a comparative study of the prioritization matrix method and the analytic hierarchy process technique...

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TOTAL QUAL ITY M ANAGEMENT, VOL. 9, NO. 6, 19 98, 421± 430

A comparative study of the prioritizationmatrix method and the analytic hierarchyprocess technique in quality functiondeployment

H. W ANG , M. X IE & T. N. G OHDepartment of Industrial and Systems Engineering, National University of Singapore, 10 Kent

Ridge Crescent, Sin gap ore 119260

Abstract As a tool to identify customer needs and translate customer requirements into technical responses, the house of quality (HOQ) has become one of the most useful techniques in total quality

management, especially in the context of quality function deployment (QFD). Recently, the analytichierarchy process (AHP) has been recommended for prioritizing the customer voice in HOQ. In this

pap er, we recommend tha t AHP be applie d not only to the customer voice, but also dir ectly to the

technical responses. Since the decision-maker can select either the prioritization matrix method or the AH P metho d for HOQ applicatio ns, an un ders tanding of their advan tages and disad vantagesbecomes important. In this paper, we compare these two methods in terms of practical applications in

industry leading to the general conclusion that if time, cost and diýculty are the major concerns in pro duct improvement, the pr ior itization matr ix metho d is preferred; whe re accuracy is the major

requirement, the AHP method would be a better choice.

Introduction

Manufacturing companies, in the face of ®erce competition in the global market, generallystrive to gain a competitive edge through high quality products with minimum costs. Thesuccess of this eþort would depend largely upon how the products meet customer require-ments, and quality function deployment (QFD) is a major technique for translating customer requirements directly into a product’s technical characteristics. QFD is a very useful manage-ment technique in m ulti-criteria decision-making because of its simplicity and clarity. It isbased on the construction and analysis of a `house of quality’ (HOQ ), w hich documentsthe transformation of customer needs into the highest-level technical characteristics. Theprioritization matrix method is used in HOQ to obtain the relative importance of thecustomer needs (see Cohen, 1995).

QFD can be credited to Professor Mizuno who applied the technique at M itsubishi



422 H. WANG, M. XIE & T. N. GOH

and books have been published on the use and bene®ts of QFD (see Balthazard & Gargeya,1995; Bicknell & Bicknell, 1995; Cohen, 1995; Eureka & Ryan, 1994; Pimblott, 1995;Pitman, 1996; Shillito, 1994; Zairi, 1995).

Recently, the analytic hierarchy p rocess (AHP) has been proposed for app lication to theHOQ to generate the relative importance of the `voice of the customer’. First developed bySaaty ( 1980), AH P is a powerful tool for p roblem-solving and decision-making in a complexenvironment. Instead of weighting the alternatives according to one criterion in only onelevel as in the prioritization matrix method, the AHP method structures a complex, multi-criteria problem hierarchically. It organizes the basic rationality by breaking down a probleminto smaller and smaller constituent parts, then guides the decision-maker through a seriesof pairwise comparison judgements to express the relative strength or intensity of impact of the elements in the hierarchy. Recently, AH P has been used by m any authors to identify andprioritize customer requirements in the HOQ (see Akao, 1990; Armacost et al. , 1994; Aswad,1989; Doukas et al. , 1995; Fukuda & Matsuura, 1993; Xie et al. , 1995).

In this paper, we suggest the use of the AHP method not only in the weighting of customer requirements, but also during the entire prioritization process in the HOQ. Wethen compare the procedures of QFD and AHP methods and discuss their advantages anddisadvantages. By considering accuracy, diýculty, time needed, costs and other factors whichmay aþect the use of the two methods in practice, we give some recommendations withregard to the choice of method.

Prioritization based on house of quality

QFD is a method for developing a design aimed at satisfying customers’ requirements andthen translating the customers’ demands into design targets. It creates a documented picturelinking characteristics which the user requires, leading to a product’s design characteristics,control characteristics during the product manufacturing process, inspection characteristicsand so on. The HOQ is the primary planning tool in QFD. It is a conceptual map thatprovides the means for interfunctional planning and communication of customer requirementsand technical responses. Some useful references on HOQ are Hauser and Clausing (1988),Cohen (1995) and Dale (1994).

In the HOQ, the relative weights of customer requirements are obtained from thecustomers themselves. The question `How important is the need to the customer?’ is answereddirectly by market research. Here, the customers need not make pairwise comparisons butare asked to g ive each requirement a number expressing relative importance according totheir own considerations and criteria, this is the basis of the prioritization matrix method inthe HOQ.

The steps to build the HOQ using the prioritization matrix method are:

(1) List customer requirements (whats).(2) List technical descriptors (hows).(3) Develop a relationship m atrix between whats and hows.

(4) Develop an interrelationship matrix b etween hows.(5) Develop prioritized customer requirements.



A COMPARATIVE STUDY OF THE PR IORITIZATION M ATRIX METH OD 423

Figure 1. The HOQ for the example, from Wasserman (1993).

requirements and technical responses makes use of a 1±3±9 or 1±3±5 scale to denote weak,medium and strong relationships.

The absolute weight of the j th technical descriptor is then given by

a j 5 Rn

i 5

1

R i j c i

Where

a j 5 row vector of absolute weights for the technical descriptors ( j 5 1, . . ., m );R i j 5 weights assigned to the relationship matrix ( i 5 1 , . . ., n , j 5 1 , . . ., m );

c i 5 column vector of degree of importance for the customer requirements ( i 5 1, . . ., n)m 5 number of technical descriptors;n 5 number of customer requirements;

We now use the example of HOQ from the paper by Wasserman (1993) to illustrate thebasic structure and procedure of the HOQ The HOQ is shown in Fig 1 We can see from




The analytic hierarchy process for prioritization

Direct use of AHP method

AHP is a systematic procedure for representing the elements of any problem hierarchically.The essential steps in the application of the AHP involve decomposing a general decisionproblem in a hierarchical fashion into subproblems that can be easily comprehended andevaluated, determining the priorities of the elements at each level of the decision hierarchy,and synthesizing the priorities to determine the overall priorities of the decision alternatives.For the AHP theory, see Dodd et al. (1995), Mobolurin and Bryson (1993), Saaty (1980,1996) and Wedley et al. (1993). The AHP has been used in many areas, such as qualitymanagement (Armacost et al. , 1994; Xie et al. , 1995), manufacturing systems (O’Brien &Smith, 1993; Shang & Sueyoshi, 1995), investment analysis (Angelis & Lee, 1996; Arinzeet al. , 1995), transportation service (Korpela & Tuominen, 1994) and resource allocation(Ramanathan & Ganesh, 1995).

Recently, AHP with some modi®cations has been used to assess the relative importanceof user quality factor requirements in the HOQ (see Armacost et al. , 1994; Doukas et al.

1995; Fukuda & Matsuura, 1993). As a powerful and robust decision analysis methodologyfor problem-solving and decision-making in a complex environment, AHP is very simple andappealing for solving large-scale real-world problems. Prioritization in the HOQ is a complex,multi-criteria decision-making problem. The weight analysis of customer requirements andtechnical responses in the HOQ is diýcult but important to the decision-maker. Therefore,the AHP method is a particularly suitable alternative for weighting customer requirementsand technical responses in the HOQ. Most of the research on the application of AHP to theHOQ in the past has been focused on using AHP to weight only the customer requirements.The A HP method can in fact be directly used in the prioritization of the technical responses.In this manner, the overall HOQ analysis becomes more complete.

The AHP method itself requires the alternatives and the criteria in the same level of thehierarchy to b e independent. W ithin the HOQ, the customer requirements can be independ-ent, but the technical responses may not be independent since they may have relationshipsas shown in the roof of the HOQ. The technical responses can be divided into more detaileddescriptors, and with the related part taken as a new technical response, the technicalresponses can become independent of each other based on some appropriate assumptions.The AHP method can then be applied to the technical responses. In our illustrative example,we assume that the technical responses are independent.

Steps of AHP in prioritization

The main operational steps of using AHP to the HOQ are:

(1) De®ne the problem.(2) Structure a hierarchy representing the problem.(3) Perform pairwise comparison judgements on the customer requirements with respect

to the goal of the HOQ




Table 1. Saaty’s intensity of importance scale

Intensity of impor tance De®nition Explanation

1 E qu al impor ta nce Tw o activ ities co ntr ibu te equ ally to the ob jective

3 Weak im po rtan ce o f E xpe rien ce a nd ju dge men t s ligh tly f avor o ne a ctiv ity ov er

o ne o ver a not her an other

5 E sse ntial o r stro ng E xpe rien ce a nd ju dge men t s tro ng ly f avor o ne a ctiv ity o ver importance another

7 D em on stra ted An a ctiv ity is stro ng ly f avo red a nd its d omin an ce d em on stra tedimportance in practice

9 A bso lu te im po rta nce T he e vid en ce f avo rin g o ne a ctiv ity o ver a no ther is o f thehighest possible order of aýrm ation

2,4,6,8 I nter m ed ia te va lue W hen c om prom ise is n ee dedbetween the two

adjacent judgements

Reciprocals of If activity i has one of the above non-zero numbers assigned to it when compared withabove non-zero activity j , then has the r eciprocal w hen compared with i numbers

Instead of using 1, 3 and 9 or 1, 3 and 5 to represent weak, medium and strong relationshipsin the HOQ, numerical values used in the AHP process are 1 to 9. The meaning of these

numbers is given in Table 1.In AHP, each pairwise comparison represents an estimate of the ratio of the priorities or

weights of compared elements. Applying Saaty’s eigenvector method to these data, estimatesof the weights are calculated for each pairwise comparison matrix for each level of thehierarchy. To synthesize the results over all levels, the priorities at each level are weighted bythe priority of the h igher level criterion with respect to which the comparison was m ade. T heweighted priorities of the decision alternatives are added componentwise to obtain an overallweight or priority of each alternative over the entire hierarchy. The resulting prioritiesrepresent the intensity of the decision-maker’s judgemental p erception of the preferences of the alternatives, taking into account the relative importance of the criteria represented in thehierarchy, and after considering the importance of the trade-oþs among the attributes. For details, see Armacost et al. (1994).

An illu stra tive example

For the example in Wasserman (1993), if we use AHP, then the whole HOQ can be lookedon as a hierarchy system, which is shown in Fig. 2. The procedure to solve this hierarchy

system by the AHP method is:

(1) Make pairwise comparison of the customer requirements with respect to the goal




Figure 2. The hierarchy systems and the weights in the HOQ.

Table 2. Pairwise comparison of customer r equirements

R equ irem ent E asy t o ho ld D oes n ot sm ear Po int la sts D oes n ot ro ll

Easy to hold 1 1/2 1/3 1Does not smear 2 1 1/2 2Point lasts 3 2 1 3Does not roll 1 1/2 1/3 1

Table 3. Pairwise comparison matrices with respect to `easy to hold’

Leng th o f pencil Hexagonal ity

Length of pencil 1 1/3Hexagonality 3 1

Table 4. Pairwise comparison matrices with respect to `does not smear’

Time between sharpening Lead dust generated Minimal erasure residue

Time between sharpening 1 1/3 1/3Lead dust generated 3 1 1Minimal erasure residue 3 1 1

Table 5. Pairwise comparison matrices with respect to `point lasts’

Tim e betw een L ead d ust M in imal er asu re




Table 6. Pairwise comparison matrices with respect to `does not roll’

Leng th o f pencil Hexagonal ity

Length of pencil 1 1/9Hexagonality 9 1

Table 7. Weights and ranking of the technical responses

Time between Lead dust M inimal erasureLength of pencil sharpening generated H exagon ality residue

Weights in AHP 0.055 0.116 0.347 0.136 0.347Ranking in AH P 5 4 1 3 1Ranking in the 5 4 1 3 1

house of quality

(4) Obtain the ®nal weights and ranking of the technical responses with respect to thegoal. Compared to the ranking in the proceeding house of quality, the AHP methodcan get the same ranking as the prioritization matrix method. The ranking of thetechnical responses in the AHP method is in Table 7.

In our illustrative example, the ranking of the technical responses in the HOQ by theprioritization matrix method is the same as that by the AHP method. However, in practice,due to the diþerence of the procedures of the two methods, the result may be diþerent.

Comparison of the prioritization matrix method and the AHP method

Number of jud gem ents req uired

The prioritization matrix m ethod generally requires fewer team judgements than does theAHP method. With the prioritization matrix method, for n choices and two factors, thenumber of team judgements required is 2 n . For n choices and three factors, the number of team judgements required is 3 n . With AHP matrices, for n choices, the number of teamjudgements required is n ( n 2 1)/2. The number of judgements needed for two factors, threefactors by the prioritization matrix method and pairwise judgements by AHP method areshown in Fig. 3. From the ®gure, we can see that as the number of choices increases, the




number of required judgements in the AHP method becomes very large, much greater thanthe judgements needed for the two factor and three factor judgements.

Diýculty in making judgements

AHP judgements are often easier and quicker to make than prioritization matrix judgements.This is because AHP judgements are more intuitive, less focused on a single criterion andless constrained than prioritization matrix judgements. Generally, comparisons between twoalternatives are far more straightforward and simple than those for more than two alternativesaccording to one criterion at the same time. In the AHP method, each easier pairwisecomparison is made instead of making an overall importance comparison as is done in theprioritization matrix method. For that very reason, the judgements may be less diýcult thanprioritization matrix judgements. For some useful reference, see Cohen (1995).

Accura cy of the jud gem ents

Since the focus on the identi®cation of customer requirements is the driving force of QFD,considerable eþort has to b e com mitted to identify those requirements properly. Sometimesa company may want a more precise and accurate analysis of customer requirements, so thatactions taken later can b e m ore eþective. In this case, the AH P method should be preferred.By pairwise comparison, the AHP method can give decision-makers a better description of the whats. In the ordinary weight judgements in the HOQ, only the customers’ roughjudgements of the relative imp ortance of each customer requirements are g iven.

In practice, inconsistency in judgements cannot be totally avoided. We must, however,ensure that the pairwise comparisons do not contain too much inconsistencies. In AHP, weuse consistency ratio (CR) to measure the degree of inconsistency. If CR £ 0.1, the compar-isons are considered acceptable. If CR > 0.1, reassessment of the entries to reduce theinconsistency is required until the C R meets the practical standard. Th us, by using CR as anindicator, AHP can oþer better judgements of the factors in the HOQ.

Cost and time needed by judgements

Although A HP can oþer a more precise analysis of the customer requirements, the cost of doing pairwise comparisons is also higher. As explained previously, the number of teamjudgements required by AHP is n ( n 2 1)/2, which is much more than the prioritization matrixjudgements in the HOQ. In industry, the life cycle cost of a product must meet marketexpectations. To enter the market and be competitive with those of other producers, industrymust try to reduce cost, improve product marketability and increase the return on investment.With regard to cost, the AHP method may have its shortcomings.

Overall, the AHP method can give an easier and more accurate analysis of customer requirements in the HOQ, but it needs more time and ®nancial resources. Compared withthe AHP method, the prioritization matrix method requires less time because fewer judge-ments are needed.




makers in an industry. For a company to stay competitive and pro®table, the price of producthas to be reduced as far as possible. To capture a market in the presence of other competitors,time is very critical. When these two factors are of uppermost concern, the prioritizationmatrix method should be used to analyze customer requirements, since it is s traightforward,simple and easy to use.

On the other hand, for long-term pro®t and long-term competitiveness considerations,a company might want to carry out a much more precise analysis and identi®cation of customer requirements. In that case, a more accurate resource allocation method such as theAHP is preferred. This is especially important for products and processes that are critical tothe reputation of the company.

The two methods can also be done step-by-step, so that a ®nal relatively accurate analysisof customer requirements can be achieved, especially when there are a large number andseveral levels of customer requirements. The prioritization matrix method can be used in thefactor screening stage. Screening is usually performed in the early stages of a project, whenit is likely that many of the factors initially considered have little or no eþect on the response.The factors which have been identi®ed as important can then be investigated more thoroughlyin subsequent stages. The decision-maker can thus use the ordinary QFD method ®rst toselect the possible important customer requirements. The AHP method can then be appliedto further identify customer requirements.

Conclusions

The prioritization matrix method and the AHP method have their own merits. The AHP

method can oþer a more p recise analysis, but requires m ore time and resource. It is easier touse the prioritization matrix method, but the results might not be as accurate as the AHPmethod can provide. In regard to which one is better for a particular industry or company,speci®c considerations based on the decision-makers’ needs are required.

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