability and availability would eachequal unity and the MTBF would be infinite. Unfortunatelythere would also be absolutely no utility derived from thesystem [4].

COST-OPTIMIZED SCHEDULED MAINTENANCE

INTERVALIn a business application the system in the preceding

example would have capital and operating costs and provideno productivity. Returning to the prime objective of reliability-centered maintenance, to preserve systemfunctionality, the needed constraint to characterize anoptimum scheduled maintenance interval can be determined.System functionaly serves the owner of a system with ameasure of utility. In a business environment the utility of a

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system can be measured by either productivity measured inmarginal revenue or costs measured in marginal expenses. Ina not-for-profit environment the utillity of a system can bemeasured by cost avoidance or costs minimalization. Sincereliability-centered maintenance describes a business activitythat is characterized as a cost center it is logical to define thecost function for a system as the constraint needed tocharacterize a scheduled maintenance interval for a system.

The cost function for a system is dependent on directand indirect expenses and capital costs. Direct costs includedirect labor expenses, direct materials expenses, and directoverhead expenses allocated to the implementation of allmaintenance activities performed to preserve systemfunctionality. Indirect costs include indirect labor expenses,indirect materials expenses, and indirect overhead expensesallocated to the sustainment of a maintenance infrastructure.Capital costs include the depreciation expenses for the capitalcost of the system and the cost of money for the capitalinvestmant amount. There is another cost associated with theloss of functionality of a system lost opportunity. When asystem is not functioning when it is scheduled to operate itaccumulates lost productivity that can be characterized asunrealized marginal revenue. Lost opportunity is marginalrevenue that is lost by the inability to operate the system

because of a failure of an LRU.Combining reliability, maintainability and

availability parameters of reliability-centered maintenancewith a systems cost functions yields the cost-optimizedscheduled maintenance interval. The theoretical primaryfeature of the cost-optimized schedule maintinance interval isthat an organization will realize the optimum costs of operation of the system that correspond to the optimummarginal revenue from operation of the system yielding theoptimum marginal profit. This objective serves as themotivation for maintenance managers and practitioners tochange the way they think about maintenance procedures and

practices and to embrace reliability-centered maintenance.Specifically, the cost-optimized scheduled maintenanceinterval should encourage maintenance managers and

practitioners to remove and replace LRUs that have yet to failin order to prevent random failures of the system. The cost-optimized scheduled maintenance interval allows themaintenance foreman of thirty years ago to plan system

breakdowns.Characterization of the cost-optimized scheduled

maintenance interval is achieved by calculation andassociation of the costs of the parameters of maintainabilitythat are realized by predictive maintenance scenarios. As thescheduled maintenance interval is allowed to vary from the

baseline MTBF (calculated for a run-to-failure maintenance policy) to zero the cost-optimized scheduled maintenanceinterval is the global solution of the system cost function.

Each value for the schedule maintenance intervaldetermines the predicted mean maintenance time which iscalculated as a function of the predicted number of correctivemaintenance actions per thousand hours, Fcp, the predictedmean corrective maintenance time, Mcpt, the predictednumber of predictive maintenance actions per thousand hours,Fpp, and the predicted mean predictive maintenance time,

Mptp. The equation for the calculation of the predicted meanmaintenance time is the weighted average of the meanmaintenance time, shown in equation 2.

ppcp

ptp ppcpt cp p F F

M F M F MMT

+

+= (2)

The logical objective for a reliability-centeredmaintenance program is to minimize the occurrences of corrective maintenance time. In an ideal reliability-centeredmaintenance environment the mean corrective maintenancetime will approach 0 hours and all maintenance time will be

predictive maintenance activities.The predicted maintenance cost, Cmp, is calculated

as a function of the predicted number of correctivemaintenance actions per thousand hours, Fcp, the predictedmean cost of corrective maintenance actions, Ccp, the

predicted number predictive maintenance actions per thousandhours, Fpp, and the predicted mean cost of the predictivemaintenance actions, Cpp. The expression for the predicted

maintenance costs is shown in equation 3.

pp ppcpcpmp C F C F C += (3)

As with the mean maintenance time the objective for a reliability-centered maintenance program is to replace thecosts for corrective maintenance with the idealized costs of

predictive maintenance. As the scheduled maintenanceinterval decreases the corrective maintenance actions per thousand hours, Fcp, is expected to decrease and the

predictive maintenance actions per thousand hours, Fpp,increases.

An assumption of reliability-centered maintenance is

that corrective maintenance costs are more than predictivemaintenance costs. An understanding of the components of these two cost categories intuitively indicates this difference.Corrective maintenance costs include hard failure of LRUsoften including destruction of the LRU and collateral damageto proximate LRUs, inconvenient location of the failure awayfrom maintenance resources, spontaneous demand for maintenance and spare parts takes more time to perform, andlost opportunity costs. Predictive maintenance costs occur

prior to hard failure preventing collateral damage to proximateLRUs. Often replaced LRUs can be repaired using rebuildkits that are less expensive than new LRUs. Scheduledmaintenance activities allow coordinated scheduling of maintenance resources minimizing total maintenance costs.

Spare parts can be stocked in time for the scheduledmaintenance actions. Predictive maintenance does not incur lost opportunity costs.

SUMMARY

Reliability-centered maintenance is an innovationthat was developed with the Boeing 474 airplane. It specifiesthe implementation of proactive maintenance condition-

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based monitoring and predictive maintenance to preservesystem functionality. While condition-based monitor technologies have flourished over the past three decades

predictive maintenance has not. Initially, the technology didnot exist to allow maintenance managers and practitioners toaccumulate the data and perform the calculations essential tothe characterization of a cost-optimized scheduledmaintenance interval for a system. Although the data hasalways been there the capability to mine that data and organizethe data in computational databases was absent until theemergence of the personal computer and database software

programs. There has also been an emergence on analyticalsoftware that can perform analysis of nonlinear, discontinuousalgorithms, to include a global evolutionary solution for thecost-optimized scheduled maintenance interval. Theeconomic competitiveness of the global marketplace demandsthat organizations utilize all business practices that serve tooptimize marginal costs. The cost-optimized scheduledmaintenance interval can serve that demand.

BIBLIOGRAPHY

1. Smith, Anthony M. (1993), Reliability-Centered Maintenance , McGraw-Hill, Inc., New York, NY.2. Moubray, John (1997), Reliability-centered Maintenance,2nd Ed ., Industrial Press, Inc., New York, NY.3. Kapur, K.C. and Lamberson, L.R. (1977), Reliability in

Engineering Design , John Wiley & Sons, New York, NY.4. Wessels, William R. [1998], Seeking an OptimalScheduled Maintenance Interval: An AnalyticalCharacterization of the Impact of Scheduled MaintenanceIntervals on the System Reliability Model, ASQ 52nd Annual Quality Congress Proceedings , pp. 484-489, Philadelphia, PA.5. Lawler, Patrick, 1993. Unpublished research and lecturenotes, U.S. Army Missile Command, Redstone Arsenal,Huntsville, AL.

6. Birolini, Alessandro, 1994. Quality and Reliability of Technical Systems , Zurich, Switzerland: Swiss FederalInstitute of Technology.

BIOGRAPHY

William R. Wessels, PhD, PE, CRE, CQEMEVATCE Corporation4940 Research DriveHuntsville, AL 35805 USA

[email protected]

Bill is a Principal Engineer employed by MEVATECCorp., in Huntsville, Alabama. He has a PhD in Industrial andSystems Engineering from the University of Alabama inHuntsville, an MBA in Decision Science from the Universityof Alabama, and a BS in Engineering from the United StatesMilitary Academy at West Point. He is a registeredProfession Engineer in Mechanical Engineering by theCommonwealth of Pennsylvania, and an ASQ CertifiedReliability Engineer and Certified Quality Engineer. Theauthor has researched and published his findings for the

prediction of failures for mining machinery, biomedicaldevices, army aviation missile weapons systems and radars,and electronics process equipment since 1975. Bill and hiswife, Tudor, live on a small farm with seven dogs, ever changing numbers of horses, donkeys, goats, geese, turkeys,chickens, and who knows how many barn cats. The beastsignore the findings of statistically rigorous algorithms, defyany statistical level of significance, behave in a random walk manner, and ridicule his expertise in analytical methodsapplied to them. Tudor finds any attempt to predict their

behavior to be a lack of common sense and a waste of time.But I continue to try.

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