IJPPM (2015) Enhancing Prioritisation of Technical Attributes in QFD

International Journal of Productivity and Performance Management
Enhancing prioritisation of technical attributes in quality function deployment
Zafar Iqbal Nigel Peter Grigg K. Govindaraju Nicola Marie Campbell-Allen
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Enhancing prioritisation of
technical attributes in quality
function deployment
Zafar Iqbal and Nigel P. Grigg
School of Engineering & Advanced Technology, Massey University,
Palmerston North, New Zealand
K. Govindaraju
Institute of Fundamental Sciences, Massey University,
Palmerston North, New Zealand, and
Nicola Marie Campbell-Allen
School of Engineering & Advanced Technology, Massey University,
Palmerston North, New Zealand
Abstract
Purpose – Quality function deployment (QFD) is a planning methodology to improve products,
services and their associated processes by ensuring that the voice of the customer has been effectively
deployed through specified and prioritised technical attributes (TAs). The purpose of this paper is two
ways: to enhance the prioritisation of TAs: computer simulation significance test; and computer
simulation confidence interval. Both are based on permutation sampling, bootstrap sampling and
parametric bootstrap sampling of given empirical data.
Design/methodology/approach – The authors present a theoretical case for the use permutation
sampling, bootstrap sampling and parametric bootstrap sampling. Using a published case study the
authors demonstrate how these can be applied on given empirical data to generate a theoretical
population. From this the authors describe a procedure to decide upon which TAs have significantly
different priority, and also estimate confidence intervals from the theoretical simulated populations.
Findings – First, the authors demonstrate not only parametric bootstrap is useful to simulate
theoretical populations. The authors can also employ permutation sampling and bootstrap sampling to
generate theoretical populations. Then the authors obtain the results from these three approaches.
qThe authors describe why there is a difference in results of permutation sampling, bootstrap and
parametric bootstrap sampling. Practitioners can employ any approach, it depends how much
variation in FWs is required by quality assurance division.
Originality/value – Using these methods provides QFD practitioners with a robust and reliable
method for determining which TAs should be selected for attention in product and service design. The
explicit selection of TAs will help to achieve maximum customer satisfaction, and save time and
money, which are the ultimate objectives of QFD.
Keywords Quality function deployment, Central-limit theorem, Confidence interval,
Folded normal distribution, Parametric bootstrapping
Paper type Research paper
1. Introduction
Quality function deployment (QFD) is an important product/service development
methodology which provides a way for its practitioners to understand customer needs
and demands for a product or service, and transform this information into required
or desirable technical attributes (Li et al., 2012). Han et al. (2001) describe QFD as an
essential management tool for guaranteeing quality in products. Schaal and Slabey
(1991), Griffin and Hauser (1993) and An et al. (2008) argue further that QFD
International Journal of
Productivity and Performance
Management
Vol. 64 No. 3, 2015
pp. 398-415
© Emerald Group Publishing Limited
1741-0401
DOI 10.1108/IJPPM-10-2014-0156
Received 9 October 2014
Revised 9 October 2014
Accepted 16 December 2014
The current issue and full text archive of this journal is available on Emerald Insight at:
www.emeraldinsight.com/1741-0401.htm
398
IJPPM
64,3

methodology not only helps in manufacturing, it also helps in the planning, designing
and processing stages of the product. To approach the process systematically, QFD
utilises a collection of matrices and vectors collectively referred to as the house of
quality (HOQ). Named after its resemblance to an actual house, the HOQ comprises
different “rooms” (sections) containing summarised information about customers’
requirements, engineering attributes, competitor ratings, etc. Figure 1 illustrates the
important sections of QFD HOQ.
In order to satisfy customers’ needs and demands, the technical team suggests
engineering or technical attributes (TAs) in relation to a product or service. The basic
purpose of the QFD methodology is to quantify “final weights” (FWs) for these TAs, which
represent an ordering of engineering priorities to satisfy these. The prioritisation facilitates
ordering of TAs from the most to the least important (Gunasekaran et al., 2006; Stehn
and Bergström, 2002; Crowe and Cheng, 1996). Once the prioritisation process has been
finalised then the design team needs to tackle the TAs from an engineering or process
perspective. Therefore the prioritisation-based undertaking of TAs plays a crucial role in
making successful product/services within short time frames and at minimum cost.
Researchers and practitioners have made various attempts to improve QFD. Some
researchers have enriched QFD by working on linguistic-numeric scales while others
Voice of Customer Customers
Rating
Technical Attributes (TAs)
VOC 1 High Δ
VOC 2
Very High Δ …
…
…
…VOC 3 Low
VOC N Very Low Δ … Δ
Very low 1
Low 2
Moderate 3
Strong 4
Correlations
(TAs)
Weak Δ 1
Moderate 3
W1 W2 W3
WM
Technical section
R
elationship
M
atrix
Voice
of Custom
ers
Correlations(VOCs)
…Final Weights
Prioritisation 2 6 1 … 3
Relationship Matrix
Customers Rating
TA1 TA2 TA3
TAM
Strong 9
Very Strong 5
Figure 1.
An example of
quality function
deployment, house
of quality
399
Enhancing
prioritisation
of technical
attributes

have introduced hybrid approaches to increase the reliability of results. For example
Garver (2012) introduced maximum scaling difference for precise identification of
customers’ importance ratings. Matzler and Hinterhuber (1998) suggested integration
of the Kano model with QFD to achieve maximum customer satisfaction. The analytic
hierarchy process (AHP) structure is further included within the QFD framework
by De Felice and Petrillo (2011) who presented a joint QFD-AHP methodology for
multiple choice decision analysis, whilst Lin et al. (2010) integrate QFD with the
analytic network process (ANP) to enhance linguistic preferences. Khoo and Ho (1996),
and Zhou (1998) used fuzzy framework, while Verma and Knezevic (1996) applied
weighted fuzzy approach to control uncertainties and lack of quantitative scales.
In order to obtain better results some researchers used QFD along with other
approaches, for example Sahney et al. (2004) adopted a joint QFD and service quality
(SERVQUAL) approch in the field of higher education. These new theories and
heuristics tend towards the quantification of FWs for the TAs. However, simple
numeric measures of FWs may not in all cases be sufficient, as it is possible for the
difference between two TAs to be merely a manifestation of random variation. As one
development intended to develop a consistent basis for reliably distinguishing between
the priority ranking of TAs, Iqbal et al. (2014) proposed a methodology to quantify the
statistical significance of the difference between any two TAs based on empirical
data given in a HOQ.
In this paper, we aim to extend the procedure adopted by Iqbal et al. (2014) to
generate a theoretical population for parametric bootstrapping (based on the Poisson
distribution). We also simulate a theoretical population by bootstrap and permutation
sampling, and then use these to investigate the nature of the difference between FWs of
TAs (d). Since there is a close relationship between significance tests and confidence
intervals, we employ both methods in order to compare their results: significant
tests help to establish the proportion of actual FW difference (d) in the theoretical
population; and confidence intervals provide the range of plausible values of FWs
differences (d) of TAs. Both procedures help with gaining a generally better picture
for comparison of results between three simulated theoretical populations. We
develop a method to estimate a confidence interval using a percentile and a standard
method from the given theoretical populations of FWs. The percentile method is
appropriate if populations do not follow normality criteria, because it focuses on
given data. The standard method provides valid results only if populations are
normal. Both methods provide approximately similar results if populations follow
a normal distribution. Finally, using a published case study as an example, we test
this approach and compare the robustness, similarities and differences in the
results computed using three methods: the sampling procedure used by Iqbal
et al. (2014), and the two adopted in this paper (i.e. bootstrap and permutation
sampling methods).
2. QFD framework (HOQ)
QFD studies help practitioners to establish a “HOQ” with the belief that products
will be designed and produced according to customers’ desires and tastes (Temponi
et al., 1999). The HOQ comprises different sections, which are sequentially and
systematically populated by information collected from customers, engineers and
competitors. Each section (room) has its own importance to the HOQ, and some (though
not all) are mandatory for QFD studies. In the next sections we discuss some of the
more important sections of the HOQ.
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2.1 Voice of customer (VOC) section
This is the first section in the QFD framework. This section contains actual customer
needs and demands, their importance ratings and the correlations between them. VOCs’
importance ratings (I), are the most important and frequently used variable for driving
the FWs of TAs. George and Leone argue that selection of customer demands – and
establishing their importance ratings – is a compulsory aspect of QFD studies because
these meaningfully affect the FWs and consequent prioritisation of TAs. Various
three-, five-, seven-, nine- and ten-point scales with different strengths have been used
in published case studies. The most commonly used scale is one- to five-point where 1
represents very low importance and 5 represents very high importance.
The customer importance rating as variable (I) is used to derive FWs by Equation (1).
2.2 Technical attributes section
Once the VOCs have been determined, the next step is to populate the TAs section. This
section defines the technical attributes required of the product or service, and their
intercorrelations. The TAs are the technical translation of VOCs to achieve maximum
customer satisfaction (Bouchereau and Rowlands, 2000). Hauser and Clausing (1988)
suggest that TAs are likely to satisfy at least one VOC requirement. TAs are
sufficiently important to QFD for Govers (1996) describes them as “the heart of QFD
methodology”. Some practitioners analyse the intercorrelation between TAs so as to
avoid any negative impacts on the system. TAs strength of relationship matrix,
together with VOCs, are used to derive FWs, as discussed in the next section.
2.3 Relationship matrix section
The relationship matrix is a table of “N” rows (VOCs) and “M” columns (TAs).
It expresses the strength of relationship between each TA and the VOCs. The
relationship matrix illustrates how the VOC requirements are satisfied through the
TAs (Han et al., 2001). The development of relationships with different intensities is a
complex procedure. Several methodologies have been developed to populate the
relationship matrix; for example Likert scales, fuzzy logic and AHP (De Felice and
Petrillo, 2011; Khoo and Ho, 1996). The most commonly used method is the Likert
scale, which often uses a three- and five-point qualitative-quantitative measurement, as
shown in Figure 2. In Likert scales low numbers indicate weak relationships while
large numbers represent a strong relationship; for example, weak ¼ 1, medium ¼ 3
and strong ¼ 5.
Relationship Matrix Scales Relationship Matrix Scales
Strength
Strength
0
2
4
6
8
10
3
1
5
7
9
0
2
4
6
8
10
12
Scale 1
Scale 2
Scale 3 Series1
Series2
Series3
Scale 4
Scale 5
1
1
1
1
1
1
1
3
3
3
3
3
3
3
3
2
2
5
5
5
5
5
9
9
9
7
7 7
4
10
Weak
Weak
Very
Weak
Moderate Strong
Very
Strong
Moderate Strong
Figure 2.
Qualitative-
quantitative rating
scales used in
the relationship
matrices
401
Enhancing
prioritisation
of technical
attributes

The relationship matrix’s intensity scales (R), integrated with customer importance
ratings (I), determine the FWs (W).
2.4 FWs of TAs and their priority
FWs are derived on the basis of the information that comprises the various sections of
the HOQ. Equation (1) shows the general mathematical expression to compute FWs
(W), which is the sum of linear relationships between the variables comprising the
sections of the HOQ. In the derivation of FWs (W), R and I are fixed variables, and X, Y,
[…] , Z are optional variables resultant from the various HOQ sections. Optional
variables might include correlations between TAs, correlations between VOCs,
benchmarking data on competitors, degree of difficulty in developing the TA, etc.:
Wj ¼
Xn
i
Ri;j Â Ii Â X Â Y Â . . . Â Zf g (1)
where R is the relationship matrix’s strength, I is the customers’ importance and
X, Y, […] , Z are some of the optional variables which some researchers may choose
to include.
Equation (1) is a generalised form of an equation adapted from articles
written by (Han et al., 2001; Wang et al., 2012; Pakdil et al., 2012; Franceschini and
Rossetto, 2002; Chang, 2006). FWs and their determine priorities may help to
guide decision making around making trade-offs in the allocation of resources
(Shen et al., 2000). The prioritised TAs provide a way of defining which TAs have the
largest effect on VOCs (Table I).
3. Enhancing the prioritisation (ranking) of technical attributes
Prioritisation of the TAs is based on FWs derived using Equation (1). The TA with the
highest FW receives top ranking, and that with the FW receives the lowest value in
ranking. The highest ranked TA will therefore become the highest priority engineering
attribute to be tackled, and will theoretically have the largest impact in terms of
achieving stated customer wants or needs (expressed as VOCs). According to statistical
sampling and significance theory, however, two TAs with different FWs could satisfy
one or more VOCs equally. This would occur when the sampling variables (derived
from the HOQ sections and used to quantify FWs), belong to the same population
and the difference between them is merely sampling (random) error. We can test the
difference (d) between two FWs to achieve a test-statistic. One important point to note
here is that traditional testing methods cannot be applied, as all the variables used in
Equation (1) are Likert scales. The Likert scales have different intervals and their
strengths also vary from case study to case study. On the other hand, we do not know
about statistical hypothetical population as these rating-scales are qualitative-quantitative
and do not follow any assumption of normality. As traditional testing procedures cannot
be adopted, we will use a given empirical relationship matrix (I) as the source to generate a
Final weights (FWs) of technical attributes (TAs)
Technical attributes TA1 TA2 TA3 … TAM
FWs W1 W2 W3 … WM
Ranking of FWs 2 3 1 … 9
Table I.
Final weights and
their ranking
402
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64,3

theoretical population of scales which represents actual given empirical data (measured
through Likert scales). Iqbal et al. (2014) describe how to test the difference between FWs
(d) using a parametric bootstrap (based on a Poisson distribution). They demonstrate how
the Poisson distribution is appropriate to generate a theoretical population of the size of
the relationship matrix. In the next section, we describe the methodology for test-statistic
p-values and confidence interval.
3.1 Methodology
3.1.1 Test-statistic(s) and p-values. In statistical significance testing, the p-value is the
probability (proportion) of obtaining a test-statistic from a given population. In QFD
studies it helps to know whether a selected TA has the same or a higher priority. In this
paper we compare each TA with the other TAs based on their FWs. So the matrix of all
possible differences (d) of M FWs becomes the test-statistic(s); i.e. there will be
M MÀ1ð Þ=2 test-statistic(s) to test (see Table II).
To derive the p-value(s), we need a large theoretical population of FW differences
d
À Á
. As described by Iqbal et al. (2014), we will generate this through the following
steps. First, we simulate a very large number of relationship matrices R of the same
size as the given size of the relationship matrix (IN,M). Next, for each generated R,
we derive FWs and their differences, where the FW differences may be positive or
negative. In fact the positive or negative sign does not have any effect and so we can
consider negative values as positive values, i.e. a folded theoretical distribution,
without the algebraic sign (folded normal distribution if it is normal distribution)
(Leone et al., 1961). Finally the proportion of each given statistic (actual FW
differences (d), M MÀ1ð Þ=2 with the generated test-statistics theoretical population
d
À Á
determine the p-values. In Section 4, a case study is tested to demonstrate the
above methods.
3.1.2 Confidence interval (CI). All (d) found in CI are plausible values based on
empirical data given in the HOQ. FW differences (d) outside the interval, however,
increase the priority and consequent importance given to a TA. So CI estimation
provides another simple way to test the significance of TAs. In order to support the
estimated p-values; CI estimation is also carried out on the same selected case study.
At 95 per cent confidence level, we estimate CI for the three theoretical populations of
FW differences. We can estimate this through two methods:
(1) The first approach is via percentile method: this approach is more simple and
straightforward. It does not require any assumptions. First we sort the
theoretical population, and then find 2.5 per cent quantiles from each side. This
will provide the upper and lower limits of CI.
TAs TA1 TA2 TA3 … TAM
TAs FWs W1 W2 W3 … WM
TA1 W1 na W1-W2 W1-W3 … W1-WM
TA2 W2 na na W2-W3 … W2-WM
TA3 W3 na na na … W3-WM
⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
TAn WN na na na … na
Table II.
Differences between
the FWs
403
Enhancing
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of technical
attributes

(2) The second approach is a standard way of computing CI and requires
normality assumptions. Due to the large size of the generated theoretical
population, the central-limit theorem ensures their asymptotic normality. So for
the current scenario, the general expression to estimate CI for (d) is the
standard way of estimating CI for a normal population, i.e. d 71:96 Â SE d
À Á
,
where d is the theoretical population of FW differences. Before applying the
standard CI method, we observe normality by plotting a QQ plot and boxplot.
If the theoretical population is found to be normal, then the CI computed by
both approaches should be the same. If the simulated populations are proved to
be normally distributed then we will consider this as folded normal distribution
(as the algebraic sign has no significance (Leone et al., 1961). The folded normal
distribution will be used to estimate one-sided CI.
4. Case study and results
A case study to improve hospitality service management has been selected from the
literature, ( Jeong and Oh, 1998). In Figure 3, the HOQ shows VOCs (the service
attributes), TAs (the service design/management requirements), the relationship
matrix and FWs (with raw importance weight). There are eight VOCs and ten TAs.
The relationship matrix is of size 8×10, with an intensity of “None” ¼ 0, “Weak” ¼ 1,
Courtesy
FastCheck-in
ComplaintHandling
Cleanliness
TimelyArrangement
RoomItemsinOrder
FoodQuality
Sanitation
EmployeeFriendliness
Price
RelativeWeight(%)
Correlations (TAs)
Service Attribute
Service Design/ Management Requirements
Front Desk Housekeeping Food & Beverage
TA1 TA2 TA3 TA4 TA5 TA6 TA7 TA8 TA9 TA10#
Ranking 3
3
3
3
3
3
3
3 3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
2 7 8 5 4 10
10
10
10 10
1010 10
10
10 10
10
10
10 10
10
10
10
10
10
10
10
10
10
9
1
1
1
1
1
1
11
1
1 1
1
1
1
1
1
11
1
1
1
1 1
1
1
6
0
0 0 0
0
15
20
15
18
14
6
7
6
494 559 438 346 478 488 157 268 705 452
First Service
Correct Billing
Problem Handling
Prompt Service
Willingness to help
Modern Equipment
Visual Appearance
Professional Appearance
Raw Importance Weight
Figure 3.
House of quality
modified form
(Jeong and Oh, 1998),
showing priority
rating of ten
technical attributes
404
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“Medium” ¼ 3 and “Strong” ¼ 10. The bottom row shows the FWs of TAs that have
been computed using Equation (1).
The bottom line of Figure 3 shows that TA9, “Employee Friendliness” has the
highest priority and TA10, “Food Quality” has the lowest priority. From the FWs in
Figure 3, we find the square symmetric matrix (Table III) of all possible differences, (d),
i.e. 10ð10À1Þ=2 ¼ 45. Note that difference 548 is the highest and 111 the lowest
between the FWs.
4.1 Test-statistic and p-values
We first apply the parametric bootstrap (Poisson), bootstrap and permutation
sampling methods to estimate the p-values for the test-statistic(s) (d) given in Table III.
Using the statistical software package “R”, and following the procedure detailed in
Section 3.1.1, we simulated theoretical populations and then derived the tables
(Appendix, Tables AI-AIII) of p-values for all statistic(s) (d) for the three populations.
In order to check the normality of theoretical populations d we generated QQ plots
and boxplots. Both sets of plots (Figure 4) clearly indicate populations are normally
distributed. As populations are normally distributed and the algebraic sign has no
effect, we will use folded normal distribution for p-values and CI (one sided).
For further analysis, first we compared TA9 (the highest ranked) with the other
TAs. To do this we generated density plots of three-folded normal populations
(Figure 5). It can be seen that all the generated populations are positively skewed. We
then represent the differences (TA9 vs the others) on these density plots by drawing
lines of different colour. The green lines show statistical non-significance, while the red
lines indicate statistically significant differences. The red area on right side of the
density plots shows 5 per cent of the total area.
The above p-value tables show that the parametric bootstrap has a high significance
level compared to bootstrap and permutation. The reason behind this difference is that
for the bootstrap and permutation sampling, the given data is sampled with and without
replacement, while parametric bootstrap generates data using Poisson to represent the
original data. There could, however, be a different result for different case studies.
Confidence interval
Now in order to determine the robustness of the above computed p-value results; we
estimate the CI for the three theoretical populations. The presence of FW differences
TAs and FWs in descending order
TAs TA9 TA2 TA1 TA6 TA5 TA10 TA3 TA4 TA8 TA7
TAs and FWs in
descending order
TAs FWs 705 559 494 488 478 452 438 346 268 157
TA7 157 548 402 337 331 321 295 281 189 111 na
TA8 268 437 291 226 220 210 184 170 78 na na
TA4 346 359 213 148 142 132 106 92 na na na
TA3 438 267 121 56 50 40 14 na na na na
TA10 452 253 107 42 36 26 na na na na na
TA5 478 227 81 16 10 na na na na na na
TA6 488 217 71 6 na na na na na na na
TA10 494 211 65 na na na na na na na na
TA2 559 146 na na na na na na na na na
TA9 705 na na na na na na na na na na
Table III.
All possible
differences between
final weights in
descending order
405
Enhancing
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attributes

within CI shows that they may be treated equally. For the percentile method, we
arranged data in descending order and obtained the lower limit by finding the 0.025th
percentile and the upper limit by finding the 0.975th percentile. We can also estimate CI
by the standard method. As we can see from Figure 4, the QQ plots and boxplots show
that all three theoretical populations are normally distributed. Table IV, shows the
estimated CIs computed by both approaches. One-sided CI is also estimated for folded
normal distribution using the percentile (0.95th percentile) and standard method.
We can see (Table V and Figure 6) that the CI for parametric bootstrap has a
shorter range compared to bootstrap and permutation which have a wider range. So the
probability of a difference in the CI is high in parametric method. We also see the CI
change by altering λ. On the other hand the CI estimated by bootstrap and permutation
is the same. This is because it makes no difference whether the large amount of
resampling is done with replacement (bootstrap) or without replacement (permutation).
5. Discussion
Figure 5 and Table IV both show that TA9 has a high significant difference from the
other TAs in the parametric bootstrap (Poisson) simulation as compared to bootstrap
and permutation sampling, while the results for bootstrap and permutation are almost
identical. The above p-value tables (Tables AI-AIII) show that the parametric bootstrap
has a high significance level compared to bootstrap and permutation. The reason
behind this difference is that for the bootstrap and permutation sampling, the original
given data is sampled with and without replacement, while parametric bootstrap
generates data using Poisson to represent the original data. There could, however, be a
different result for different case studies.
For the CI from Table V and Figure 6 we see that for the parametric bootstrap we
obtain a shorter-range simulated theoretical population as compared to bootstrap and
permutation which have a wider range. So the probability of a difference in the CI is
Normal Q-Q Plot Normal Q-Q Plot Normal Q-Q Plot
Theoretical Quantiles Theoretical Quantiles Theoretical Quantiles
SampleQuantiles
SampleQuantiles
SampleQuantiles
–500
500
0
–500
500
0
–500
500
0
–500
500
0
–400
–200
0
200
400
–400
–200
0
200
400
–4 –2 0 2 4 –4 –2 0 2 4 –4 –2 0 2 4
Figure 4.
QQ plot and
boxplots for the
three theoretical
populations
406
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DensityplotofPoissonTheoritical
PopulationofFWsDifferences
PoissonTheoriticalPopulation
Density
0100200300400500
0.000
0.002
0.004
0.006
0200400600800
0.000
0.001
0.002
0.003
DensityplotofPermutation
TheoriticalPopulationofFWsDifferences
PermutationTheoriticalPopulation
Density
DensityplotofBootstrapTheoritical
PopulationofFWsDifferences
0.000
0.001
0.002
0.003
Density
BootstrapTheoriticalPopulation
0200400600800
Figure 5.
Density plots of
three-folded normal
distribution, showing
the differences in
position of TA9 to
the other TAs
407
Enhancing
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high in parametric method. We also see the CI changes by altering λ. On the other hand
the CI estimated by bootstrap and permutation has similar limits. This is because
when a large theoretical population is simulated for relationship matrix whether with
replacement (bootstrap) or without replacement (permutation), it makes no difference.
For all three sampling approaches, we compared the significance method with CI.
We have shown that the signifiance method provides practitioners with the extent
(p-value) of actual difference (d) so that practitioners can see how far/close they are from
acceptance region. Whereas CI provide limits and makes the job easy for practitioners
to decide based on the least significant difference. Practitioners can choose any of
these three approaches to decide about two TAs. It depends how much variation in
FWs is acceptable for them. For smaller difference they can follow parametric
bootstrap approach while for larger distance in FWs both bootstrap and permutation
are appropriate.
6. Conclusions
In this paper, we demonstrate how theoretical populations can be simulated from given
data used in QFD studies not only for parametric bootstrap (which is used by Iqbal
et al., 2014) but also by permutation sampling and bootstrap sampling, in cases where
we are unable to identify the actual population or make any assumptions about it.
We further demonstrate how statistical inference can be made about the equal
importance of two TAs when they have different FWs. We found that the parametric
bootstrap (Poisson) method of inference results in a high rate of rejection for the
equality of two TAs, but that this rate of rejection can be altered by changing λ (the
Poisson mean). The bootstrap (with replacement sampling) and permutation (without
replacement sampling) both produced the same results. All three methods support
large number theory and follow central-limit theorem to obtain the same results by
percentile and standard method. The CI method helps us to determine the least
significant difference and makes the job of assessing whether two TAs have the same
TAs TA7 TA8 TA4 TA3 TA10 TA5 TA6 TA10 TA2
Methods TAs FWs 157 ($) 268 ($) 346 ($) 438 ($) 452 ($) 478 ($) 488 ($) 494 ($) 559 ($)
Poisson TA9 705 0.000 0.000 0.000 0.005 0.009 0.015 0.022 0.024 0.127
Bootstrap TA9 705 0.007 0.034 0.083 0.198 0.222 0.274 0.297 0.311 0.484
Permutation TA9 705 0.007 0.033 0.084 0.200 0.229 0.279 0.300 0.316 0.487
Table IV.
p-values for the
difference of TA9
from the other TAs
Theoretical Population Method
Two sided
(5 per cent) One sided 5%
CI for parametric bootstrap(λ ¼ 3) Percentile −186 186 186
Standard −185.69 185.69 187.59
CI for parametric bootstrap(λ ¼ mean ¼ (1+3+10)/3) Percentile −232 231 232
Standard −231.41 −231.41 233.91
CI for bootstrap Percentile −404 403 404
Standard −404.71 404.71 407
CI for permutation Percentile −405 404 407
Standard −407.37 407.37 409
Table V.
Confidence intervals
for three populations
by percentile and
standard method
408
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64,3

Density
Density
Density
0.000
0.001
0.002
0.003
0.004
0.0000
0.0005
0.0010
0.0015
0.0000
0.0005
0.0010
0.0015
ParametricBootstrap(Poisson)
TheoriticalPopulation
PermutationTheoriticalPopulationBootstrapTheoriticalPopulation
–2002000–5005000–5005000–400400600
ClClCl
0.95
0.950.95
0.0250.0250.0250.025
0.0250.025
Figure 6.
Density plots and
95 per cent
confidence interval
for three theoretical
populations
409
Enhancing
prioritisation
of technical
attributes

importance easier. It is also important to point out that such optimisation methods,
whilst of value in cases where a prioritisation between similarly ranked TAs is
required, do not require to be applied in all cases. Other pragmatic factors such as cost,
development time, deployment methods, convenience and so on (see Wasserman, 1993)
may override the need to utilise a statistical or algorithm-based decision tool.
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411
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attributes

Appendix
TAsTA9TA2TA1TA6TA5TA10TA3TA4TA8TA7
TAsandFWsin
descendingorder
TAsFWs705559494488478452438346268157
TA71570.00000.00030.00050.00080.00080.00150.00450.04550.2300na
TA82680.00000.00180.02130.01850.03250.04930.07230.4055nana
TA43460.00000.02730.11880.12900.16600.25350.3245nanana
TA34380.00500.20530.54900.59450.66780.8758nananana
TA104520.00850.25350.66450.68780.7743nanananana
TA54780.01500.38280.85750.9088nananananana
TA64880.02180.45300.9468nanananananana
TA104940.02430.4835nananananananana
TA25590.1268nanananananananana
TA9705nananananananananana
Table AI.
p-values generated
from parametric
bootstrap (Poisson)
412
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64,3

TAsandFWsin
descendingorder
TAsFWs705559494488478452438346268157
TA71570.00740.05140.10390.10880.12040.15600.17650.36590.5976na
TA82680.03350.16170.28010.29240.31280.37770.41420.7070nana
TA43460.08260.30590.47830.49470.52440.61230.6593nanana
TA34380.19800.56220.78940.81060.84570.9444nananana
TA104520.22190.60640.83930.86270.8984nanananana
TA54780.27420.69610.93660.9597nananananana
Table AII.
p-values generated
from bootstrap
413
Enhancing
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of technical
attributes

TAsandFWsin
descendingorder
TAsFWs705559494488478452438346268157
TA71570.00700.05220.10520.11270.12250.15980.17950.36750.5980na
TA82680.03340.16300.28200.29410.31610.38240.41750.7074nana
TA43460.08390.31090.48200.49640.53060.61450.6610nanana
TA34380.19970.56400.79090.80910.84720.9444nananana
TA104520.22890.61140.83920.86320.9014nanananana
TA54780.27850.69870.93890.9611nananananana
Table AIII.
p-values generated
from permutation
sampling
414
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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 the Massey University, New Zealand. He leads Massey University’s
postgraduate teaching and research-based programmes in the quality systems area. Associate
Professor Nigel P. Grigg is the corresponding author and can be contacted at: N.Grigg@massey.ac.nz
Dr K. Govindaraju is a Senior Lecturer in Statistics in the Institute of Fundamental Sciences
at the Massey University, New Zealand.
Nicola Marie Campbell-Allen is a Lecturer in Quality Management in the School of Engineering
and Advanced Technology, Massey University, New Zealand.
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