IRJET- Testing Improvement in Business Intelligence Area
IJQRM (2014) Statistical Comparison of Final Scores In QFD
1. QUALITY PAPER
Statistical comparison of final
weight scores in quality function
deployment (QFD) studies
Zafar Iqbal and Nigel P. Grigg
School of Engineering and Advanced Technology, Massey University,
Palmerston North, New Zealand
K. Govindaraju
Institute of Fundamental Sciences, Massey University, Palmerston North,
New Zealand, and
Nicola Campbell-Allen
School 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 the
customer” into engineering/technical specifications (HOWs) to be followed in designing of products or
services. For the method to be effective, QFD practitioners need to be able to accurately differentiate
between 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 are
significantly different and investigate the robustness of different rating scales used in QFD practice in
contributing to these differences.
Design/methodology/approach – Using a range of published QFD examples, the paper uses a
parametric bootstrap testing procedure to test the significance of the differences between the FWs by
generating simulated random samples based on a theoretical probability model. The paper then
determines the significance or otherwise of the differences between: the two most extreme FWs and all
pairs of FWs. Finally, the paper checks the robustness of different attribute rating scales (linear vs
non-linear) in the context of these testing procedures.
Findings – The paper demonstrates that not all of the differences that exist between the FWs of
HOW attributes are in fact significant. In the absence of such a procedure, there is no reliable
analytical basis for QFD practitioners to determine whether FWs are significantly different, and they
may wrongly prioritise one engineering attribute over another.
Originality/value – This is the first article to test the significance of the differences between FWs of
HOWs 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. Introduction
Quality function deployment (QFD) is a methodology used to translate the “voice of
the 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 2012
Revised 4 June 2013
Accepted 5 June 2013
International Journal of Quality &
Reliability Management
Vol. 31 No. 2, 2014
pp. 184-204
q Emerald Group Publishing Limited
0265-671X
DOI 10.1108/IJQRM-06-2013-0092
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31,2
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2. design of products or services. Akao (1990) has reported that when appropriately
applied, QFD has been effective in substantially reducing product development lead
times. The main goal in implementing QFD is to improve the quality of the product or
service based on customer-defined requirements and expectations. Although QFD is a
popular and widely used technique, as Enriquez et al. (2004 cited in Garver, 2012) point
out, on-going research still seeks to examine the assumptions and methods used within
QFD with a view to continuously improving the methodology and there is a need to be
able to accurately determine importance scores for the customer because with inaccurate
data “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 methodology
is intended to effectively deploy the VOC. It consists of distinct “rooms” (denoted by
rectangles), topped by a “roof” (denoted by the triangle at the top). Engineers and other
product/service development practitioners collect data from customers relating to their
requirements and desires (WHATs). These are weighted for importance, and assigned
a customer priority rating. They are then translated into engineering factors and
requirements (HOWs). The triangular elements shown are used to record the strengths
of intercorrelations between the WHATs or the HOWs. The relationship matrix
records the strengths of the correlations between WHATs and HOWs. Data on
competitor performance is further integrated, and a vector of final weights (FWs) for
engineering priorities (HOWs) can be calculated (the bottom element of the HOQ).
Figure 1.
A typical HOQ
Statistical
comparison of
FW scores
185
3. For the method to be effective, therefore, the differences observed between the FWs
scores should be meaningful and statistically significant. Otherwise, the FW scores
will not provide a valid and reliable basis for the determination of engineering
priorities in the design of the product or service.
The first aim of the research which is presented in this paper was to determine
whether the resulting FWs in a number of QFD examples are in fact (statistically)
significantly different from each other, as measured against the background level of
common cause (random) variation that exists within the relationship matrix from which
they have been derived. Using a range of empirical examples taken from literature, we
use a parametric bootstrap testing procedure to test the statistical significance of the
differences between the FWs via two testing procedures: first, we test the statistical
significance 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, but
QFD practice employs a wide range of rating scales. The second aim of our research
was therefore to investigate the robustness of relationship scales by applying different
linear and non-linear changes to the originally reported rating scales. Our findings in
relation to these aims, as reported in this paper, have implications for practitioners,
academics and others involved in QFD research, in determining the degree of
importance to place on FWs.
2. QFD and its factors
In developing a HOQ, the customer, competitor and engineering data that populate the
matrices and vectors are of an inherently qualitative nature, and are operationalised
into numerical values through rating scales that transform linguistic criteria into
numeric data. A wide variety of practice is observable in the application of these
linguistic-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 most
closely aligns with the perceived “reality”; but there is also wide variation in the scales
that are applied by practitioners. In the following section we explicate the commonly
used linguistic-numeric scales and outline their use in QFD.
2.1 Customer priority rating scale
Once a QFD developer has converted the VOC into specific requirements (WHATs),
customers are asked to assign priority ratings to those WHATs. The resulting customer
priority ratings are used, together with relationship matrix, to derive the FWs of HOWs
(the engineering/technical criteria required to achieve the WHATs). Table I summarises
several different priority rating scales for importance of WHATs as reported in literature.
Authors Customers priority rating scale
Bouchereau and Rowlands (2000) 1-3
Dikmen et al. (2005) 1-9
Tanik (2010) 1-10
Majid and David (1994) and Utne (2009) 1-5
Olewnik and Lewis (2008), Masui et al. (2003) 1, 3, 9
Park and Kim (1998) Proportions of 1
Table I.
Table of customers
rating scale
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4. 2.2 Relationship matrix
In the HOQ, the relationship matrix denotes the strength of relationship between
WHATs and HOWs. In literature, three-point or five-point linguistic-numeric scales are
mostly used for different strengths of relationships. For example: for “weak”,
“medium” and “strong” relationship (Tan et al., 1998), used 1, 3, 5, respectively; (Jeong
and 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 see
five-point scales 1, 3, 5, 7, 9 reported by Chan and Wu (1998), and 1, 2, 3, 4, 5 by Crowe
and Cheng (1996) to represent “very weak”, “weak”, “medium”, “strong” and “very
strong” relationships. From these and other scales we have observed, the scales are
generally based on a median value of 3. For our study these scales will play an
important role in testing the FWs, as described in Section 1.4.
2.3 Competitor’s data and improvement ratio
Although some practitioners use and some do not use competitors’ data, it is
considered good practice to look at the competitors in the market and make this
assessment part of a robust QFD process (Jeong and Oh, 1998). Table II shows the
most widely used qualitative scales of company’s position in market with customer’s
point of view. Competitors’ data not only contribute to the FWs of HOWs, but also help
to determine current position in the market and to set future goals. The improvement
ratio, also shown in Table II, may substantially change the ranking of FWs. The
empirical 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 can
also be a part of the FWs along with customers priority rating.
2.4 HOWs final weights
The 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 of
HOWs.
Method 1:
FWj ¼
Xr
i¼1
Rij £ Pi i ¼ 1; . . . ; r; j ¼ i; . . . ; c ð1Þ
where: R is the relationship matrix; and P is customers priority rating (Franceschini
and 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), Hoyle
and Chen (2007) 1-5
Goal – next highest
level chosen as
compare
to current level of
company
Improvement ratio –
goal/company
current
level
Utne (2009) 1-4
Jeong and Oh (1998) 1-7
Table II.
Table of competitor’s
rating scale, company
goals and improvement
ratio
Statistical
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187
5. Method 2:
FWj ¼
Xr
i¼1
Rij £ Pi £ Ii i ¼ 1; . . . ; r; j ¼ i; . . . ; c ð2Þ
where: R is the relationship matrix; P is customers priority rating; and I is
improvement ratio (Jeong and Oh, 1998; Bouchereau and Rowlands, 2000; Hoyle and
Chen, 2007).
Using these methods, FW ratings are obtained that address the customers’ needs, in
order to design or improve products and services. The FWs then must be prioritised to
determine which technical aspect to tackle in which order. The following approaches for
prioritising the FWs have been discussed in literature: analytic hierarchy process (AHP),
“fuzzy QFD”, “statistically extended QFD”; and “dynamic QFD” (Mehrjerdi, 2010). Most
practitioners use customer priority ratings and the relationship matrix to find the FWs
of HOWs. Some also make use of competitor’s data in the determination. The final
HOWs weights give the importance of each technical aspect to be resolved. Usually, the
weights are ranked in descending order, with the number 1 ranked weight being the
most important HOW to resolve, followed by the number 2 ranked weight and so on.
Table III shows the customer priority rating (“customer weight”), relationship matrix
and 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 the
most 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 cause
variation 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 0
W2 3 0 1 5 3 0 0 0 0 0 0 0 0
W3 1 0 0 1 0 5 0 0 1 0 0 0 0
W4 2 0 5 0 0 0 0 0 0 0 0 0 0
W5 4 0 0 0 0 1 0 0 0 5 0 0 0
W6 8 0 0 0 0 0 0 3 3 0 5 0 0
W7 5 0 0 0 0 0 5 3 0 0 0 0 0
W8 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 HOWs
in Table III, sorted into
in descending order
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6. differences between FWs indicate special cause variation, and therefore are statistically
significant.
Hypothesis significance/insignificance testing is a vital aspect of statistical
inference. In our testing of FWs, if the difference between two FWs is found to be
insignificant, 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 FW
values. If testing reveals significant differences between FWs, alternatively, then the
variation between FWs is attributable to some special cause and we can infer that one
weight does indeed have priority over another. As we require various different
engineering factors to develop/improve a product or service, then knowing whether or
not two factors are genuinely different from each other in the presence of given data
will be beneficial for engineers and practitioners. This can save time and cost, and
improve the quality of decision making when using QFD. In the next section we will
therefore investigate a statistical procedure to test the statistical significance between
the FWs of HOWs.
3. Methodology: testing of FW differences using a parametric bootstrap
method
3.1 Monte Carlo testing
Monte Carlo theory was first applied by scientists for the development of nuclear
weapons in Las Alamos in 1940, and Monte Carlo methods have various applications in
various disciplines (mathematics, statistics, physics, engineering, chemistry and so on
(Kalos and Whitlock, 2009). The approach simulates random numbers based on some
probability distribution, and the random numbers are then used as a data set for
statistical inference. The major use of Monte Carlo simulation is to estimate some
functions of probability distributions using expectation (James, 2009). Monte Carlo
methods can be used for testing the significance, whereby the significance of a given
statistic can be assessed by comparing it with a sample of test-statistics obtained by
simulating random samples based on a theoretical model. Monte Carlo methods also
help 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) test
The permutation test, introduced by Fisher (1971), can be applied to test whether two
random samples have come from the same population (Kenett and Zacks, 1998).
It determines whether any test-statistic under a null hypothesis genuinely signifies a
difference between the groups (significant result), or whether the data have come
from just one group (non-significant result). Under this test, the distribution of the
test-statistic under the null hypothesis is obtained by permuting all possible
arrangements of the possible values of the data points. This leads to obtaining the
range of possible values for the test-statistic, which will be a realisation of our
test-statistic from original data if the null hypothesis holds true. If the test-statistic
from the original data is extreme in relation to the generated distribution, the null
hypothesis can be rejected. In permutation testing, the main emphasis is therefore on
the data rather than upon underlying assumptions about populations: that is, random
sampling, normality, constant variance and independence (Manly, 2007).
Statistical
comparison of
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189
7. 3.3 Non-parametric bootstrapping
Bootstrapping helps to draw statistical inferences based on the data given, without
complex assumptions and theory (Kenett and Zacks, 1998). This technique was first
considered in a systematic manner by Efron (1979). In non-parametric bootstrapping
resampling is conducted with replacement, and resampling the values, each with
probability 1/n, helps to model the unknown population. In permutation testing
sampling is done without replacement, whereas in non-parametric bootstrap sampling is
done with replacement. The major use of non-parametric bootstrap to find confidence
limits for population parameters, but it also been used in tests of significance (Manly,
2007).
3.4 The parametric bootstrap
Finally, instead of using the hypothesised value of the parameter, another approach in
computational 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 of
test-statistics (James, 2009). In the case of QFD, we know the FWs for HOWs are derived
from data which isof a qualitative nature,but we do not know about the parent population
nor any assumptions about the population. So we cannot apply traditional parametric
hypothesis tests (such as z-test, t-test or F-test). From the previous discussion, we have
illustrated that most relationshipmatrices use a scale ofthe form:1,3, 9;1,3,10;1,2,3, 5;or
1, 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 distribution
with mean of l ¼ 3. In the following illustrations, we therefore use a Poisson distribution
with l ¼ 3 as parametric bootstrap distribution to test the significance of FWs of HOWs,
which is best representative in our case.
4. Results
4.1 Determining the significance of differences between extreme FW ratings
Table V shows an example of a HOQ relationship matrix data showing customer
weights, relationship matrix and the FWs of HOWs, from Masui et al. (2003).
Table VI shows the FWs ranked in ascending order. This more clearly
demonstrates the magnitude of the difference between the highest and lowest FW
ratings (respectively, H12 and H2).
In the first instance we tested the significance of the difference between these
extreme FWs. The test-statistic is the absolute value or modulus of H12-H2 (denoted as
abs (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 HOWs
FWs for all 10,000 samples in the same way as for the original relationship matrix. We
then 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 observed
test-statistic of abs (H2-H12). In this procedure, if the probability of our observed
test-statistic is less than 5 percent on the theoretical sampling distribution, then the
difference can be considered significant, indicating that there is a significant difference
between these two FW rating values, and that they can be used as a reliable basis for
prioritising action. If the probability of our observed test-statistic is greater than
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9. 5 percent on the theoretical distribution, then there is no statistical evidence that the
FW ratings are different.
Figures 2 and 3 show the histogram and density plots for our example. The p-value
was 0.006, which shows a highly significant difference, implying that H2 and H12 are
in fact different. H2 has significantly higher weight than H12, and it is of more
importance 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
HOWs
ranking
H12 H14 H17 H16 H8 H15 H18 H7 H6 H3 H4 H5 H9 H10 H13 H11 H1 H2
Final
weights
18 27 27 37 39 39 72 78 91 93 115 120 171 171 229 273 276 282
Table VI.
Ranking of HOWs FWs
in ascending order
Figure 2.
Histogram for empirical
distributionofabs(H2-H12)
with probability line
Figure 3.
Density plot of empirical
distribution of abs
(H2-H12) with probability
line with p-value ¼ 0.006
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10. We now present four further empirical examples from literature, with associated
density 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 for
each examples with a line representing the observed difference from highest to lowest
FW rating. The p-value is reported below each density plot.
In the preceding examples, Tables VII, IX and X show FWs where there is a
significant difference between the highest and lowest FWs. In these cases, it is
appropriate to prioritise the top ranked weight over the lowest ranked weight.
Table VIII shows an instance where there is no significant difference between the
highest 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
Statistical
comparison of
FW scores
193
11. Figure 5.
Density plot of empirical
distribution of abs (H1-H4)
with probability line with
p-value ¼ 0.630
Figure 4.
Density plot of empirical
distribution of abs (H2-H7)
with probability line with
p-value ¼ 0.0002
Figure 6.
Density plot of empirical
distribution of abs (H9-H7)
with probability line and
p-value ¼ 0.000
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12. 4.2 Determining the significance of differences between all FW ratings
We next extended this analysis to consider the significance of differences between all
the FWs, by taking differences of all possible pairs of FWs of HOWs. Following the
same procedure to test the significance of any two, a general programme was written
using the statistical software “R” which checked the significance of the difference of all
pairs one by one and generated a p-value ( p-values less than 0.05 indicates significance
differences). For illustration purposes we will consider the FWs of HOWs shown in
Table V (Masui et al., 2003).
The null hypothesis (Ho) is that all of the FWs are of the same importance (meaning
that the variation between FWs is due to common cause). This was tested against the
alternative hypothesis (HA) that at least one of them is significantly different from
others (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 of
size 22 £ 18 (the size of relationship matrix), using Poisson distribution with l ¼ 3 and
found 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) from
the resulting empirical distribution of 10,000 abs (Hi-Hj). We observed whether the
p-value was less than 0.05, representing a significant difference. For the above
example, the following table of p-values resulted (Table XI). The highlighted area
shows that the difference is significant.
Table XI reveals that H2 is the most significantly different from others, and H12 the
least significantly different. Between any two HOW factors, in order to reliably
determine the priority to resolve we can therefore examine the associated p-value. If the
p-value is less than 0.05 we can prioritise the HOWs factor with higher FWs. Such a
smaller p-value shows that a given FW varies significantly from others due to special
cause, and should be addressed first for resolution.
4.3 Scale robustness checking
As a final stage in this analysis, we analysed the robustness of the scales used in the
relationship 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
Statistical
comparison of
FW scores
195
14. of differences between influences the FWs. As we have demonstrated, practitioners use
different linguistic-numeric scales. In this part of the analysis, we investigated whether a
linear or non-linear change in the scale affected the overall ranking of FWs, and whether
the significance of FWs also remained the same under these conditions.
Beginning with the linear conversion, the relationship matrix is the matrix which
shows the strength of relationship between voice of customers, WHATs (Wi) and voice
of engineers HOWs (Hi). From Masui et al. (2003) we know the strength scale for
relationship matrix 0, 1, 3, 9 has been used to find the FWs shown in Table VI. We made
two linear changes from 0, 1, 3, 9 to 0, 2, 4, 10; and from 0, 1, 3, 9 to 0, 3, 5, 11 and obtained
the 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 observed
that the FWs changed, but their ranking remained almost the same. Further, the
statistical significance of the final HOWs weights did not substantially (comparing
Tables AI and AII in Appendix 1). Moving onto the nonlinear conversion, we next
make two non-linear changes from 0, 1, 3, 9 to 0, 2, 4, 6; and from 0, 1, 3, 9 to 0, 5, 7 and
we 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 the
FWs, but the ranking again remained virtually unchanged, and the p-values similarly
(refer to Appendix 2).
HOWs
ranking
H12 H17 H14 H16 H15 H8 H18 H7 H6 H3 H4 H5 H10 H9 H13 H1 H11 H2
Final
weights
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 scale
0, 2, 4, 10
HOWs
ranking
H12 H17 H14 H16 H15 H8 H18 H7 H6 H3 H4 H5 H10 H9 H13 H1 H11 H2
Final
weights
26 33 37 47 49 85 88 106 117 119 149 152 221 225 303 348 351 366
Table XIII.
HOWs FWs arranged in
ascending order for scale
0, 3, 5, 11
HOWs
ranking
H17 H12 H14 H16 H15 H8 H18 H6 H7 H3 H4 H5 H10 H9 H13 H1 H2 H11
Final
weights
21 22 29 29 33 35 56 79 82 83 93 94 157 165 181 216 222 237
Table XV.
HOWs FWs arranged in
ascending order for scale
0, 1, 5, 7
HOWs
ranking
H17 H12 H14 H16 H15 H18 H8 H6 H7 H3 H4 H5 H10 H9 H13 H1 H2 H11
Final
weights
18 18 24 26 28 48 54 68 68 70 84 84 132 138 170 192 204 204
Table XIV.
HOWs FWs arranged in
ascending order for scale
0, 2, 4, 6
Statistical
comparison of
FW scores
197
15. 5. Conclusions
In relation to the first aim of the research, in this paper we have demonstrated that not all
of the differences between the FWs of HOW attributes may be significant. Indeed, for
one of our literature-derived examples (Tan et al., 1998) we have demonstrated that in the
context of common cause variation, even the most extreme HOW FWs are not
significantly different from each other. This finding implies that the engineering
attributes necessary to maximise customer satisfaction may, in the course of a QFD
analysis, be prioritised inappropriately, and action may be taken in respect of one HOW
requirement in preference to another, where there is in fact no statistical difference
between their ratings. A practical implication of this is that organisations may engage in
costly or time consuming activity resulting from the prioritisation of an engineering
attribute, 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 a
pragmatic signpost of the most important engineering factors to prioritise, i.e. the one or
two which have very much higher FWs than the rest (for example, the literature example
from Jeong and Oh (1998), shown earlier in Table IX, shows two extreme FWs that are
clearly and distinctly different from each other). Such a rule of thumb would work
effectively in such cases. However, such a decision making criterion lacks statistical
validity, and will break down where FW differences are less clearly demarcated. For the
example given by Tan et al. (1998) shown earlier in Table VIII, there are no clearly
distinct FWs. In the absence of a formal and rigorous procedure for determining
significance, the practitioner has no real means of determining whether two ratings are
different as compared with the common cause variation present in the relationship
matrix. For QFD to be maximally effective, and in order to overcome this issue, we
advocate that use of a parametric bootstrap testing procedure for FWs can help
practitioners to make more reliable and valid choices when deciding upon which HOWs
to prioritise and which to treat as practically equivalent. We recommend that this
approach can be adopted by engineers and QFD practitioners to enable them to prioritise
more effectively when operating QFD. Although this would be a cumbersome analytical
practice, software can be easily developed that facilitates this testing procedure.
In relation to our second aim, we have further demonstrated that these findings hold
true regardless of the choice of rating scale that is applied. That is, differences between
FWs 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, gives
practitioners relative freedom to continue utilising whichever rating scale has been
found to best suit their normal QFD procedures and practices.
References
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About the authors
Zafar 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 Advanced
Technology at Massey University, New Zealand.
Nigel P. Grigg is an Associate Professor (quality systems) in the School of Engineering and
Advanced Technology at Massey University, New Zealand. He leads Massey University’s
postgraduate teaching and research-based programmes in the quality systems area.
K. Govindaraju is a Senior Lecturer in statistics in the Institute of Fundamental Sciences at
Massey University, New Zealand.
Nicola Campbell-Allen is a Lecturer in quality management in the School of Engineering and
Advanced Technology, Massey University, New Zealand.
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