ijqrm (2014) statistical comparison of final scores in qfd

QUALITY PAPER

Statistical comparison of finalweight scores in quality function

deployment (QFD) studiesZafar Iqbal and Nigel P. Grigg

School of Engineering and Advanced Technology, Massey University,Palmerston North, New Zealand

K. GovindarajuInstitute of Fundamental Sciences, Massey University, Palmerston North,

New Zealand, and

Nicola Campbell-AllenSchool of Engineering and Advanced Technology, Massey University,

Palmerston North, New Zealand

Abstract

Purpose – Quality function deployment (QFD) is a methodology to translate the “voice of thecustomer” into engineering/technical specifications (HOWs) to be followed in designing of products orservices. For the method to be effective, QFD practitioners need to be able to accurately differentiatebetween the final weights (FWs) that have been assigned to HOWs in the house of quality matrix.The paper aims to introduce a statistical testing procedure to determine whether the FWs of HOWs aresignificantly different and investigate the robustness of different rating scales used in QFD practice incontributing to these differences.

Design/methodology/approach – Using a range of published QFD examples, the paper uses aparametric bootstrap testing procedure to test the significance of the differences between the FWs bygenerating simulated random samples based on a theoretical probability model. The paper thendetermines the significance or otherwise of the differences between: the two most extreme FWs and allpairs of FWs. Finally, the paper checks the robustness of different attribute rating scales (linear vsnon-linear) in the context of these testing procedures.

Findings – The paper demonstrates that not all of the differences that exist between the FWs ofHOW attributes are in fact significant. In the absence of such a procedure, there is no reliableanalytical basis for QFD practitioners to determine whether FWs are significantly different, and theymay wrongly prioritise one engineering attribute over another.

Originality/value – This is the first article to test the significance of the differences between FWs ofHOWs and to determine the robustness of different strength of scales used in relationship matrix.

Keywords Quality function deployment, House of quality, Parametric bootstrapping,Relationship matrix

Paper type Research paper

1. IntroductionQuality function deployment (QFD) is a methodology used to translate the “voice ofthe customer” (VOC) into engineering and technical specifications to be followed in the

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/0265-671X.htm

Received 9 December 2012Revised 4 June 2013Accepted 5 June 2013

International Journal of Quality &Reliability ManagementVol. 31 No. 2, 2014pp. 184-204q Emerald Group Publishing Limited0265-671XDOI 10.1108/IJQRM-06-2013-0092

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design of products or services. Akao (1990) has reported that when appropriatelyapplied, QFD has been effective in substantially reducing product development leadtimes. The main goal in implementing QFD is to improve the quality of the product orservice based on customer-defined requirements and expectations. Although QFD is apopular and widely used technique, as Enriquez et al. (2004 cited in Garver, 2012) pointout, on-going research still seeks to examine the assumptions and methods used withinQFD with a view to continuously improving the methodology and there is a need to beable to accurately determine importance scores for the customer because with inaccuratedata “the entire House of quality (HOQ) is built upon a weak foundation” (Garver, 2012).

Figure 1 shows a typical “HOQ”, as used within QFD. This structured methodologyis intended to effectively deploy the VOC. It consists of distinct “rooms” (denoted byrectangles), topped by a “roof” (denoted by the triangle at the top). Engineers and otherproduct/service development practitioners collect data from customers relating to theirrequirements and desires (WHATs). These are weighted for importance, and assigneda customer priority rating. They are then translated into engineering factors andrequirements (HOWs). The triangular elements shown are used to record the strengthsof intercorrelations between the WHATs or the HOWs. The relationship matrixrecords the strengths of the correlations between WHATs and HOWs. Data oncompetitor performance is further integrated, and a vector of final weights (FWs) forengineering priorities (HOWs) can be calculated (the bottom element of the HOQ).

Figure 1.A typical HOQ

Statisticalcomparison of

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For the method to be effective, therefore, the differences observed between the FWsscores should be meaningful and statistically significant. Otherwise, the FW scoreswill not provide a valid and reliable basis for the determination of engineeringpriorities in the design of the product or service.

The first aim of the research which is presented in this paper was to determinewhether the resulting FWs in a number of QFD examples are in fact (statistically)significantly different from each other, as measured against the background level ofcommon cause (random) variation that exists within the relationship matrix from whichthey have been derived. Using a range of empirical examples taken from literature, weuse a parametric bootstrap testing procedure to test the statistical significance of thedifferences between the FWs via two testing procedures: first, we test the statisticalsignificance of the differences between only the highest and lowest ranked FWs; second,we test the significance of the differences between all pairs of FW ratings.

The relationship matrix plays a key role in determining the final HOW weights, butQFD practice employs a wide range of rating scales. The second aim of our researchwas therefore to investigate the robustness of relationship scales by applying differentlinear and non-linear changes to the originally reported rating scales. Our findings inrelation to these aims, as reported in this paper, have implications for practitioners,academics and others involved in QFD research, in determining the degree ofimportance to place on FWs.

2. QFD and its factorsIn developing a HOQ, the customer, competitor and engineering data that populate thematrices and vectors are of an inherently qualitative nature, and are operationalisedinto numerical values through rating scales that transform linguistic criteria intonumeric data. A wide variety of practice is observable in the application of theselinguistic-numeric scales. In the rating of customer priority, competitor position, etc.there is not only potential variability in determining which value on a given scale mostclosely aligns with the perceived “reality”; but there is also wide variation in the scalesthat are applied by practitioners. In the following section we explicate the commonlyused linguistic-numeric scales and outline their use in QFD.

2.1 Customer priority rating scaleOnce a QFD developer has converted the VOC into specific requirements (WHATs),customers are asked to assign priority ratings to those WHATs. The resulting customerpriority ratings are used, together with relationship matrix, to derive the FWs of HOWs(the engineering/technical criteria required to achieve the WHATs). Table I summarisesseveral different priority rating scales for importance of WHATs as reported in literature.

Authors Customers priority rating scale

Bouchereau and Rowlands (2000) 1-3Dikmen et al. (2005) 1-9Tanik (2010) 1-10Majid and David (1994) and Utne (2009) 1-5Olewnik and Lewis (2008), Masui et al. (2003) 1, 3, 9Park and Kim (1998) Proportions of 1

Table I.Table of customersrating scale

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2.2 Relationship matrixIn the HOQ, the relationship matrix denotes the strength of relationship betweenWHATs and HOWs. In literature, three-point or five-point linguistic-numeric scales aremostly used for different strengths of relationships. For example: for “weak”,“medium” and “strong” relationship (Tan et al., 1998), used 1, 3, 5, respectively; ( Jeongand Oh, 1998) used 1, 3, 10; and (Bouchereau and Rowlands, 2000; Dikmen et al., 2005;Ghiya et al., 1999; Majid and David, 1994; Zhang, 1999) used 1, 3 and 9. We also seefive-point scales 1, 3, 5, 7, 9 reported by Chan and Wu (1998), and 1, 2, 3, 4, 5 by Croweand Cheng (1996) to represent “very weak”, “weak”, “medium”, “strong” and “verystrong” relationships. From these and other scales we have observed, the scales aregenerally based on a median value of 3. For our study these scales will play animportant role in testing the FWs, as described in Section 1.4.

2.3 Competitor’s data and improvement ratioAlthough some practitioners use and some do not use competitors’ data, it isconsidered good practice to look at the competitors in the market and make thisassessment part of a robust QFD process ( Jeong and Oh, 1998). Table II shows themost widely used qualitative scales of company’s position in market with customer’spoint of view. Competitors’ data not only contribute to the FWs of HOWs, but also helpto determine current position in the market and to set future goals. The improvementratio, also shown in Table II, may substantially change the ranking of FWs. Theempirical examples that we are using in our study do not include improvement ratios,but if some QFD process includes both competitors’ data and improvement ratio, it canalso be a part of the FWs along with customers priority rating.

2.4 HOWs final weightsThe different parts of the HOQ are used to calculate the FWs of technical descriptors(HOWs). In literature, the following two popular ways are used to find the FWs ofHOWs.

Method 1:

FW j ¼Xr

i¼1

Rij £ Pi i ¼ 1; . . . ; r; j ¼ i; . . . ; c ð1Þ

where: R is the relationship matrix; and P is customers priority rating (Franceschiniand Rossetto, 2002; Thakkar et al., 2006; Tan et al., 1998).

Author(s) Low – high Goal Improvement ratio

Tanik (2010), Hochman and O’Connell(1993), Dikmen et al. (2005), Chin et al.(2001), Bouchereau and Rowlands(2000), Hoyleand Chen (2007) 1-5

Goal – next highestlevel chosen ascompareto current level ofcompany

Improvement ratio –goal/companycurrentlevel

Utne (2009) 1-4Jeong and Oh (1998) 1-7

Table II.Table of competitor’s

rating scale, companygoals and improvement

ratio


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Method 2:

FW j ¼Xr

i¼1

Rij £ Pi £ I i i ¼ 1; . . . ; r; j ¼ i; . . . ; c ð2Þ

where: R is the relationship matrix; P is customers priority rating; and I isimprovement ratio ( Jeong and Oh, 1998; Bouchereau and Rowlands, 2000; Hoyle andChen, 2007).

Using these methods, FW ratings are obtained that address the customers’ needs, inorder to design or improve products and services. The FWs then must be prioritised todetermine which technical aspect to tackle in which order. The following approaches forprioritising the FWs have been discussed in literature: analytic hierarchy process (AHP),“fuzzy QFD”, “statistically extended QFD”; and “dynamic QFD” (Mehrjerdi, 2010). Mostpractitioners use customer priority ratings and the relationship matrix to find the FWsof HOWs. Some also make use of competitor’s data in the determination. The finalHOWs weights give the importance of each technical aspect to be resolved. Usually, theweights are ranked in descending order, with the number 1 ranked weight being themost important HOW to resolve, followed by the number 2 ranked weight and so on.Table III shows the customer priority rating (“customer weight”), relationship matrixand the FWs of HOWs in a published example from Tan et al. (1998).

Table IV shows the FWs from Table III sorted into descending order, with H1 as themost important (with priority weight 51) down to H4 as the least (with priority weight 9).We now test the statistical significance of these FWs in relation to the common causevariation underscoring each FW value. That is, we will determine the extent to which the

Technical aspects (HOWs)Customer weights H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12

Voice of customer (WHATs)W1 6 5 0 0 0 1 0 0 0 0 0 0 0W2 3 0 1 5 3 0 0 0 0 0 0 0 0W3 1 0 0 1 0 5 0 0 1 0 0 0 0W4 2 0 5 0 0 0 0 0 0 0 0 0 0W5 4 0 0 0 0 1 0 0 0 5 0 0 0W6 8 0 0 0 0 0 0 3 3 0 5 0 0W7 5 0 0 0 0 0 5 3 0 0 0 0 0W8 7 3 3 0 0 0 0 0 0 0 0 3 5

Final weights 51 34 16 9 15 25 39 25 20 40 21 35

Source: From Tan et al. (1998)Table III.Empirical data for QFD

No. 1 2 3 4 5 6 7 8 9 10 11 12

HOWs H1 H10 H7 H12 H2 H6 H8 H11 H9 H3 H5 H4

Final weights 51 40 39 35 34 25 25 21 20 16 15 9

Table IV.Final weight of HOWsin Table III, sorted intoin descending order

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differences between FWs indicate special cause variation, and therefore are statisticallysignificant.

Hypothesis significance/insignificance testing is a vital aspect of statisticalinference. In our testing of FWs, if the difference between two FWs is found to beinsignificant, then this will imply that although the FW values differ from each other,the variation between these weights is not significantly different to the common cause(random) variation within the relationship matrix data that contributed to the FWvalues. If testing reveals significant differences between FWs, alternatively, then thevariation between FWs is attributable to some special cause and we can infer that oneweight does indeed have priority over another. As we require various differentengineering factors to develop/improve a product or service, then knowing whether ornot two factors are genuinely different from each other in the presence of given datawill be beneficial for engineers and practitioners. This can save time and cost, andimprove the quality of decision making when using QFD. In the next section we willtherefore investigate a statistical procedure to test the statistical significance betweenthe FWs of HOWs.

3. Methodology: testing of FW differences using a parametric bootstrapmethod3.1 Monte Carlo testingMonte Carlo theory was first applied by scientists for the development of nuclearweapons in Las Alamos in 1940, and Monte Carlo methods have various applications invarious disciplines (mathematics, statistics, physics, engineering, chemistry and so on(Kalos and Whitlock, 2009). The approach simulates random numbers based on someprobability distribution, and the random numbers are then used as a data set forstatistical inference. The major use of Monte Carlo simulation is to estimate somefunctions of probability distributions using expectation ( James, 2009). Monte Carlomethods can be used for testing the significance, whereby the significance of a givenstatistic can be assessed by comparing it with a sample of test-statistics obtained bysimulating random samples based on a theoretical model. Monte Carlo methods alsohelp to use bootstrap method in the field of ecology, environmental science, genetics,etc. where focus in on estimation of percentile confidence limits (Manly, 2007).

3.2 Permutation (randomization) testThe permutation test, introduced by Fisher (1971), can be applied to test whether tworandom samples have come from the same population (Kenett and Zacks, 1998).It determines whether any test-statistic under a null hypothesis genuinely signifies adifference between the groups (significant result), or whether the data have comefrom just one group (non-significant result). Under this test, the distribution of thetest-statistic under the null hypothesis is obtained by permuting all possiblearrangements of the possible values of the data points. This leads to obtaining therange of possible values for the test-statistic, which will be a realisation of ourtest-statistic from original data if the null hypothesis holds true. If the test-statisticfrom the original data is extreme in relation to the generated distribution, the nullhypothesis can be rejected. In permutation testing, the main emphasis is therefore onthe data rather than upon underlying assumptions about populations: that is, randomsampling, normality, constant variance and independence (Manly, 2007).


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3.3 Non-parametric bootstrappingBootstrapping helps to draw statistical inferences based on the data given, withoutcomplex assumptions and theory (Kenett and Zacks, 1998). This technique was firstconsidered in a systematic manner by Efron (1979). In non-parametric bootstrappingresampling is conducted with replacement, and resampling the values, each withprobability 1/n, helps to model the unknown population. In permutation testingsampling is done without replacement, whereas in non-parametric bootstrap sampling isdone with replacement. The major use of non-parametric bootstrap to find confidencelimits for population parameters, but it also been used in tests of significance (Manly,2007).

3.4 The parametric bootstrapFinally, instead of using the hypothesised value of the parameter, another approach incomputational inference is to use an estimate of the parameter derived from the sample.In this case, samples can be simulated from some fitted model to obtain a sample oftest-statistics (James, 2009). In the case of QFD, we know the FWs for HOWs are derivedfrom data which is of a qualitative nature, but we do not know about the parent populationnor any assumptions about the population. So we cannot apply traditional parametrichypothesis tests (such as z-test, t-test or F-test). From the previous discussion, we haveillustrated that most relationship matrices use a scale of the form: 1, 3, 9; 1, 3, 10; 1, 2, 3, 5; or1, 3, 5. These have a measure of central tendency (median) value approximately equal to 3.These can be adequately represented by using a (non-parametric) Poisson distributionwith mean of l ¼ 3. In the following illustrations, we therefore use a Poisson distributionwith l ¼ 3 as parametric bootstrap distribution to test the significance of FWs of HOWs,which is best representative in our case.

4. Results4.1 Determining the significance of differences between extreme FW ratingsTable V shows an example of a HOQ relationship matrix data showing customerweights, relationship matrix and the FWs of HOWs, from Masui et al. (2003).

Table VI shows the FWs ranked in ascending order. This more clearlydemonstrates the magnitude of the difference between the highest and lowest FWratings (respectively, H12 and H2).

In the first instance we tested the significance of the difference between theseextreme FWs. The test-statistic is the absolute value or modulus of H12-H2 (denoted asabs (H12-H2)), under the null hypothesis that the technical aspects HOWs H12 and H2

are of same importance.We generated 10,000 samples, each of size 22 £ 18 (the size of relationship matrix)

using a Poisson distribution with l ¼ 3 as the generator, and determined the HOWsFWs for all 10,000 samples in the same way as for the original relationship matrix. Wethen developed a histogram and density plot of the 10,000 resulting abs (H2-H12)values, and found the probability value ( p-value) associated with our observedtest-statistic of abs (H2-H12). In this procedure, if the probability of our observedtest-statistic is less than 5 percent on the theoretical sampling distribution, then thedifference can be considered significant, indicating that there is a significant differencebetween these two FW rating values, and that they can be used as a reliable basis forprioritising action. If the probability of our observed test-statistic is greater than

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Table V.Customers priority

weights, relationshipmatrix and FWs


FW scores

191

5 percent on the theoretical distribution, then there is no statistical evidence that theFW ratings are different.

Figures 2 and 3 show the histogram and density plots for our example. The p-valuewas 0.006, which shows a highly significant difference, implying that H2 and H12 arein fact different. H2 has significantly higher weight than H12, and it is of moreimportance to prioritise this technical aspect to effectively meet the VOC.

No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

HOWsranking

H12 H14 H17 H16 H8 H15 H18 H7 H6 H3 H4 H5 H9 H10 H13 H11 H1 H2

Finalweights

18 27 27 37 39 39 72 78 91 93 115 120 171 171 229 273 276 282Table VI.Ranking of HOWs FWsin ascending order

Figure 2.Histogram for empiricaldistribution of abs (H2-H12)with probability line

Figure 3.Density plot of empiricaldistribution of abs(H2-H12) with probabilityline with p-value ¼ 0.006

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We now present four further empirical examples from literature, with associateddensity plots and p-values for the FWs. Tables VII-X show the HOW ranking and FWs(ranked into descending order), and Figures 4-7 show the associated density plots foreach examples with a line representing the observed difference from highest to lowestFW rating. The p-value is reported below each density plot.

In the preceding examples, Tables VII, IX and X show FWs where there is asignificant difference between the highest and lowest FWs. In these cases, it isappropriate to prioritise the top ranked weight over the lowest ranked weight.Table VIII shows an instance where there is no significant difference between thehighest and lowest ranked weights (respectively H1 ¼ 51 and H4 ¼ 9). In this case, H1

and H4 are values within the range of common cause variation within the HOQ matrix,and it would be inappropriate to prioritise H1 over H4 for subsequent action.

No. 1 2 3 4 5 6 7

HOWs ranking H2 H6 H1 H4 H3 H5 H7

Final weights 129 107 103 99 72 69 41

Source: From Majid and David (1994)Table VII.

Ranked FWs

No. 1 2 3 4 5 6 7 8 9 10 11 12

HOWs ranking H1 H10 H7 H12 H2 H6 H8 H11 H9 H3 H5 H4

Final weights 51 40 39 35 34 25 25 21 20 16 15 9

Source: From Tan et al. (1998)Table VIII.Ranked FWs

No. 1 2 3 4 5 6 7 8 9 10

HOWs ranking H9 H2 H1 H6 H5 H10 H3 H4 H8 H7

Final weights 705 559 494 488 478 452 438 346 268 157

Source: From Jeong and Oh (1998)Table IX.

Ranked FWs

No. 1 2 3 4 5

HOWs ranking H3 H5 H4 H2 H1

Final weights 630 630 270 210 105

Source: From Wang et al. (1998)Table X.

Ranked FWs


FW scores

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Figure 5.Density plot of empiricaldistribution of abs (H1-H4)with probability line withp-value ¼ 0.630

Figure 4.Density plot of empiricaldistribution of abs (H2-H7)with probability line withp-value ¼ 0.0002

Figure 6.Density plot of empiricaldistribution of abs (H9-H7)with probability line andp-value ¼ 0.000

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4.2 Determining the significance of differences between all FW ratingsWe next extended this analysis to consider the significance of differences between allthe FWs, by taking differences of all possible pairs of FWs of HOWs. Following thesame procedure to test the significance of any two, a general programme was writtenusing the statistical software “R” which checked the significance of the difference of allpairs one by one and generated a p-value ( p-values less than 0.05 indicates significancedifferences). For illustration purposes we will consider the FWs of HOWs shown inTable V (Masui et al., 2003).

The null hypothesis (Ho) is that all of the FWs are of the same importance (meaningthat the variation between FWs is due to common cause). This was tested against thealternative hypothesis (HA) that at least one of them is significantly different fromothers (or the variation between FWs is due to special cause) using, for test-statistic,abs (Hi-Hj) where i ¼ 1, 2, . . . 17, j ¼ i þ 1. We again generated 10,000 samples, each ofsize 22 £ 18 (the size of relationship matrix), using Poisson distribution with l ¼ 3 andfound the final rating for HOWs associated with all samples. We the found abs (Hi-Hj)for all samples, and the probability (proportion) of each original abs (Hi-Hj) fromthe resulting empirical distribution of 10,000 abs (Hi-Hj). We observed whether thep-value was less than 0.05, representing a significant difference. For the aboveexample, the following table of p-values resulted (Table XI). The highlighted areashows that the difference is significant.

Table XI reveals that H2 is the most significantly different from others, and H12 theleast significantly different. Between any two HOW factors, in order to reliablydetermine the priority to resolve we can therefore examine the associated p-value. If thep-value is less than 0.05 we can prioritise the HOWs factor with higher FWs. Such asmaller p-value shows that a given FW varies significantly from others due to specialcause, and should be addressed first for resolution.

4.3 Scale robustness checkingAs a final stage in this analysis, we analysed the robustness of the scales used in therelationship matrix. That is, the extent to which the scale adopted affects the magnitude

Figure 7.Density plot of empirical

distribution of abs (H3-H1)with probability line and

p-value ¼ 0.090


FW scores

195

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60.

004

0.00

3H

917

1N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

993

0.28

60.

063

0.05

60.

042

H10

171

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.28

50.

060

0.05

20.

040

H13

229

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.41

60.

384

0.32

3H

11

273

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.94

50.

863

H1

276

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.90

0H

228

2N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A

Table XI.Table of p-values for allcomparisons (abs (Hi-Hj))

IJQRM31,2

196

of differences between influences the FWs. As we have demonstrated, practitioners usedifferent linguistic-numeric scales. In this part of the analysis, we investigated whether alinear or non-linear change in the scale affected the overall ranking of FWs, and whetherthe significance of FWs also remained the same under these conditions.

Beginning with the linear conversion, the relationship matrix is the matrix whichshows the strength of relationship between voice of customers, WHATs (Wi) and voiceof engineers HOWs (Hi). From Masui et al. (2003) we know the strength scale forrelationship matrix 0, 1, 3, 9 has been used to find the FWs shown in Table VI. We madetwo linear changes from 0, 1, 3, 9 to 0, 2, 4, 10; and from 0, 1, 3, 9 to 0, 3, 5, 11 and obtainedthe following two new HOWs FWs ranking in ascending order (Tables XII and XIII).

In Tables XII and XIII when we made a linear change to original scale, we observedthat the FWs changed, but their ranking remained almost the same. Further, thestatistical significance of the final HOWs weights did not substantially (comparingTables AI and AII in Appendix 1). Moving onto the nonlinear conversion, we nextmake two non-linear changes from 0, 1, 3, 9 to 0, 2, 4, 6; and from 0, 1, 3, 9 to 0, 5, 7 andwe obtained the following two new HOWs ranked FWs (Tables XIV and XV).

We in this case, we observed that the nonlinear conversion to the scales changed theFWs, but the ranking again remained virtually unchanged, and the p-values similarly(refer to Appendix 2).

HOWsranking


Finalweights

22 30 32 42 44 62 80 92 104 106 132 136 196 198 266 312 312 324

Table XII.HOWs FWs arranged in

ascending order for scale0, 2, 4, 10

HOWsranking


Finalweights

26 33 37 47 49 85 88 106 117 119 149 152 221 225 303 348 351 366

Table XIII.HOWs FWs arranged in


HOWsranking


Finalweights

21 22 29 29 33 35 56 79 82 83 93 94 157 165 181 216 222 237

Table XV.HOWs FWs arranged in


HOWsranking


Finalweights

18 18 24 26 28 48 54 68 68 70 84 84 132 138 170 192 204 204

Table XIV.HOWs FWs arranged in



FW scores

197

5. ConclusionsIn relation to the first aim of the research, in this paper we have demonstrated that not allof the differences between the FWs of HOW attributes may be significant. Indeed, forone of our literature-derived examples (Tan et al., 1998) we have demonstrated that in thecontext of common cause variation, even the most extreme HOW FWs are notsignificantly different from each other. This finding implies that the engineeringattributes necessary to maximise customer satisfaction may, in the course of a QFDanalysis, be prioritised inappropriately, and action may be taken in respect of one HOWrequirement in preference to another, where there is in fact no statistical differencebetween their ratings. A practical implication of this is that organisations may engage incostly or time consuming activity resulting from the prioritisation of an engineeringattribute, where an attribute requiring less effort or cost may be an equal priority.

For many QFD situations, an application of Pareto’s 80/20 principle will provide apragmatic signpost of the most important engineering factors to prioritise, i.e. the one ortwo which have very much higher FWs than the rest (for example, the literature examplefrom Jeong and Oh (1998), shown earlier in Table IX, shows two extreme FWs that areclearly and distinctly different from each other). Such a rule of thumb would workeffectively in such cases. However, such a decision making criterion lacks statisticalvalidity, and will break down where FW differences are less clearly demarcated. For theexample given by Tan et al. (1998) shown earlier in Table VIII, there are no clearlydistinct FWs. In the absence of a formal and rigorous procedure for determiningsignificance, the practitioner has no real means of determining whether two ratings aredifferent as compared with the common cause variation present in the relationshipmatrix. For QFD to be maximally effective, and in order to overcome this issue, weadvocate that use of a parametric bootstrap testing procedure for FWs can helppractitioners to make more reliable and valid choices when deciding upon which HOWsto prioritise and which to treat as practically equivalent. We recommend that thisapproach can be adopted by engineers and QFD practitioners to enable them to prioritisemore effectively when operating QFD. Although this would be a cumbersome analyticalpractice, software can be easily developed that facilitates this testing procedure.

In relation to our second aim, we have further demonstrated that these findings holdtrue regardless of the choice of rating scale that is applied. That is, differences betweenFWs that are significant will generally remain so regardless of the scale that is applied.This finding means that the choice of QFD rating scale is not critical, givespractitioners relative freedom to continue utilising whichever rating scale has beenfound to best suit their normal QFD procedures and practices.

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Bouchereau, V. and Rowlands, H. (2000), “Methods and techniques to help quality functiondeployment (QFD)”, Benchmarking: An International Journal, Vol. 7 No. 1, pp. 8-20.

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Crowe, T.J. and Cheng, C.C. (1996), “Using quality function deployment in manufacturingstrategic planning”, International Journal of Operations & Production Management, Vol. 16No. 4, pp. 35-48.

Dikmen, I., Talat Birgonul, M. and Kiziltas, S. (2005), “Strategic use of quality functiondeployment (QFD) in the construction industry”, Building and Environment, Vol. 40 No. 2,pp. 245-255.

Efron, B. (1979), “Bootstrap methods: another look at the jacknife”, Annals of Statistics, Vol. 7No. 1, pp. 1-26.

Enriquez, F.T., Osuna, A.J. and Bosch, V.G. (2004), “Prioritising customer needs at spectatorevents: obtaining accuracy at a difficult QFD arena”, The International Journal of Quality& Reliability Management, Vol. 21 No. 9, pp. 984-990.

Fisher, R.A. (1971), The Design of Experiments, Oliver and Boyd, London.

Franceschini, F. and Rossetto, S. (2002), “QFD: an interactive algorithm for the prioritization ofproduct’s technical design characteristics”, Integrated Manufacturing Systems, Vol. 13No. 1, pp. 69-75.

Garver, M.S. (2012), “Improving the house of quality with maximum difference scaling”,International Journal of Quality & Reliability Management, Vol. 29 No. 5, pp. 576-594.

Ghiya, K.K., Bahill, A.T. and Chapman, W.L. (1999), “QFD: validating robustness”, QualityEngineering, Vol. 11 No. 4, pp. 593-611.

Hochman, S.D. and O’Connell, P.A. (1993), “Quality function deployment: using the customer tooutperform the competition on environmental design”, Proceedings of 1993 IEEE InternationalSymposium on Electronics and the Environment, Arlington, VA, 10-12 May, pp. 165-172.

Hoyle, C. and Chen, W. (2007), “Next generation QFD: decision-based product attribute functiondeployment”, paper presented at International Confereence on Engineering Design,ICED’07, Cite Des Sciences Et De L’Industrie, Paris, France, 28-31 August.

James, E.G. (2009), Computational Statistics, Springer, New York, NY.

Jeong, M. and Oh, H. (1998), “Quality function deployment: an extended framework for servicequality and customer satisfaction in the hospitality industry”, International Journal ofHospitality Management, Vol. 17 No. 4, pp. 375-390.

Kalos, M.H. and Whitlock, P.A. (2009), Monte Carlo Methods, Wiley, Hoboken, NJ.

Kenett, R. and Zacks, S. (1998), Modern Industrial Statistics, Design and Control of Quality andReliability, Brooks/Coles Publishing Company, Pacific Grove, CA.

Majid, J. and David, R. (1994), “Total quality management applied to engineering education”,Quality Assurance in Education, Vol. 2 No. 1, pp. 32-40.

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Masui, K., Sakao, T., Kobayashi, M. and Inaba, A. (2003), “Applying quality function deploymentto environmentally conscious design”, International Journal of Quality & ReliabilityManagement, Vol. 20 No. 1, pp. 90-106.

Mehrjerdi, Y.Z. (2010), “Quality function deployment and its extensions”, International Journal ofQuality & Reliability Management, Vol. 27 No. 6, pp. 616-640.

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FW scores

199

Tan, K., Xie, M. and Chia, E. (1998), “Quality function deployment and its use in designinginformation technology systems”, International Journal of Quality & ReliabilityManagement, Vol. 15 No. 6, pp. 634-645.

Tanik, M. (2010), “Improving ‘order handling’ process by using QFD and FMEA methodologies:a case study”, International Journal of Quality & Reliability Management, Vol. 27 No. 4,pp. 404-423.

Thakkar, J., Deshmukh, S. and Shastree, A. (2006), “Total quality management (TQM) inself-financed technical institutions: a quality function deployment (QFD) and force fieldanalysis approach”, Quality Assurance in Education, Vol. 14 No. 1, pp. 54-74.

Utne, I.B. (2009), “Improving the environmental performance of the fishing fleet by use of qualityfunction deployment (QFD)”, Journal of Cleaner Production, Vol. 17 No. 8, pp. 724-731.

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Further reading

Garver, M.S. (2009), “A maximum difference scaling application for customer satisfactionresearchers”, International Journal of Market Research, Vol. 51 No. 4, pp. 481-500.

About the authorsZafar Iqbal is an Assistant Professor of statistics at The Islamia University of Bahawalpur,Pakistan, and a doctoral research student based in the School of Engineering and AdvancedTechnology at Massey University, New Zealand.

Nigel P. Grigg is an Associate Professor (quality systems) in the School of Engineering andAdvanced Technology at Massey University, New Zealand. He leads Massey University’spostgraduate teaching and research-based programmes in the quality systems area.

K. Govindaraju is a Senior Lecturer in statistics in the Institute of Fundamental Sciences atMassey University, New Zealand.

Nicola Campbell-Allen is a Lecturer in quality management in the School of Engineering andAdvanced Technology, Massey University, New Zealand.

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

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Appendix 1

HO

Ws

H12

H17

H14

H16

H15

H8

H18

H7

H6

H3

H4

H5

H10

H9

H13

H1

H11

H2

HO

Ws

FW

s22

3032

4244

6280

9210

410

613

213

619

619

826

631

231

232

4

H12

22N

A0.

879

0.84

40.

703

0.67

50.

455

0.28

00.

200

0.12

80.

125

0.04

60.

035

0.00

20.

002

0.00

00.

000

0.00

00.

000

H17

30N

AN

A0.

963

0.82

90.

783

0.55

10.

347

0.24

80.

178

0.16

10.

063

0.05

30.

003

0.00

10.

000

0.00

00.

000

0.00

0H

14

32N

AN

AN

A0.

849

0.81

90.

590

0.37

80.

271

0.18

40.

167

0.06

70.

053

0.00

10.

002

0.00

00.

000

0.00

00.

000

H16

42N

AN

AN

AN

A0.

965

0.71

00.

487

0.36

70.

255

0.24

90.

105

0.08

00.

006

0.00

40.

000

0.00

00.

000

0.00

0H

15

44N

AN

AN

AN

AN

A0.

740

0.49

50.

367

0.26

00.

250

0.10

60.

087

0.00

40.

004

0.00

00.

000

0.00

00.

000

H8

62N

AN

AN

AN

AN

AN

A0.

744

0.57

60.

442

0.42

30.

191

0.16

90.

013

0.01

10.

001

0.00

00.

000

0.00

0H

18

80N

AN

AN

AN

AN

AN

AN

A0.

813

0.65

20.

621

0.33

10.

299

0.03

20.

031

0.00

10.

000

0.00

00.

000

H7

92N

AN

AN

AN

AN

AN

AN

AN

A0.

820

0.78

40.

455

0.40

50.

054

0.05

40.

002

0.00

00.

000

0.00

0H

610

4N

AN

AN

AN

AN

AN

AN

AN

AN

A0.

957

0.60

80.

559

0.08

50.

084

0.00

40.

000

0.00

00.

000

H3

106

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.62

80.

566

0.09

60.

093

0.00

50.

000

0.00

00.

000

H4

132

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.92

90.

246

0.22

50.

019

0.00

10.

001

0.00

1H

513

6N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

261

0.24

90.

015

0.00

10.

001

0.00

1H

10

196

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.96

00.

192

0.03

60.

030

0.01

6H

919

8N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

219

0.03

80.

036

0.01

9H

13

266

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.40

80.

396

0.28

5H

131

2N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

993

0.81

8H

11

312

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.82

0H

232

4N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A

Table AI.p-value table for

relationship strengthscale 0, 2, 4, 10


FW scores

201

Appendix 2

HO

Ws

H12

H17

H14

H16

H15

H8

H18

H7

H6

H3

H4

H5

H10

H9

H13

H1

H11

H2

HO

Ws

FW

s26

3337

4749

8588

106

117

119

149

152

221

225

303

348

351

366

H12

26N

A0.

892

0.83

20.

691

0.65

60.

268

0.24

30.

142

0.09

40.

087

0.02

10.

019

0.00

00.

000

0.00

00.

000

0.00

00.

000

H17

33N

AN

A0.

932

0.79

00.

768

0.33

20.

307

0.17

50.

127

0.11

80.

033

0.02

90.

000

0.00

10.

000

0.00

00.

000

0.00

0H

14

37N

AN

AN

A0.

846

0.81

50.

376

0.33

60.

201

0.13

80.

127

0.04

30.

031

0.00

20.

001

0.00

00.

000

0.00

00.

000

H16

47N

AN

AN

AN

A0.

964

0.48

10.

445

0.27

60.

198

0.18

40.

059

0.04

60.

002

0.00

10.

000

0.00

00.

000

0.00

0H

15

49N

AN

AN

AN

AN

A0.

500

0.47

30.

292

0.20

90.

209

0.06

50.

056

0.00

20.

002

0.00

00.

000

0.00

00.

000

H8

85N

AN

AN

AN

AN

AN

A0.

945

0.69

90.

544

0.52

90.

227

0.20

80.

015

0.01

00.

000

0.00

00.

000

0.00

0H

18

88N

AN

AN

AN

AN

AN

AN

A0.

740

0.59

20.

559

0.26

80.

231

0.01

50.

015

0.00

00.

000

0.00

00.

000

H7

106

NA

NA

NA

NA

NA

NA

NA

NA

0.83

70.

806

0.42

30.

400

0.03

20.

032

0.00

00.

000

0.00

00.

000

H6

117

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.96

20.

552

0.52

50.

056

0.04

80.

001

0.00

00.

000

0.00

0H

311

9N

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

582

0.54

00.

070

0.05

10.

001

0.00

00.

000

0.00

0H

414

9N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

951

0.18

20.

156

0.00

50.

001

0.00

00.

000

H5

152

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.19

90.

179

0.00

70.

000

0.00

00.

000

H10

221

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.92

70.

145

0.01

60.

020

0.00

9H

922

5N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

150

0.02

10.

020

0.01

1H

13

303

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.40

40.

388

0.25

2H

134

8N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

948

0.73

7H

11

351

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.77

6H

236

6N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A

Table AII.p-value table forrelationship strengthscale 0, 3, 5, 11

IJQRM31,2

202

HO

Ws

H17

H12

H14

H16

H15

H18

H8

H6

H7

H3

H4

H5

H10

H9

H13

H1

H2

H11

HO

Ws

FW

s18

1824

2628

4854

6868

7084

8413

213

817

019

220

420

4

H17

18N

A0.

992

0.90

70.

870

0.84

80.

575

0.49

00.

350

0.35

00.

334

0.22

10.

215

0.03

60.

027

0.00

50.

002

0.00

10.

001

H12

18N

AN

A0.

906

0.87

90.

855

0.58

10.

501

0.35

50.

349

0.33

30.

223

0.22

90.

035

0.02

90.

007

0.00

20.

001

0.00

1H

14

24N

AN

AN

A0.

961

0.93

60.

658

0.57

00.

420

0.41

70.

394

0.26

50.

262

0.04

70.

038

0.00

90.

002

0.00

10.

001

H16

26N

AN

AN

AN

A0.

962

0.68

90.

601

0.43

90.

432

0.42

30.

276

0.28

40.

050

0.04

00.

008

0.00

20.

001

0.00

1H

15

28N

AN

AN

AN

AN

A0.

708

0.62

00.

461

0.45

90.

437

0.30

30.

302

0.05

70.

046

0.01

00.

003

0.00

10.

001

H18

48N

AN

AN

AN

AN

AN

A0.

908

0.70

30.

707

0.67

80.

507

0.50

90.

121

0.10

00.

026

0.01

00.

004

0.00

4H

854

NA

NA

NA

NA

NA

NA

NA

0.79

00.

786

0.75

50.

575

0.57

60.

148

0.12

70.

033

0.00

90.

005

0.00

7H

668

NA

NA

NA

NA

NA

NA

NA

NA

0.99

20.

959

0.76

30.

757

0.22

40.

200

0.06

00.

023

0.01

10.

014

H7

68N

AN

AN

AN

AN

AN

AN

AN

AN

A0.

963

0.76

40.

759

0.22

70.

197

0.06

10.

025

0.01

30.

012

H3

70N

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

797

0.78

40.

245

0.21

20.

065

0.02

50.

012

0.01

5H

484

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.99

30.

369

0.31

30.

114

0.04

40.

026

0.02

6H

584

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.36

80.

316

0.11

20.

048

0.02

70.

029

H10

132

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.90

60.

477

0.26

80.

180

0.17

8H

913

8N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

550

0.32

00.

226

0.22

7H

13

170

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.67

80.

524

0.52

4H

119

2N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

824

0.81

9H

220

4N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

994

H11

204

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

Table AIII.p-value table for

relationship strengthscale 0, 2, 4, 6


FW scores

203

HO

Ws

H17

H12

H14

H16

H15

H8

H18

H6

H7

H3

H4

H5

H10

H9

H13

H1

H2

H11

HO

Ws

FW

s21

2229

2933

3556

7982

8393

9415

716

518

121

622

223

7

H17

21N

A0.

977

0.87

70.

876

0.82

50.

796

0.52

40.

277

0.25

90.

251

0.18

50.

173

0.01

10.

011

0.00

30.

000

0.00

00.

000

H12

22N

AN

A0.

894

0.89

50.

833

0.81

00.

519

0.29

80.

275

0.26

50.

195

0.18

70.

016

0.01

00.

005

0.00

00.

001

0.00

0H

14

29N

AN

AN

A0.

994

0.93

60.

903

0.61

40.

350

0.31

80.

324

0.24

00.

230

0.01

60.

013

0.00

50.

001

0.00

10.

000

H16

29N

AN

AN

AN

A0.

937

0.90

80.

618

0.35

70.

328

0.32

00.

228

0.23

00.

018

0.01

40.

005

0.00

10.

001

0.00

0H

15

33N

AN

AN

AN

AN

A0.

963

0.67

70.

401

0.37

00.

358

0.27

10.

260

0.02

00.

017

0.00

70.

001

0.00

00.

000

H8

35N

AN

AN

AN

AN

AN

A0.

695

0.41

50.

380

0.37

30.

279

0.26

90.

022

0.01

80.

006

0.00

10.

000

0.00

0H

18

56N

AN

AN

AN

AN

AN

AN

A0.

661

0.63

30.

612

0.49

30.

478

0.06

00.

049

0.02

50.

003

0.00

30.

001

H6

79N

AN

AN

AN

AN

AN

AN

AN

A0.

949

0.93

40.

797

0.77

80.

145

0.11

30.

059

0.01

30.

009

0.00

5H

782

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.97

70.

835

0.81

70.

163

0.12

80.

069

0.01

40.

011

0.00

6H

383

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.84

30.

834

0.17

30.

132

0.07

30.

013

0.01

00.

005

H4

93N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

979

0.23

70.

188

0.10

70.

024

0.01

60.

008

H5

94N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

240

0.19

40.

108

0.02

60.

019

0.00

9H

10

157

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.87

20.

654

0.27

10.

222

0.13

7H

916

5N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

761

0.34

00.

295

0.19

2H

13

181

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

0.50

60.

454

0.30

7H

121

6N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

905

0.68

3H

222

2N

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

AN

A0.

773

H11

237

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

Table AIV.p-value table forrelationship strengthscale 0, 1, 5, 7

IJQRM31,2

204

ijqrm (2014) statistical comparison of final scores in qfd

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