taguchi concepts and applications

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Taguchi concepts and their applications in marine and offshore

safety studiesHOW SING SII * , TOM RUXTON AND JIN WANG

Taguchi concepts have been developed into an engineering method of qualityimprovement referred to as Quality Engineering in Japan and as Robust Designin the West, which is a disciplined engineering process that seeks to nd the besttrade-off of a product design. A safety optimization framework using Taguchiconcepts is proposed in this paper. An example is used to demonstrate the appli-cation of the framework in maritime safety studies. Following a brief review ofTaguchi concepts and techniques used in Robust Design, this paper discusses howthe Taguchi concepts such as quality loss function, signal-to-noise ratio,orthogonal arrays, degree of freedom and analysis of variance may be synthe-sized in maritime safety engineering studies. Brainstorming, an integral part ofthe Taguchi philosophy, is also briey discussed. Orthogonal arrays are used tostudy many parameters simultaneously with a minimum of time and resources toproduce an overall picture for more detailed safety-based design and operationaldecision-making. The signal-to-noise ratio is employed to measure quality; in thiscase, risk level. The loss function is considered as an innovative means for deter-mining the economic advantage of improving system safety or operational safety.Noise factors are considered as any uncontrollable or uncontrolled variables orany other undesired inuences. Control factors are the variables that are set by

the designers that will characterize the performance as well as safety level of asystem throughout its life cycle. The outcomes of this paper may provide thefundamental knowledge for safety analysts to utilize the Taguchi concepts andmethodologies. A hypothetical example with simple analysis techniques is usedto illustrate how the Taguchi method can be used to extract from expert judge-ments those factors the experts judge as most vital when they perform risk esti-mation for a ship with the purpose of determining insurance rates.

1. Introduction

Taguchi methods of robust experimental design have traditionally beenemployed in manufacturing settings (Roy 1990). A literature review indicates thatthere appears to be virtually no study that uses Taguchi experimental design tooptimize a safety-based decision-support study in any discipline of engineeringapplications (Sii et al. 2000a, b). This limitation can be traced, in part, to the originalintention of Dr Genchi Taguchi of using his robust experimental design to optimizeengineering processes (Roy 1990).

Beyond the original intention of Taguchi to apply his methods to manufacturingsettings, there are other reasons perceived why Taguchi methods have not been

J. ENG. DESIGN, 2001, VOL. 12, NO. 4, 331358

Received July 2001. School of Engineering & Advanced Technology, Staffordshire University, UK. School of Engineering, Liverpool John Moores University, UK.* To whom correspondence should be addressed. e-mail: [email protected]

Journal of Engineering Design

ISSN 0954-4828 print/ISSN 14661387 online 2001 Taylor & Francis Ltdhttp://www.tandf.co.uk/journals

DOI: 10.1080/0954482011008594 0


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employed at all in safety-based decision-making study. Firstly, the safety of a systemis very difcult to measure precisely or quantitatively. This induces problems in theapplication of Taguchi methods as they actually depend heavily on the accuratemeasurement of variation of quantied parameters of a process. Secondly, the

outcome of a safety-based decision-making problem is inherently much more incon-sistent in quality than its manufacturing counterpart. This is primarily due to the factthat the safety performance of a system depends largely on the operational behav-iour of the human operators. High variation in quality makes it difcult to makebona dejudgements about the system performance since Taguchi methods rely ononly a small part of the total information pertaining to variations. Finally, safety-related problems generally speaking have more unknown or imprecisely knownnoise factors associated with them compared with the manufacturing counterparts.Despite these attributes of a safety-related problem, the example given in this paperhas demonstrated that by appropriately identifying a quantitative measure of

safety, Taguchis concepts of Robust Design can be employed successfully tooptimize safety-related decision-making problems.

The classical reliability and quality theories are concerned with failures, i.e. tominimize the number of failures. However, safety requires failures to be avoidedwith a large degree of condence, not minimized. Here, the Taguchi method has adifferent approach, illustrated by the quote from Genichi Taguchi: If you wantquality measure function. Especially, the dynamic Taguchi method emphasizes thatyou must measure function and ensure that there is a sufcient margin from thenominal design specication to the functional limits (tolerance limits), given thevariations from the processes and the usage conditions and environment. Thismargin is a measure of the robustness of the design, and is measured by Taguchi indecibels. The concept is in line with the safety margin of classical mechanical designphilosophy. Safety-related failures are here dened as no function or malfunction,especially structural failures. Safety issues pertaining to deviation from normalintended operation is not considered here (a chain saw that cuts wood can just aswell cut esh). However, operational procedures are covered. It is proposed toemphasize that the methods of this paper can be used in many design trade-offsituations involving expert judgements and is therefore generally applicable, alsooutside the area of safety.

Everyone appreciates the importance of safety. In nearly all circumstances,safety is considered in the context of doing something or, more specically, in theprocess of meeting an objective. Here, safety is dened not by the risk of failures,but the probability of intended (safe) operation. Engineering safety involves broadlythree dimensions of management, engineering and operation, underpinned by thehuman factors of behaviour, decision and error. The goal for marine and offshoreoperations can be stated as follows: To be competitive in meeting the clients speci-cations with solutions that are cost-effective at an acceptable level of safety (Kuo1998).

In the context of commercial operations, competitiveness means level of prot-ability; however, in non-commercial activities, effectiveness would be more appro-priate as it has to take into account the specic objective of the activity concerned.The real challenge is that success in achieving the goal in any project is to meet allfour sets of criteria simultaneously: i.e. safety, competitiveness, specication, andcost-effectiveness. Risk is dened as the probability of undesirable event and theprobability of it occurring. Safety is the ability of an entity not to cause critical or

332 How Sing Sii, Tom Ruxton and Jin Wang


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catastrophic events, under given conditions. It is measured by the probability thatan entity will not cause critical or catastrophic events, under given conditions(Villemeur 1992).

In engineering terms, this is often referred to as a special multiple-level multiple-

variable optimization problem. Multiple-level means that each of the parameters,such as specication, comprises requirements with varying degrees of complexity.Multiple-variable implies that there is more than one variable or factor involved.Optimization aims to nd the best solution to the problem and, in this case, themost competitive solution is being sought. Existing optimization techniques can beused to solve the problem in which the relationships within each parameter andbetween each other are known and expressible in mathematical terms. However,when some of the relations are qualitative, such as those relating to human factors,the solution to optimization problems can be extremely difcult to deal with.

Stochastic uncertainty in engineering systems occurs during the design and oper-

ational processes of these systems. It arises from a lack of knowledge of the exactvalue of a design or environmental parameter due to a process beyond the controlof a designer. To be able to make design decisions, it is necessary to incorporate thisuncertainty in the design model (Zhou et al. 1992). This improves our understand-ing of the state of a design by including the performance of the product within itsenvironment.

The objective of safety analysis during the concept design stage of a largeengineering system is to provide safety-related input in the process of designing anddeveloping a feasible and acceptable system. The concept design shall comply withboth the companys requirements for a safe and economically attractive solution,together with the requirements given by the regulatory bodies. At the initial conceptdesign stages, owing to inadequate data and information with a high level of uncer-tainty, conventional approaches may not be able to model safety and cost for designand operation decision-making effectively and efciently. There has been an ever-increasing demand for cost-effective methods that reduce risk level (if not totallyeliminate!) while improving quality of the designed system. This paper contributesto this effort by extending the applicability of an old tool (Taguchi methods fordesign optimization) from manufacturing to a safety-based decision support study.A real-world example pertaining to the effects of different levels of design features

and ship owner management quality on the overall ships risk level is illustrated. Thisis used to show that the Taguchi method can be used by experts in risk estimationto prioritize and extract from expert judgements those factors the experts judge asmost important for a ship with the purpose of determining insurance rates. Thisexample has demonstrated that an unusually cost-effective tool, Taguchis robustexperimental design, hitherto employed to optimize product specications andprocess parameters in manufacturing settings, can be employed, with equal effec-tiveness, to optimize the factors that inuence safety-based decision support studies.

A great deal of engineering effort is consumed in conducting experiments toobtain information needed to guide decisions related to a particular artefact. Itwould further complicate the situation once safety is integrated into design,especially at the initial concept design stage. This is due to the typical problemsassociated with a lack of reliable safety data or a high level of uncertainty in safetydata. This is particularly true when dealing with the high level of innovative changein design and optimization of maritime and offshore engineering systems withinboth technical and economic constraints.

Taguchi concepts and their applications in marine and offshore safety 333


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Taguchis Quality Engineering and Robust Design offer a useful method toevaluate the performance of a system when uncertainty is present and to measurethe quality at the design stage. In the ensuing section, Taguchis philosophy isexplained and his method is introduced together with the techniques involved in

carrying out experiments and analysis. The principal interest of this project is tomodel quality characteristics in terms of safety into a safety-based design andoperation decision support model to provide a means for making better designdecisions.

2. The Taguchi methods and Robust Design

Delivering reliable, high-quality products and processes at low cost and in a shortdevelopment time has become the key to survival in todays global economy. Drivenby the need to compete on cost, time factor in design and performance, many

quality-conscious organizations are increasingly focusing on the optimization ofproduct design. This reects the realization that quality cannot be achieved econ-omically through inspection. Designing for quality is cheaper than trying to inspectand re-engineer it after a product hits the production oor, or after it gets to thecustomer (Gunter 1987). Thus, new philosophy, technology and advanced statisticaltools must be employed to design high-quality products at low cost.

Products have characteristics that describe their performance relative tocustomer requirements or expectations (Ross 1988). Characteristics such as cost andweight of a component or the durability of a switch concern the customer. Thequality of a product/process is measured in terms of these characteristics. Typically,the quality is also measured throughout its life cycle. The ideal quality a customercan expect is that every product delivers the target performance each time theproduct is used under all intended operating conditions and throughout its intendedlife, and that there will be no harmful side effects (Phadke 1989). The quality of aproduct is measured in terms of the total loss to society due to functional variationand harmful side effects (Taguchi 1986). The ideal quality loss is zero.

The classical Taguchi method was Off-line quality control as opposed to thethen current On-line quality control or statistical process control. Use of theTaguchi method for design came later. Since the late 1950s, Dr Genichi Taguchi has

introduced several new statistical tools and concepts of quality improvement thatdepend heavily on the statistical theory for design of experiments (Gunter 1987,Phadke 1989, Wille 1990). These methods of design optimization developed byTaguchi are referred to as Robust Design (Phadke 1989). The Robust Designmethod provides a systematic and efcient approach for nding the near-optimumcombination of design parameters so that the product is functional, exhibits a highlevel of performance, and is robust to noise factors (Bendell 1988, Phadke 1989).Noise factors are those parameters that are uncontrollable or are too expensive tocontrol.

Delivering a high-quality product at low cost is an interdisciplinary probleminvolving engineering, economics, statistics, and management (Phadke 1989). In thecost of a product, one must consider the operating cost, the manufacturing cost, andthe cost of new product development. A high-quality product has low costs in allthree categories. Robust Design is a systematic method for keeping the producerscost low while delivering a high-quality product and keeping the operating cost low.Taguchi espoused an excellent philosophy for quality control in manufacturing



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industries (Roy 1990). His philosophy is founded on three very simple and funda-mental concepts. These concepts are stated in (Roy 1990) as follows.

Quality should be designed into the product and not inspected into it. Quality is best achieved by minimizing the deviation from the target. The

product should be designed in such a way that it is immune to uncontrollableenvironmental factors (noise factors).

The cost of quality should be measured as a function of deviation from thestandard and the losses should be measured system-wide.

A leading indicator of quality is required by which one can evaluate the effect ofchanging a particular design parameter on the products performance, but also onthe variations about the nominal value (robustness). This indicator is called signal-to-noise ratio. It isolates the sensitivity of the systems performance to noise factorsand converts a set of observations into a simple number.

A product under investigation may exhibit a distribution that has a mean valuethat differs from the target value. The rst step towards improving quality is toachieve a distribution as close to the target as possible. Efciency experimentationis required to nd dependable information with minimum time and resources aboutthe design parameters (Phadke 1989).

Robust Design has been used very successfully in Japan in designing reliable,high-quality product at low cost in such areas as automobiles and consumer elec-tronics (Cullen and Hollingnum 1987, Sullivan 1987, Logothetis and Salmon 1988,Phadke 1989, Wille 1990). During the early 1980s, industries in the Western coun-

tries had begun to recognize Taguchis Robust Design methods as a simple but effec-tive approach to improving quality and reducing cost (Gunter 1987). The applicationof these methods is becoming widespread in many US and European industries.

3. The design processThe early design phase of a product or process has the greatest impact on life-

cycle cost and quality (Kackar 1985, Phadke 1989, Taguchi et al. 1989). Therefore,signicant cost savings and improvements in quality can be realized by optimizingproduct designs. The three major steps in designing a quality product are: system

design, parameter design, and tolerance design (Taguchi 1986, Bendell 1988, Phadke1989, Taguchi et al. 1989).

System design is a process of applying scientic and engineering knowledge toproduce a basic functional prototype design (Kackar 1989). The prototype modeldenes the conguration and attributes of the product undergoing analysis ordevelopment. The initial design may be functional but it may be far from optimal interms of quality and cost.

The next step, parameter design, is an investigation conducted to identify thesettings of design parameters that optimize the performance characteristic andreduce the sensitivity of engineering designs to the source of variation (noise)(Kackar 1985). Parameter design requires some form of experimentation for theevaluation of the effect of noise factors on the performance characteristic of theproduct dened by a given set of values for the design parameters. This experimen-tation aims to select the optimum levels for the controllable design parameters usingthe Robust Design method.

Experimenting with the design variables one at a time or by trial and error until



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that can be studied using that array. Note that this design reduces 81 (3 4) congur-ations to 9. Some of the commonly used orthogonal arrays are shown in gure 2(Bendell 1988). As gure 2 shows, there are greater savings in testing for the largerarrays.

Using an L9 OA means that nine experiments are carried out in search of the 81control factor combinations that give the near-optimal mean, and also the near-minimum variation away from this mean. To achieve this, the Robust Design methoduses a statistical measure of performance called the signal-to-noise (S/N) ratio(Phadke 1989). Borrowed from electrical control theory, the S/N ratio developed byDr Taguchi is a performance measure to choose control levels that best cope withnoise (Bryne and Taguchi 1986, Bendell 1988, Phadke 1989). The S/N ratio takesboth the mean and the variability into account. In its simplest form, the S/N ratio isthe ratio of the mean (signal) to the standard deviation (noise). The S/N equationdepends on the criterion for the quality characteristic to be optimized. While there

are many different possible S/N ratios, three of them are considered standard andare generally applicable in the following situations (Bryne and Taguchi 1986,American Supplier Institute 1989, Phadke 1989).

Biggest-is-best quality characteristic (strength, yield, speed and cargocapacity).

Smallest-is-best quality characteristic (contamination, weight, energyconsumption and turn around time).

Nominal-is-best quality characteristic (dimension, control systems such assteering and motor control).

Whatever the type of quality or cost characteristic, the transformations are such thatthe S/N ratio is always interpreted in the same way; the larger the S/N ratio, thebetter (Bryne and Taguchi 1986).

By making use of OA, the Robust Design approach improves the efciency ofgenerating the information necessary to design systems that are robust to variationsin manufacturing processes and operating conditions. As a result, development timecan be shortened and research and development costs can be reduced considerably.Furthermore, a near-optimum choice of parameters may result in wider tolerances


L4 (23) 3 2 4 8

L8 (27) 7 2 8 128L9 (34) 4 3 9 81

L12 (211

) 11 2 12 2048L16 (215) 15 2 16 32768

L16 (45) 5 4 16 1024

L18 (21)x (37) 1 2 18 43747 3

Orthogonalarray

Number offactors

Number oflevels perfactor

Number oftrial requiredby orthogonalarray

Number oftrails in atraditional fullfactorialexperiment

Figure 2. Some commonly used orthogonal arrays.


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so that low-cost components and production processes can be used (Bendell 1988,Logothetis and Salmon 1988, Phadke 1989).

The third step, tolerance design, is the process of determining tolerances aroundthe nominal settings identied in the parameter design process (Kackar 1985). Toler-

ance design is required if Robust Design cannot produce the required performancewithout special components or high process accuracy (Bendell 1988). It involvestightening of tolerances on parameters where their variability could have a largenegative effect on the nal system. Typically, tightening tolerances leads to highercost (Phadke 1989).

Most US and European engineers focus on system and tolerance design toachieve performance. The common practice in product and process design is to basean initial prototype on the rst feasible design (system design). Then the reliabilityand stability against noise factors are studied and problems are corrected by request-ing costlier components with tighter tolerances (tolerance design) (Cullen and

Hollingnum 1987, Phadke 1989). In other words, parameter design is largely over-looked. As a result, the opportunity to improve quality while decreasing cost isusually missed (Taguchi 1986, Cullen and Hollingnum 1987, Phadke 1989).

Recently, however, the use of Taguchis Quality Engineering methods has beenincreasing in the US. Many companies are now realizing that new tools are requiredfor survival in the increasingly competitive world-class market. Thus, it is expectedthat the application of these methods will become widespread as low life-cycle cost,operability, and quality issues replace performance as the driving design criteria(Bryen and Taguchi 1986, Phadke 1989).

4. Background of Taguchi concepts

The fundamental principle of Robust Design is to improve the quality of aproduct by minimizing the effects of the causes of variation without eliminatingthose causes. Efcient experimentation is necessary to nd dependable informationabout design parameters. The information should be obtained with minimum timeand resources. Estimated effects of parameters must be valid even when otherparameters are changed (requiring adaptability including interactions and non-linear effects). Employing the signal-to-noise ratio to measure quality and orthogo-

nal arrays to study many parameters simultaneously are the keys to high-quality androbust design.

Since variation in product performance is similar to quality loss, analysis ofvariance (ANOVA) will be carried out to interpret experimental data and factoreffects. ANOVA is a statistically based decision tool for detecting variations aroundaverage performance of groups of items tested, and assigning these to the controlfactors and their interactions (Ross 1988, Roy 1990).

Phadke (1989), following Taguchi, measures the quality of a product in terms ofthe total loss to society due to functional variation and harmful side effects. Underideal conditions, the loss would be zero, i.e. the greater the loss, the lower the quality(Phadke 1989). The following sections discuss how this quality loss can be quanti-ed, factors that inuence this loss, and how this quality loss can be avoided.

In this paper, the term quality loss is referred to as the cost of losing or repair-ing the vessel (there is a risk but not a certain loss). The risk will probably beexpressed as an insurance premium based on expert judgement, not on actual lossor repair cost.



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4.1. The Taguchi quality loss function

How can quality loss be measured? Quality is often measured in terms of thefraction of the total number of units that are defective. This is referred to as fractiondefective. However, this implies that all units that are within the tolerances of the

requirements are equally good. In reality, a product that is exactly on target givesthe best performance. As the products response deviates from the target, its qualitybecomes progressively worse. Therefore, one should not be focusing on meeting thetolerances, but on meeting the target.

The quality loss is crucial in Taguchis theory. It is based on the assumption thatwhen a functional characteristic y deviates from the specied target value m, thecustomer and the society in general experiences an economical loss due to poorerproduct quality. This economic loss is expressed as the loss function L(y). Based onthis, Taguchi denes the quality loss for not being on target by means of thequadratic quality loss function (Taguchi 1986, Phadke 1989):

L(y) = k(y 2 m)2 (1)

where y is the quality characteristic of a product/process, k is a constant called thequality loss coefcient, and m is the target value fory.

When the functional characteristic deviates from the target, the correspondingquality loss increases. Furthermore, when the performance of the product is outsidethe tolerances, the product is considered defective. A convenient way to determinethe constant k is to determine rst the functional limits for the value ofy. Let m D0 be the safety range for a vessel. Suppose the cost (loss) of losing or repairing thevessel is A

0when the vessel goes beyond the safety range. By substitution into

equation (1), one can obtain:

Dk

A

02

0= (2)

With the substitution of equation (2) into equation (1), one is able to calculate thequality loss for a given value ofy. More on the determination ofk can be found inPhadke (1989).

4.2. Signal-To-Noise Ratio (S/N ratio)

How can one avoid quality loss? Taguchi has developed a signal to noise ratio toprovide a way of measuring the robustness of a product, i.e. ability to function withuncontrollable factors. In other words, he has used the signal-to-noise ratio as apredictor of quality loss after making certain simple adjustments to the systemsfunction (Taguchi 1986, Phadke 1989). This ratio isolates the sensitivity of thesystems function to noise factors and converts a set of observations into a singlenumber. It is used as the objective function to be maximized in Robust Design(Phadke 1989).

The ratio takes into account the mean and the variance of the test results, and isper denition to be maximized. This leads to several specialized S/N ratios, depend-

ing on the nature of the comparison variable. There are three basic S/N ratios, butaccording to Fowlkes and Creveling (1995) the variety of S/N ratios is limitless. Thethree possible categories of quality characteristics or most widely used S/N ratios areas follows.

Smallest-is-better: h =210logn

y1

ii

n2

1=

, e.g. seeking the minimum light weight/dead weight ratio.



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Nominal-is-best: h = 210logs

m2

2

, e.g. maintaining cell guide tolerances.

Larger-is-better: h = 210logn y

1 1

ii

n

21=

, e.g. seeking the maximum prot or the

highest efciency.Here h represents the S/N ratio, and s2 the mean value and the variance of thevariables,yi is the comparison variable in experiment i for a certain combination ofcontrol factor levels, and n is the number of experiments performed for that combi-nation. There are other formulations of the S/N ratio, which can be found in Taguchi(1986), Pladke (1989) and Roy (1990).

The conversion to the S/N ratio can be viewed as a scale transformation forconvenience of better manipulation. It offers a way to carry out a trade-off betweentwo characteristics, namely variation and mean value based on objective knowledge.

Taguchi recommends rst to reduce the variation, and as step two to adjust the meanto the nominal value. Analysis using the S/N ratio has two main advantages.

It provides a guideline to the selection of the optimum level based on leastvariation around the target and also on the average value closest to the target.

It offers objective comparison of two sets of experimental data with respect tovariation around the target and the deviation of the average from the targetvalue.

For the robust design of a product, the following two steps are required.

Maximize the S/N ratio h. During this step, the levels of the control factors tomaximize h are selected while ignoring the mean. Adjust the mean on target. For this step, some control factors are used to bring

the mean on target without changing h.

Further information on quality loss and S/N ratios can be found in texts written byPhadke (1989), Taguchi (1986), Ross (1988), Roy (1990) and Suh (1990). They allprovide detailed discussions on how to apply statistical methods and Taguchisapproach in the selection of design parameters for satisfying functional require-ments.

4.3. Life-cycle quality loss

For a ship owner, it may be of interest to study how life-cycle considerations tin the theory of Taguchi. Lety1,y2, . . .,yn be n representative measurements of thequality characteristic y taken through the life cycle of a product, e.g. a ship, andassume that y shall be as close to a specied target value, m, as possible. Then theaverage quality loss, Q, caused by this product may be expressed as:

Q =n

1[L(y1) + L(y2) + . . . + L(yn)] =

n

k[(y1 2 m)

2 + (y2 2 m)2 + . . . + (yn 2 m)

2]

= k ( )m sm n

n 12 2- +

-

where m =n

y1

ii

n

1=

(mean) s2 = ( )mn

y1

1i

i

n2

1--

=

(variance)

When n is large, i.e. there are many measurements during the life of the product(e.g. a ship), the expression can be simplied as Q = k [(m 2 m)2 + s2].



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This simplied expression shows that the average quality loss depends on thefollowing two terms.

The deviation of quality characteristicy relative to the target value m. The mean variance ofy relative to the observed mean value ofy.

It is usually easy to reduce or eliminate the rst term; reducing the variance of aproduct is generally more difcult and expensive. A systematic approach to optimizethe performance is Taguchis two-step optimization process.

4.4. Taguchis two-step optimization process

Taguchis two-step optimization process focuses on the products performanceon the target. It consists of the following two steps.

The rst step of the process is to reduce the variability of the product perform-

ance by selecting parameter values for minimum variability. The second step is to select and adjust parameters with strong inuence on themean and weak inuence on the variability to put the performance on thetarget by identifying the inuences of the different design parameters on themean and variance.

4.5. Orthogonal arrays

In Taguchis theory, design parameters are set based on studies of the behaviourof the concept under different operating conditions. The parameters are set in such away that the sensitivity of the concept performance with respect to uncontrollable

factors is minimized. The sensitivity is analysed by the use of experiments and, throughanalysis of the information need and the use of OA (the core of the Taguchi experi-mental design technique), the experiment efciency is optimized. The experimentsmay be either analytical, a simulation (Monte Carlo), or physical, and the results areanalysed using an appropriate comparison variable and a so-called S/N ratio.

The term orthogonal refers to the balance of the various combinations of factorsso that no single factor is given more or less weight in the experiment than otherfactors. Orthogonality also refers to the fact that the effect of each factor can bemathematically assessed independently of the effects of the other factors (Fowlkes

and Creveling 1995). In OA, the columns are mutually orthogonal. Most booksdealing with the Taguchi theory provide standardized OA. In a more advanced para-meter design set-up, control factors with varying number of levels (usually 2, 3 and4) can be performed simultaneously. It is also possible to study the interactionbetween the control factors in an experiment.

4.6. Degree of freedom

Degree of freedom is a concept that is useful to determine how much informationcan be derived from an experiment in a matrix representation. The degree offreedom (DOF) of a matrix experiment is one less than the combinations of levelsin the experiment (i.e. number of rows in the orthogonal array): DOFexp = numberof combinations 2 1.

The degree of freedom needed to describe a factor effect (i.e. a factors contri-bution to the result) is one less than the number of levels (values) tested for thatfactor: DOFf= number of levels 2 1.

The problem of solving a set of simultaneous equations for a set of unknowns is



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a good mathematical analogy for the experiment. The number of equations is anal-ogous to the degree of freedom of a matrix experiment. The number of unknownsis analogous to the total degree of freedom of the factorial effects: (Total DOF)f=(number of factors)(DOFf).

The DOF is used to select an appropriate orthogonal array for the experiment,i.e. for the testing of the parameter combinations. As a general rule, the selectedstandardized orthogonal array must have at least the same degree of freedom as theexperiment. In addition, the number of rows (run) must be at least one more thanthe (Total DOF)f. One reason for the rationality of the Taguchi experiments is there-fore that they do not produce more information than is needed for most engineer-ing decisions.

4.7. Control factors

The control factors are values that can be specied freely by the designer. It is

designers responsibility to determine the best values of these parameters. Eachcontrol factor can take multiple values, called levels. Their settings or levels areselected to minimize the sensitivity of the products response to all noise factors andachieve target value (Ross 1988, Phadke 1989).

4.8. Noise factors

Noise factors are treated like the control factors in terms of DOF calculation andselection of orthogonal arrays, but might be more often represented by two-levelparameters reecting a probable operating interval. An example of this may be fuel

price, where one may set an extreme high and expected price as the operatinginterval. The distinction between controllable and uncontrollable factors is veryoften an economical question, and in the extreme case with unlimited resourcesavailable all factors may be controllable.

4.9. ANOVA terms and notations

The ANOVA computes parameters such as degree of freedom, sums of squares,mean squares, etc., and organizes them in a standard tabular format. Theseparameters and their inter-relationships are dened as shown in the following usingthe notation:

V = mean squares (variance)S = sum of squaresS9 = pure sum of squaresf = degree of freedome = error (experimental)F = variance ratioP = percent contributionT = total (of results)N

= number of experimentsC.F. = correction factorn = total degrees of freedom

4.9.1. Variance. The variance of each factor is determined by the sum of the squareof each trial sum result involving the factor, divided by the degree of freedom of thefactor. Thus:



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VA = SA/ fA (for factor A)

VB = SB/ fB (for factor B)

Ve = Se/ fe (for error terms)

4.9.2. Variance ratio. The variance ratio is the variance of the factor divided by theerror variance.

FA = VA/ Ve

FB = VB/ Ve

Fe = Ve/ Ve = 1

4.9.3. Pure sum of squares. The pure sum of squares is:

S9A = SA 2fA 3 Ve

S9B = SB 2fB 3 Ve

S9e = Se + (fA + fB) 3 Ve

4.9.4. Percent contribution. The percent contribution of each factor is the ratio ofthe factor sum to the total, expressed in percentage.

PA = SA 3 100/ ST

PB

= SB3 100/ S

T

Pe = Se 3 100/ ST

where ST is the total sum of square, obtained by:

ST = ( . . . )( . . . )

Y Y Yi

Y Y Yi

i12

22 2 1 2

2

+ + -+ +

.

4.9.5. Total variance

ST = Sum of square of all trial run results 2 C.F.

where C.F. = T2/Nand T = (Y1

+ . . . + YN).

4.10. Condence intervals. The calculations shown in the ANOVA table (table 3)are only estimates of the population parameters. These statistics are dependent onthe size of the sample being investigated. As sample size increases, the precision ofthe estimate would be improved. For large samples, the estimates approach the truevalue of the parameter. In statistics, it is therefore customary to represent the valuesof a statistical parameter as a range within which it is likely to fall, for a given levelof condence. This range is termed as the condence interval (C.I.). If the estimateof the mean value of a set of observations is denoted by E(m), then the C.I. for the

mean and intervals are obtained according to the following procedure:

Upper condence level = Mean + C.I.

Lower condence level = Mean 2 C.I.

C.I. =N

FxV

e

e (Roy 1990)



14/28

where Fis the Fvalue from the Fdistribution tables (F-ratio tables) at a required con-dence level, and at DOF 1 and error DOF 8 (Roy 1990), Ve is the variance of errorterm (from ANOVA), and Ne is the effective number of replications (= {total numberof results (or number of S/N ratio) / {DOF of mean (= 1 always) + DOF of all factors

included in the estimate of the mean) or the total number of units in one level.The Fvalue is sometimes refereed to as the Fratio, used to test for the signi-cance of factor effects. It is the statistical analogue to Taguchis S/N ratio for controlfactor effect versus the experimental error. The Fratio uses information based onsample variances (mean squares) to dene the relationship between the power ofthe control factor effects (a type of signal) and the power of the experimental error(a type of noise) (Fowlkes and Creveling 1995).

4.11. Brainstorming

Brainstorming is an integral part of the Taguchi philosophy. Taguchi regards

brainstorming as an essential step in the design of effective experiments. Throughbrainstorming sessions, clear statements of the problems are established, and theobjectives, the desired output characteristics, the methods of measurement and theappropriate experiments are designed. Taguchi does not prescribe a standardmethod of brainstorming as applicable to all situations. The nature and content ofthe brainstorming session will vary widely depending on the problem. The generalagenda for a brainstorming session may include the following.

Assigning project title and dening objective. Identifying quality characteristics.

Determining how each attribute is measured. Determining control factors, noise factors, factor levels. Outlining scopes of project (how many experiments, how many repetitions). Assigning task.

5. A safety optimization framework using Taguchi concepts

A safety optimization framework using Taguchi concepts for maritime safetyengineering applications is presented in this section. The proposed frameworkconsists of the following steps.

1. Dene the problem. The rst step is to describe the specic maritime safetyproblem in detail, either in qualitative or quantitative terms. Then dene theobjective parameter that is to be optimized.

2. Identify factors and their interactions. The brainstorming technique isnormally used among a panel of experts to identify all the possible factors,the levels, their interactions and other pertinent information about the opti-mization problem. Sometimes factor screening may be required to providea quick and simple way of ranking factors according to their importance inthe optimization. This will reduce the number of identied factors in orderto perform the optimization more efciently.

3. Select an appropriate OA. To select the correct standard OA, it is necessaryto determine the total degrees of freedom to nd the minimum number oflevel combinations to be tested. The number of factors and their interactionsas identied after the screening in step 2 will determine the total degrees offreedom according to the equation given in section 5.4.6.



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4. Conduct experiment. This begins with the selection of a correct quality lossfunction to represent the description of loss attributed in the case. This is apurely mathematical analysis and the S/N ratio for each treatment is calcu-lated according to the selected standard S/N ratio expressions as described

in section 5.4.2. The calculated S/N ratios are then normalized beforeproceeding to the next step.5. Conduct ANOVA and other Taguchi-related analyses. This step mainly

performs all the relevant operations in ANOVA. The main effects of eachfactor as well as interaction of factors are determined, and then sum ofsquares for each main effect of factor is computed. The variance of eachfactor is calculated. The results are presented in a table. It is worth notingthat in a Taguchi test it is not always possible to compute all interactions.

6. Identify signicant factors and their interactions. The contribution of eachfactor and their interactions are determined through division, i.e. the sum of

squares of each factor is divided by the total sum of squares of all the factors.Pooling is recommended when a factor is determined to be insignicant byperforming a test of signicance against the error term at a desired con-dence level.

7. Find the optimal combination of factor levels to minimize the system risk level.The non-linearity analysis is carried out to investigate the non-linearity ofthe S/N ratio with respect to factor levels of each factor as well as their inter-actions to identify the optimal combination of factor levels. The non-linear-ity graphs are developed to demonstrate the outcomes of this investigation.

8. Recommend for implementation. Safety-related recommendations pertain-ing to engineering design, operation and management are made based onthe outcomes of the optimization.

This procedure will be illustrated through an example described in the next section.The requirements for a verication experiment are essential to identify and assessthe validity of the results obtained against those known judgements made by theexperts, even though it is not performed in the example given in this paper.However, a verication experiment is to be made by presenting the optimum combi-nation obtained to the experts.

6. A safety-based optimization example: application of Taguchi concepts in

maritime safety studies

A hypothetical example is designed by authors for illustration purposes todemonstrate that the Taguchi method is a potential tool for maritime engineeringsafety studies. The example illustrates how the Taguchi method can be used toextract from expert judgements those factors that the experts judge most importantwhen they estimate the risk level for a ship with the purpose of determining insur-ance rates. This method can be used wherever a design trade-off is combined withsubjective expert judgement.

6.1. Background information

The ships safety is substantially affected by many factors, including ship ownermanagement quality, crew operation quality, enhanced survey programme, degreeof machinery redundancy, re-ghting capability, navigation equipment level, corro-sion control, preventive maintenance policy, etc. (Burton et al. 1997). To identify the



16/28

salient factors and interactions that cause excessive variations, a trial application ofTaguchi methods is performed here to optimize each factor to attain the optimalsafety for the ship.

6.2. Step 1: dene the problemVarying levels of various factors, such as design features, ship owner manage-ment quality, crew operation quality, etc., have different degrees of inuence onships overall safety performance throughout its life cycle. This will further becomplicated when all these factors are evaluated simultaneously to obtain the opti-mized solution. The prime objective of this study is to help identify the factors andtheir associated reasons for high risks, and to suggest measures, including exactparameters settings, that would reduce the overall risk level of the ship.

6.3. Step 2: identify factors and their interactions

The brainstorming technique is used to gather relevant information to determinefactors affecting ship safety. The resulting list of signicant factors affecting shipsafety is presented in table 1. These factors are determined based on the informationacquired. In the eight factors, seven have three levels and one has two levels. Therewill be a signicant interaction between two factors, namely the ship owner manage-ment quality and the enhanced survey programme. Risk level values between 1 and50 are assigned to each factor at each level by experts. The higher the risk levelvalue, the more risky the system. These risk level values do not represent anyabsolute or exact degree of risk encountered by the ship and they are used only forrelatively indicative purposes. To facilitate further discussion, the factors areassigned alphabet identiers.

6.4. Step 3: select an appropriate OA

To choose an appropriate array, degrees of freedom must be computed rst.Given seven factors with three levels, one factor with two levels, and one interaction


Factor identier Factor Level 1 Level 2 Level 3

A Preventative Adequate Average Sketchy (identify

maintenance policy the malfunctionparts)

B Degree of machinery 75% High 50% Average 25% Lowredundancy

C Fire-ghting High Average Lowcapability

D Ship owner Good Moderate Poormanagement quality (inadequate

procedures)E Enhanced survey Yes (adequate) No Nil

programme

F Navigation High Average Lowequipment levelG Corrosion control Good Average PoorH Crew operation Competence Average Poor

quality (well-trained) (inadequateknowledge)

Table 1. List of factors affecting ship safety.


17/28

of a two-level and a three-level factor, the number of degrees of freedom for theexperiment is computed to be 7(3 2 1) + 1(2 2 1) + (3 2 1)(2 2 1) + 1 = 18. Sincethere are factors with two and three levels, the L18 array is selected. Table 2 showsthe experimental design for an L18 array. In all, 18 treatments must be used for the

experiment with the factor levels as shown. For this study, however, three levels ofrisk are used in table 3, representing judgements made by three experts.

The assignment of factors to columns is accomplished as follows:

since factor E is a two-level factor, it is assigned to column 1; as factors E and D are deemed to have signicant interaction in brainstorm-

ing sessions, factor D is assigned to column 2; other factors are thereafter assigned to columns 38 arbitrarily: factor A to

column 3, factor B to column 4, and so on, as clearly depicted in table 3.

Interaction is not assigned to any column since it can be computed without loss ofany information or confounding. It is noted that interactions cannot always becomputed in a Taguchi experiment and that, in some Taguchi test plans, the inter-actions to be estimated must be assigned to columns according to the linear graphs.

6.5. Step 4: Conduct experiments

Three sets of experiments are conducted for each treatment as dictated by theL18 array of table 2, where the risk levels are assigned by three experts. Results arepresented in table 3.

Then, for each treatment, the S/N ratio is calculated using the following formula:

S/N ratio for ith treatment = 210log10 sn1 2 = 210log10

n1 Y Y Yi i i1

222

32+ +

where Yij, j = 1, 2 or 3 is the jth response of the ith treatment representing judge-ments made by three experts. These values are normalized by subtracting 227 (theaverage of the S/N ratio) from each S/N ratio. The S/N ratio values and their normal-ized values are also presented in table 3.


Treatment 1 2 3 4 5 6 7 8

1 1 1 1 1 1 1 1 12 1 1 2 2 2 2 2 23 1 1 3 3 3 3 3 3

4 1 2 1 1 2 2 3 35 1 2 2 2 3 3 1 16 1 2 3 3 1 1 2 27 1 3 1 2 1 3 2 38 1 3 2 3 2 1 3 19 1 3 3 1 1 2 3 2

10 2 1 1 3 3 2 2 111 2 1 2 1 1 3 3 212 2 1 3 2 2 1 1 313 2 1 1 2 3 1 1 214 2 2 2 3 1 2 1 3

15 2 2 3 1 2 3 2 116 2 3 1 3 2 3 1 217 2 3 2 1 3 1 2 318 2 3 3 2 1 2 3 1

Table 2. L18 of Taguchi experimental design.


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6.6 Step 5: conduct ANOVA; and step 6: identify signicant factors and their

interactions

Based on the normalized S/N ratio data in table 3, ANOVA is conducted. As arst step, for each level of each factor, the main effect is computed.

For example:

Factor A, level 1: main effect = 6.64 2 3.93 2 6.6 + 0.81 2 5.19 2 3.2 = 211.47Factor A, level 2: main effect = 10.04 + 10.4 + 0.32 + 9.29 2 5.75 2 6.14 = 18.16Factor A, level 3: main effect = 20.49 + 2.88 2 3.28 2 0.84 + 3.95 2 2.01 = 0.21

The main effects of other factors are computed likewise. For computing the effectof interaction of factors D and E, all possible combinations (3 x 2 = 6) of D and Eare considered.

Level of factor D: 1 2 3 1 2 3Level of factor E: 1 1 1 2 2 2Interaction level assigned: 1 2 3 4 5 6

Thereafter, the effect of interaction is computed as an average of each level. Thesum of squares for each main effect is computed using the standard methodology.

Calculation of the D 3 E column:

D1E1 = 6.64 + 10.04 2 0.49 = 16.19

D2E1 = 23.93 + 10.4 + 2.88 = 9.35

D3E1 = 26.6 +0.32 2 3.28 = 29.56

D1E2 = 0.81 + 9.29 2 0.84 = 9.26

D2E2 = 25.19 2 5.75 + 3.95 = 26.99

D3E2 = 23.2 2 6.14 2 2.01 = 211.35


Trial Factor identier Risk level S/N ratio Normalizednumber E D A B C F G H S/N ratio*

1 1 1 1 1 1 1 1 1 6 13 11 220.36 6.642 1 1 2 2 2 2 2 2 6 8 7 216.96 10.04

3 1 1 3 3 3 3 3 3 24 25 22 227.49 20.494 1 2 1 1 2 2 3 3 25 28 25 230.93 23.935 1 2 2 2 3 3 1 1 7 6 7 216.60 10.406 1 2 3 3 1 1 2 2 17 14 17 224.12 2.887 1 3 1 2 1 3 2 3 46 47 50 233.60 26.608 1 3 2 3 2 1 3 1 22 17 25 226.68 0.329 1 3 3 1 3 2 1 2 33 33 32 230.28 23.28

10 2 1 1 3 3 2 2 1 21 22 18 226.19 0.8111 2 1 2 1 1 3 3 2 8 8 7 217.71 9.2912 2 1 3 2 2 1 1 3 25 24 25 227.84 20.8413 2 2 1 2 3 1 3 2 42 42 38 232.19 25.19

14 2 2 2 3 1 2 1 3 42 47 412

32.752

5.7515 2 2 3 1 2 3 2 1 11 17 14 223.05 3.9516 2 3 1 3 2 3 1 2 33 33 31 230.20 23.2017 2 3 2 1 3 1 2 3 47 47 42 233.14 26.1418 2 3 3 2 1 2 3 1 25 33 26 229.01 22.01

* 2(227) is added to each S/N ratio.Table 3. Ship safety in terms of risk levels under various treatments.


19/28

For example: for the interaction of factors D and E, the formula used is slightlydifferent since it has six levels. Specically:

ST = sum of squares of all trial run results 2 C.F.

where C.F. = T2

/ N, T= (Y1 + Y2 + Y3 + . . . Yi), and i is the number of trials or treat-ment, or

ST = . . .. . .

Y Y Yi

Y Y Yi

i

12

22 2 1 2

2

+ + -+ + +

ST for D 3 E = {16.192 + 9.352 + (29.562) + 9.262 + (26.392) + (211.352)}

2 {16.19 + 9.35 2 9.56 + 9.26 2 6.99 2 11.35}2 / 6 = 703.91 2 7.94 = 696.43

ST forA = {(11.47)2 + (18.16)2 + (0.21)2} (6.9)2 / 3 = 445.52

The main effects are presented in table 4.Then the table for ANOVA is ready to be developed. At the outset, a signi-

cance level of 0.05 or a condence level of 95% was set as the cut-off point forpooling an effect into error. The ANOVA table is developed as follows.

The rst column is simply the factor identier. The second column is taken from table 4, and is the sum of squares for each

factor. The third column is developed by simply nding the percentage of each sum

of squares with respect to the total sum of squares of all factors and interaction. The fourth column lists the degree of freedom for each factor. The fth column lists the variance for each factor. The variance values are

computed by dividing sum of squares by the degree of freedom of each factor. The sixth column tries to pool in error. In an attempt to nd factors that can

be pooled in the error, as a rst step, all factors that contributed less than 2.5%to the overall sum of squares are pooled into the error term.

The seventh column shows the Fvalues. Each Fvalue is the variance ratio thatis computed by dividing the variance of the factor by the error variance.

FA = VA/ Ve

where FA is the F value for factor A, VA the variance for factor A, and Ve the

variance for error terms.In this case (table 5),

Ve = sum of squares for factors B, C and G = 2.27 + 1.49 + 0.72 = 4.48


Level A B C D E F G H D 3 E

1 211.47 6.53 4.45 25.45 15.98 22.33 3.97 20.11 16.192 18.16 5.8 6.34 2.36 29.08 24.12 4.94 10.54 9.353 0.21 25.43 23.89 220.9 13.35 22.01 223.75 29.56

4 9.265 26.996 211.35Total 6.9 6.9 6.9 6.9 6.9 6.9 6.9 6.9 6.9Sum of 445.52 89.90 59.26 1074.2 314 184.76 28.33 1063.7 696.43squares

Table 4. Main and interaction effects.


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Since factors B, C and G contribute less than 2.5% to the overall sum of squares,they are pooled into the error term (that factors B, C and G are small shows anexpert bias towards short time risk and disregard of operational efciency).

Fvalue for factorA = 222.76 / 4.48 = 49.72

This resulted in an Fvalue of 10.03 for factor B, 6.61 for factor C, and 3.16 for factorG, which are not signicant enough to be considered independent main effects,based on our signicance condence level of 95%. Thus, factors C, B and G arepooled into error terms. They are found insignicant and the variations arising from

these constituted the error variations. These Fvalues are compared against the Fvalues provided for 5% signicance in appropriate Fdistribution tables (Roy 1990).The effect of factorsA, B, D, E, F, and H, and the interaction of factors D x E isfound signicant at 99.5% condence levels.

6.7. Non-linearity analysis

It is determined to investigate the non-linearity of these factors since mostfactors are at three levels. An investigation of the non-linearity of the S/N ratio withrespect to factor levels is carried out to identify the optimal combination of factorlevels. Firstly, the average values of the main effects are computed for each factor,

as can be seen in table 6. For factorA, for instance, the average value at three levelsis computed as follows.

The total value of the S/N ratio when factor A is at level 1 = 211.47 (refer totable 3). Hence, the average value of the S/N ratio of factor A at level 1 = (211.47/6 + 27) = 25.09, where 27 is added back that was originally subtracted in table 3.Division by 6 is simply due to the fact that there are six terms containing factor Aat level 1.

The other values for factor A at levels 2 and 3 are computed in a similar way.Also, the same procedure yielded the rest of the main effects and interaction effects

shown in table 6. The upper and lower condence levels of 1.99 are calculated instep 7.

6.8. Step 7: nd the optimal combination of factor levels to minimize system risk

level

Based on tables 4 and 6, the non-linearity graphs for each of the factors (except


Source/factors Sum of Sum of Degree of Variance Pooled in F value Minimumsquares squares freedom error condence

(%) (%)

A 445.52 11.26 2 222.76 49.72 >99.5

B 89.90 2.27 2 44.95 Pooled 10.03 >99.5C 52.26 1.49 2 29.63 Pooled 6.61 >99.5D 1074.2 27.15 2 537.1 119.9 >99.5E 314 7.94 1 314 70.1 >99.5F 184.76 4.67 2 92.38 20.62 >99.5G 28.33 0.72 2 14.17 Pooled 3.16 >99.5H 1063.7 26.89 2 531.85 118.72 >99.5D 3 E 696.43 18.06 2 348.22 77.73 >99.5Sum 3956.1

Table 5. The nal ANOVA table after pooling insignicant factors.


21/28

factor E, which has two levels and hence is not subject to non-linearity investigation)and interaction are developed. These are shown in gures 311. The combinationthat yields the largest value of S/N ratio is determined from these graphs to be asfollows:

Factor A B C D E F G H D 3 E

Optimal level 2 1 2 1 1 3 2 1 1

Thus,A2, B1, C2, D1, E1, F3, G2, and H1, provide the best combination for the lowestpossible risk level for the whole system. Keeping in mind that factors C and G arenot signicant, the management must keep factors A, B, D, E, F, and H at theoptimal levels to reduce the risk level of the ship as judged by experts to themaximum extent.

6.9. Condence intervals

Finally, to get an idea about the current variability of each factor, condence

intervals (CIs) are computed. These are also shown in table 6. The followingprocedure is used to develop the intervals (Roy 1990):

Upper condence level = mean + CI

Lower condence level = mean 2 CI

CI =N

F V

e

e

Thus, for factorsA, B, C, D, E, F, G, and H,

CI = . . .6

5 32 4 48 1 99=

The CI for interaction D 3 E:

CI =. .

.3

5 32 4 482 82=


Level A B C D E F G H D 3 E

1 25.09 28.09 27.74 31.24 29.66 27.39 27.66 30.35 32.402 30.03 27.97 28.06 27.39 25.49 26.31 27.82 28.71 30.123 27.04 26.10 26.35 23.52 29.23 26.70 23.04 23.81

4 30.095 24.676 23.22Upper +1.99 +1.99 +1.99 +1.99 +1.99 +1.99 +1.99 +1.99 +2.82condencelevelLower 21.99 21.99 21.99 21.99 21.99 21.99 21.99 21.99 22.82condencelevel 2 1 2 1 1 3 2 1 1Optimallevel

Table 6. Condence intervals and optimal setting of factors.


22/28

These condence intervals are reected in table 6.


-15

-10

- 5

0

5

1 0

1 5

2 0

1 2 3

Factor Level

Main effect of factor A

S/N-Ratio

Figure 3. The non-linearity graph for factor A.

- 8- 6

- 4

- 2

0

2

4

6

8

1 2 3

Main effect of factor B

Factor level

S/N-Ratio

Figure 4. The non-linearity graph for factor B.


23/28


-6

-4

-2

0

2

4

6

8

1 2 3S/N-Ratio

Main effect of factor C

Factor level

Figure 5. The non-linearity graph for factor C.

-30

-20

-10

0

1 0

2 0

3 0

1 2 3S/N-Ratio

Main effect of factor D

Factor level

Figure 6. The non-linearity graph for factor D.


24/28


-15

-10

-5

0

5

10

15

20

1 2S/N-Ratio

Factor level

Main effect of factor E

Figure 7. The non-linearity graph for factor E.

-6-4

-2

0

2

4

6

8

10

12

14

16

1 2 3

S/N-Ratio

Main effect of factor F

Factor level

Figure 8. The non-linearity graph for factor F.


25/28


- 3

- 2- 1

0

1

2

3

4

5

6

1 2 3

S/N-Ratio

Factor level

Main effect of factor G

Figure 9. The non-linearity graph for factor G.

-30-25

-20

-15

-10

-5

0

5

10

15

20

25

1 2 3S/N-Ratio

Main effect of factor H

Factor level

Figure 10. The non-linearity graph for factor H.


26/28

6.10. Step 8: recommend for implementation

As a result of the earlier study, the following changes are recommended in thedesign, operation and management system.

Average level of preventative maintenance policy should be adopted. FactorA2 is made operative.

High degree of machinery redundancy is recommended. Factor B1 is morepreferable.

Average re-ghting capability is adequate for the system. Factor C2 isselected.

Ship owner management quality should be high. Factor D1

is strongly urged. Enhanced survey programme should be adopted. Factor E1 is strongly urged. Low navigation equipment is adequate. Factor F3 is selected. Average corrosion control is recommended. Factor G2 is selected. Competent crew operation quality is essential. Factor H1 is strongly recom-

mended.

7. ConclusionsThis paper has introduced the Taguchi philosophy in quality improvement in

maritime safety engineering. It provides a basic understanding and skill in utilizingthe Taguchi concepts and methodologies in safety-related applications. A safetyoptimization framework using Taguchi concepts is proposed, and an applicationexample is used to demonstrate how Taguchi concepts can be used to improve safetyperformance of a ship throughout its life cycle via optimizing its design features,operational characteristics, and ship owner management quality. Moreover, theTaguchi method can be used to extract from expert judgements those factors the


-15

-10

-5

0

5

10

15

20

1 2 3 4 5 6S/N-Ratio

Main effect of interaction DxE

Factor level

Figure 11. The non-linearity graph for factor D 3 E.


27/28

experts judge most critical when they carry out risk estimation for a ship with thepurpose of determining insurance rates. This method can be a powerful and conveni-ent tool whenever a design trade-off is combined with subjective expert judgementsin any engineering discipline. The results of this study show that the Taguchi

methods, which have been employed for improving manufacturing processes, mayprovide an alternative tool for risk analysis in maritime safety engineering. Safetyanalysts, designers, regulatory bodies, and ship managers may use this study andincorporate Taguchi methodology in their design, operation and decision-makingprocesses to deal with safety-related matters.

ReferencesAMERICAN SUPPLIER INSTITUTE INC., 1989, Taguchi Methods: Implementation Manual

(Dearborn, MI: American Supplier Institute Inc.).BENDELL, A., 1988, Introduction to Taguchi methodology. Taguchi Methods: Proceedings of

the 1988 European Conference, (London: Elsevier Applied Science), pp. 114.BRYNE, D. M. and TAGUCHI, S., 1986, The Taguchi approach to parameter design. ASQC

Quality Congress Transactions (Anaheim, CA), p.168.BURTON, I .L. ,CUCKSON, B. R. and THANOPOULOS, G. P., 1997, The assessment of ship suscep-

tibility to loss or damage using classication society information. Conference Proceed-ings of Marine Risk Assessment: A Better Way to Manage Your Business, 89 May(London: IMarE).

CULLEN, J. and HOLLINGNUM, J., 1987, Implementing Tool Quality (New York: Springer-Verlag).

FISHER, R. A., 1925, Statistical Methods for Research Workers (London: Oliver & Boyd).FOWLKES,W.Y. and CREVELING, C. M., 1995, Engineering Methods for Robust Product Design:

Using Taguchi Methods in Technology and Product Development(New York: Addison-Wesley).

GUNTER, B., 1987, A perspective on the Taguchi methods. Quality Progress, June, 4452.KACKAR, R., 1985, Off-line quality control, parameter design, and the Taguchi methods.

Journal of Quality Technology, 17(4), 176188.KUO, C., 1998, Managing Ship Safety (London: LLP).LOGOTHETIS, N. and SALMON, J.P., 1988, Tolerance design and analysis of audio-circuits.

Taguchi Methods: Proceedings of the 1988 European Conference (London: ElsevierApplied Science), pp. 161175.

MEISL, C. J., 1990, Parametric cost analysis in the TQM environment. Presented at the 12thannual Conference of International Society of Parametric Analysis (San Diego, CA).

PHADKE, S. M., 1989, Quality Engineering Using Robust Design (Englewood Cliffs, NJ:

Prentice Hall).ROSS, P. J., 1988, Taguchi Techniques for Quality Engineering (New York: McGraw-Hill).ROY, R. K., 1990, A Primer on the Taguchi Method (New York: Van Nostrand & Reinhold).SII,H.S. ,RUXTON, T. and WANG, J., 2000a, Taguchi concepts and their applications in marine

and offshore safety studies. INEC 2000: Marine Engineering Challenges for 21st

Century (Hamburg: Congress Centrum Hamburg), 1416 March.SII, H. S., RUXTON, T. and WANG, J., 2000b, A role for Taguchis methods in marine and

offshore safety studies. MT 2000: Marine Technology 2000 (Poland: TechnicalUniversity of Szezecin, Faculty of Maritime Technology), 37 May.

SUH, N. P., 1990, The Principles of Design (New York: Oxford University Press).SULLIVAN, L. P., 1987, The power of Taguchi methods. Quality Progress, June, 149152.

TAGUCHI

, G., 1986,Introduction to Quality Engineering

(Dearborn, MI: Asian ProductivityOrganisation (distributed by American Supplier Institute Inc.)).TAGUCHI, G. and KONISHI, S., 1987, Orthogonal Arrays and Linear Graphs (Dearborn, MI:

American Supplier Institute Inc.).TAGUCHI, G., ELSAYED, E. and HSIANG, T., 1989, Quality Engineering in Production Systems

(New York: McGraw Hill).TIPPETT, L. C. H., 1934, Application of statistical methods to the control of quality in indus-

trial production.Journal of Manchester Statistical Society, England.



28/28

VILLEMEUR, A., 1992, Reliability, Availability, Maintainability and Safety Assessment, Vol. 1:Methods and Techniques (Chichester: John Wiley & Sons).

WILLE, R., 1990, Landing gear weight optimisation using taguchi analysis. Presented at the49th Annual International Conference of Society of Allied Weight Engineers Inc.(Chandler, AR).

ZHOU, Q.-J. , ALLEN, J. K. and MISTREE, F., 1992, Decisions under uncertainty: the fuzzycompromise decision support problem. Engineering Optimisation, 20, 2143.


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