Post on 04-Jan-2022
International Journal of Quality & Reliability M
anagement
Introducing Multivariate Markov Modelling within QFD to
Anticipate Future Customer Preferences in Product Design
Journal: International Journal of Quality & Reliability Management
Manuscript ID IJQRM-11-2016-0205
Manuscript Type: Quality Paper
Keywords: Quality Management, QFD, AHP, Linear Programming, Product
Development, Markov Modelling
Abstract:
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International Journal of Quality & Reliability M
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Introducing Multivariate Markov Modelling within QFD to Anticipate
Future Customer Preferences in Product Design
Purpose: The aim of this paper is to provide an enhanced version of Quality Function
Deployment (QFD) that captures customers’ present and future preferences, accurately
prioritizes product specifications and eventually translates them into desirable quality
products. Under rapidly changing environments, customer requirements and preferences
are constantly changing and evolving, rendering essential the realization of the dynamic
role of the “Voice of the Customer” in the design and development of products.
Design/ methodology/ approach: The proposed methodological framework
incorporates a Multivariate Markov Chain (MMC) model to describe the pattern of
changes in customer preferences over time, the Fuzzy AHP method to accommodate the
uncertainty and subjectivity of the “Voice of the Customer” and the LP-GW-AHP to
discover the most important product specifications in order to structure a robust QFD
method. This enhanced QFD framework (MMC-QFD-LP-GW-Fuzzy AHP) takes into
consideration the dynamic nature of the “Voice of the Customer”, captures the actual
customers’ preferences (WHATs) and interprets them into design decisions (HOWs).
Findings: The integration of MMC models into the QFD helps to handle the sequences
of customers’ preferences as categorical data sequences and to consider the multiple
interdependencies among them.
Originality/value: In this study, a MMC model is introduced for the first time within
QFD, in an effort to extend the concept of listening to further anticipating to customer
wants. Gaining a deeper understanding of current and future customers’ preferences
could help organizations to design products and plan strategies that more effectively and
efficiently satisfy them.
Keywords: Quality Management, QFD, Fuzzy AHP, Linear programming, Product
Development, Markov Modelling.
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INTRODUCTION
Quality Function Deployment (QFD) is a well-established Total Quality
Management (TQM) method that offers a structured framework to design and develop
high quality products. It has been implemented to align manufacturing process
parameters with market requirements (Olhager and West, 2002) by focusing on what
customers deem important and by ensuring that the desired characteristics are
incorporated into the final product (Ahmed and Amagoh, 2010). Thus, QFD provides a
mechanism for translating the “Voice of the Customer” (VoC) (WHATs) into product
specifications (HOWs), from conceptual design to manufacturing (Ahmed and Amagoh,
2010; Cristiano et al., 2000; Dror and Sukenik, 2011; Dror and Barad, 2006; Tan, 2001;
Yang et al., 2012; Zare Mehrjerdi, 2010). The “Voice of the Customer” is a detailed set
of customers’ needs, wants, expectations, and preferences, both spoken and unspoken
(El-Haik and Shaout, 2011; Griffin and Hauser, 1993), gathered at specific points in
time, previous or present (Shen et al., 2001).
Product development is more likely to succeed when it mirrors customer needs
and preferences throughout the design, manufacturing, market introduction and
consumption stages (Chong and Chen, 2010b; Karkkainen et al., 2001). However,
variations in customer preferences may occur over the product design and development
process compromising the outcome of the QFD implementation. In fact, the longer the
development process lasts, the higher the probability for a shift in customer needs and
preferences to occur even before the introduction of the product (Adams et al., 1998;
Chong and Chen, 2010b; Perreault et al., 2011; Raharjo et al., 2006).
Moreover, although, some product features might create a delightful experience
in the introduction stage, these features might alter during product life cycle (Witell and
Fundin, 2005), rendering design specifications obsolete. For example, the same product
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features that initially bring a feeling of excitement, are taken for granted as time passes,
even if they initially exceeded customer expectations (Kano et al., 1984; Kano, 2001).
Costly consequences may result from a lack of acknowledgement of the time sensitive
nature of customer preferences (Engelbrektsson and Söderman, 2004). In this vein, as
long as the design is sensitive to the dynamic nature of customer’s requirements and
preferences, the offered product will more likely fulfill them at the time of launching
and during the consumption stages (Chong and Chen, 2010b).
According to Chong and Chen (2010a, 2010b) and Karkkainen and Elfvengren
(2002) a series of managerial problems such as design iterations, compliance fixes,
failures in resource allocation, high R&D risks and revision of marketing strategies
could be avoided when predicting and satisfying future customer preferences. The early
identification of future customer needs may result in gaining customer satisfaction and
achieving competitive advantage (Karkkainen et al., 2001). Therefore, it is important to
realize the dynamic nature of the “Voice of the customer” and to integrate it in the
product design and development process (Wang, 2012) suggesting that organizations
should act proactively to address emerging customer requirements. However, asking
customers straightforward about their future needs and preferences is not the
recommended way to elicitate the desired information (Karkkainen et al., 2001; Chong
and Chen, 2010a), suggesting that there is a need to employ alternative approaches.
The adoption of stochastic processes to describe sequences of customers’
preferences has been proposed to tackle the above issues (Asadabadi, 2016; Wu and
Shieh, 2006, 2008; Shieh and Wu, 2009). In particular, the utilization of Markov Chains
could provide information necessary to capture the dynamic nature of customer
preferences and predict future behavior. By exploiting the Markov Chain property,
suggesting that the future state depends on the current state or on a desired sequence of
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precedent events (Bhat and Miller, 2002; Isaacson and Madsen, 1976; Kijima, 2013;
Norris, 1997; Rabiner, 1989), it is possible to structure the behavior of a system
according to an appropriate stochastic model. The introduction of Markov Chain
modelling into QFD results in extending the concept of listening to the “Voice of the
Customer” to the concept of capturing the evolving “Voice of the Customer”.
Towards this direction, the methodological contribution of this paper is the
development of the enhanced Multivariate Markov Chain-QFD-LP-GW-Fuzzy AHP
framework. In particular, in this study, a first-order Multivariate Markov Chain model
(Ching et al., 2002) is implemented for the first time in conjunction with the QFD
method. More specifically, a first-order Multivariate Markov Chain model is embedded
into the extended QFD methodology, QFD-LP-GW-Fuzzy AHP, to improve its
robustness. QFD-LP-GW-Fuzzy AHP provides a systematic procedure to capture the
actual “Voice of the Customer” (WHATs) and to accurately translate it into design
decisions (HOWs) (Kamvysi et al., 2014), while the Multivariate Markov Chain
(MMC) model helps to describe the pattern of changes in customer preferences over
time. It should be noted that MMC models have been chosen, since they exhibit certain
characteristics making them advantageous over the Markov Chain models that have
already been used with QFD (Asadabadi, 2016; Shieh and Wu, 2009; Wu and Shieh,
2006; 2008). Their incorporation into the extended QFD helps to model the changing
customers’ preferences as categorical data sequences and to take into account the
multiple interdependencies among them. Managerially wise, by capturing the dynamic
nature of customer requirements, this paper could help organizations to redefine the
customer experience meeting both current and future needs and ensure a continuous and
high level of customer satisfaction in the delivery of products.
The paper is organized as follows. First, the benefits of introducing Markov
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Chain models into QFD along with a review of previous Markov Chains-QFD
methodological approaches are provided. Then, the enhanced QFD methodology is
described, followed by an illustrative example that presents its implementation and
validates its applicability. The paper concludes with concluding remarks, managerial
implications and future research directions.
THE CONTRIBUTION OF MARKOV CHAINS IN IDENTIFYING THE
FUTURE “VOICE OF THE CUSTOMER”
QFD, which is firmly and coherently grounded on the principles of TQM, helps
addressing gaps between specific and holistic components of customer expectations and
perceptions (Andronikidis et al., 2009). More specifically, it aims at delivering superior
quality through a customer-driven process utilizing a series of planning matrices –
Houses of Quality (HOQ), establishing explicit relationships between the “Voice of the
Customer” (WHATs) and design specifications (HOWs) and communicating this
information throughout the design and development process (Chan et al., 2009; Cohen,
1995; Karsak, 2004; 2008; Murali et al., 2016; Simons and Bouwman, 2006). The
introduction of Markov Chain models into QFD helps satisfy both current and future
customer needs and expectations by pursuing the following goals:
(1) Gain a deeper understanding of customer needs and preferences (WHATs). The
employment of Markov Chain models in a well-designed QFD-based product
realization contributes to the identification of both current and future customer
expectations.
(2) Prioritize more accurately product features (HOWs), based on a timely update of
customer preferences information (WHATs). The accurate capture of the true
“Voice of the Customer” facilitates the translation process of “WHATs” into
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“HOWs”.
(3) Increase the likelihood of developing design proposals/ solutions that deliver
competitive advantage. Predicting the future “Voice of the Customer” gives an
advantage in design, resource allocation and customer satisfaction, considering
that the proposed design decisions are based on both current and future
expectations. In this fashion customer demands are proactively identified and
served, eliminating corrective interventions during the design and development
process.
(4) Strengthen relationships with customers through improved product design. The
integration of Markov Chain models into QFD reinforces organization’s efforts
to place the customer explicitly in the centre of its activity, since it helps
designers to define more easily and accurately customer-impacting processes and
product features, which in turn leads to improvements in design. Customers’
preferences are used as a driver to re-think the offered product or how initial
ideas could be further developed into more refined and clear cut concepts. The
ability to anticipate and satisfy customers desires gives the organization a market
leading position not only in identifying and deploying ideas for products and
effective strategies, but also in creating and building strong long-term
relationships with customers. Besides long-term customer relationships result in
higher sales and profits (Lassar et al., 2000; Perreault et al., 2011).
Wu and Shieh (2006, 2008) were the first who combined Markov Chain models
with QFD addressing the dynamic nature of consumers’ preferences over time. They
considered the utilization of Markov Chain models for analyzing and identifying the
trend of customer requirements and products’ technical specifications. Initially, they
introduced a discrete-time homogeneous Markov Chain model of first order into the
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HOQ to predict the behavior of consumer requirements and the corresponding technical
specifications (Wu and Shieh, 2006). A similar approach was used by Wu and Shieh
(2008) to model the relationship between consumer demand and their corresponding
technical specifications and to identify trends of the final weights of technical
specifications. Considerable advantage of the proposed models (Wu and Shieh, 2006;
2008) is that they are easy to construct and study through matrix analysis, since they are
actually a simple class of stochastic processes. Subsequently, Shieh and Wu (2009)
utilized hidden Markov Chains to detect the pattern of change in the “Voice of the
Customer” within the QFD context in different economic conditions. Hidden Markov
Chains provide a flexible content to analyze dynamic customer and technical
requirements, even though they imply the presence of certain regulatory conditions
(observed events). Finally, Asadabadi (2016) proposed a QFD approach that employs a
discrete-time homogeneous Markov Chain model of first order to track the changing
priorities of customers’ needs, and the ANP method to incorporate possible relations
between the QFD elements into the translation process. Nevertheless, it should be noted
that all the above-mentioned methodological approaches adopt Markov Chain models
that neither handle the sequences of changing priorities as categorical data sequences
nor explore possible correlations among them in order to develop proper prediction
rules (Ching and Ng, 2006). Moreover, it should be noted that all the above-mentioned
methodological approaches are based on the traditional QFD, with the exception of
Asadabadi’s approach (Asadabadi, 2016), which adopts the ANP method. Traditional
QFD by design employs simple qualitative inputs and judgments in interpreting data,
entailing a number of shortcomings (Andronikidis et al., 2009; Bouchereau and
Rowlands, 2000). Furthermore, in all previous methodological approaches crisp
numbers are used to estimate the relative weights of customer requirements and
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technical features, presupposing the availability of accurate and representative data
measured on an ordinal scale. Also, limitation is observed in the way the relative and
final weights of “WHATs” and “HOWs” are computed. A reliable quantitative method
such as the linear programming method LP-GW-Fuzzy AHP (Kamvysi et al., 2014)
enhances the prioritization process in the QFD environment. The above observations
foster the utilization of alternative Markov Chain models in conjunction with the
extended QFD methodological framework-QFD-LP-GW-Fuzzy AHP- in order to
produce improved results in predicting consumers’ preferences.
THE MULTIVARIATE MARKOV CHAIN-QFD-LP-GW-FUZZY AHP
FRAMEWORK
Initially, the methodological framework QFD-LP-GW-Fuzzy AHP decomposes
the decision problem into a hierarchy of three clusters: a goal cluster containing the goal
element, a criteria cluster (and subcriteria) at the intermediate level and at the lowest
level the alternatives’ cluster. Then, an in-depth questionnaire survey is conducted
where respondents compare each pair of decision elements considering a specific parent
element. In the enhanced QFD framework, addressing each set of preferences expressed
by a specific respondent for a given pairwise comparison in n successive time periods as
a categorical data sequence, is one of the reasons for choosing Multivariate Markov
Chain models (MMC) to anticipate the dynamic nature of the “Voice of the Customer”.
According to Ching et al. (2002) and Ching et al. (2013) MMCs are considered
appropriate for describing categorical data sequences. The other reason is the assumed
correlation among the categorical data sequences that stem from a series of pairwise
comparisons conducted with respect to a common decision element. Ching et al. (2002),
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Ching et al. (2013) and Ching and Ng (2006) proposed MMCs to determine the
behavior of multiple interdependent categorical data sequences generated by similar
sources or the same source and capture both the intra-transition and inter-transition
probabilities among the data sequences.
In particular, a first order MMC, proposed by Ching et al. (2002), is introduced
into the QFD-LP-GW-Fuzzy AHP methodological framework. The steps of the
methodology are described in Figure 1. Often, a large number of parameters might
discourage practitioners from implementing MMCs, however, the number of parameters
in this model is only s2
m2 + s
2, where s is the number of sequences and m the number of
possible states. Furthermore, the parameters are calculated relatively easy by solving
linear programming (LP) models. A comparison of first order MMC model and first
order Markov Chain model demonstrates superiority of the first in prediction accuracy,
since it simultaneously considers multiple data sequences and explores how they are
correlated (Ching et al., 2002).
An additional advantage of the proposed framework (Multivariate Markov
Chain-QFD-LP-GW- Fuzzy AHP) is the utilization of the Fuzzy AHP and the linear
programming method LP-GW-AHP to capture and prioritize the actual “Voice of the
Customer” in QFD (Kamvysi et al., 2014). As customers’ preferences are usually
characterized by ambiguity, vagueness and diversity of meaning (Cho et al., 2016; Yan
et al., 2014), often crisp numbers fail to express the subjectivity and elusiveness of
decision-making (Chan and Kumar, 2007; Chang, 1996; Chang and Wang, 2009;
Karsak, 2004; Kuo et al., 2010; Lin et al., 2005; Zare Mehrjerdi, 2010). Fuzzy AHP is
adopted to accommodate the potential uncertainty of subjective judgments. The
linguistic assessment of customer requirements is converted into triangular fuzzy
numbers (TFNs), used to construct the pairwise comparison matrices of AHP (Jakhar
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and Barua, 2014). By employing the TFNs to express customers' preferences and cross-
functional team’s assessments, the inherent subjectivity of human judgment is taken
into account and becomes an integral part of the proposed methodology. Then, the LP-
GW-Fuzzy AHP utilizes the principles of linear programming to replace the eigenvalue
method (EV) in the computation of the priority vector of “HOWs”. This improves the
hitherto inaccurate prioritization of “HOWs”. A key feature of the LP-GW-Fuzzy AHP
methodology is that it solves only one LP model for deriving local weights from
comparison matrices and does not require normalization of the derived weight vector
thus avoiding rank reversal. The LP-GW-Fuzzy AHP methodology compared to the EV
is at least equally successful, more easily applicable and produces the true relative
weights for perfectly consistent pairwise comparison matrices. Finally, LP-GW-Fuzzy
AHP takes advantage of all available information from pairwise comparison matrices
and estimates final weights that are consistent with decision makers’ subjective
judgments.
PRESENTATION AND APPLICATION OF THE PROPOSED FRAMEWORK
This section presents and illustrates the Multivariate Markov Chain-QFD-LP-
GW-Fuzzy AHP methodological framework (Figure 1) using a numerical example. Our
effort concentrates on the first HOQ, where two customer requirements (CR) represent
the “WHATs” and three technical specifications (TS) represent the “HOWs”. The
objective is to determine which technical specifications to deploy in order to meet
evolving customer requirements. A group of decision-makers is assumed and the
approach of Aggregation of Individual Priorities (AIP) is employed (Forman and
Peniwati, 1998).
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---------------------
Figure 1
---------------------
Specifically, the proposed methodological framework takes into account the sequence
of responses of each participant to each pairwise comparison. Under the general idea of
AIP we obtain the overall weights through the geometric mean of the individual
priorities resulted by the pairwise comparisons of each respondent. Since, the same
process is repeated for every customer to produce the individual priorities, we
demonstrate it for one participant only.
The basic steps of implementing MMC in conjunction with QFD-LP-GW-Fuzzy AHP
are:
(Step-1) Structuring the decision hierarchy: The problem is structured as a three level
hierarchy: the “goal” cluster i.e. delivering a product of high quality; the “criteria”
cluster comprising customer requirements; and the “alternatives” level consisting of
technical specifications.
(Step-2) Collecting input data by making pair-wise comparisons: Customers express
preferences on all pairs of technical specifications regarding customer requirements on
AHP scale, being aware of its matching linguistic variables (Table 1). The procedure is
repeated for n consecutive time points, (here n equals 12). The repetition of the survey
for n consecutive time points allows monitoring changes in the expressed preferences
given by the same participants after comparing each pair of technical specifications.
This procedure is realized through simulation.
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---------------------
Table 1
---------------------
(Step-3) Forming categorical data sequences: The number of categorical data
sequences is equal to the number of questions (pairwise comparisons) that need to be
answered to complete the Relationship Matrix of the HOQ, considering that each
categorical data sequence is a set of preferences expressed by each customer when
repeatedly compares a certain pair of technical specifications n successive times. There
are three technical specifications, thus each customer is asked to perform 3 ×(3 − 1)/2 =3 pairwise comparisons regarding each requirement. Consequently, each customer
requirement corresponds to three categorical data sequences (s=3). The following S1, S2,
S3 categorical data sequences are generated from pairwise comparisons with respect to
the first customer requirement in 12 successive time periods. Hence, these three data
sequences are related to each other.
S1= {7, 5, 9, 7, 7, 5, 9, 9, 8, 9, 9, 7}
S2= {7, 3, 9, 7, 7, 3, 9, 6, 5, 6, 6, 7}
S3= {6, 3, 7, 5, 6, 3, 7, 8, 7, 5, 5, 6}
The data sequences comprise 17 states (m=17) due to the nine-point AHP scale, which
enumerates along with the reciprocals, seventeen crisp values {1/9, 1/8, 1/7, 1/6, 1/5,
1/4, 1/3, 1/2, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
(Step-4) Employing the MMC model: An MMC model of 17 states (=m) is proposed to
describe the behavior of the categorical data sequences.
(Step-5) Calculating the transition frequencies and constructing the corresponding
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transition frequency matrices: First, the transition frequencies are estimated for each
data sequence to construct the transition m×m frequency matrices F(ii)
(where i=1,...,s
and s=3).
Then, the inter-transition frequencies among data sequences are calculated and the
respective inter-transition frequency matrices F(ij)
(where i, j=1,...,s and s=3) are
formed, where F(ij)
denotes the inter-transition frequency matrix of going from states in
the ith
sequence to states in the jth
sequence.
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(Step-6) Structuring the first order transition matrices: By normalizing the transition
and inter-transition frequency matrices the first order transition matrices �(��)and �(� ) (i, j=1,...,s and s=3) are formed (unit row sums).
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(Step-7) Estimating the stationary vector: The MMC model has a stationary vector ��
which is estimated by computing the probability distribution of each categorical data
sequence ��(�), where s=1,2,3: �� = (��(�), ��(�), ��(�)). To find ��(�) it is essential to count
the frequency of occurrence of each state in each of the following sequences.
1
9
1
8
1
7
1
6
1
5
1
4
1
3
1
2
1 2 3 4 5 6 7 8 9
x�(1) = (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2
12, 0,
4
12, 1
12, 5
12)
x�(2) = (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2
12, 0,
1
12, 3
12, 4
12, 0,
2
12)
x�(3) = (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2
12, 0,
3
12, 3
12, 3
12, 1
12, 0)
(Step-8) Computing the weighting factors of transition matrices by solving minimization
Linear Programming (LP) models: Parameters � �, where j,k=1,...,s and s=3, are the
weighting factors of transition matrices and their values are obtained by solving LP
model (1):
���� � (1)
subject to
(� � ⋯ � ) ≥ ��(j) – �� � � � … � � !
(� � ⋯ � ) ≥ −��(j) + �� � � � … � � !
∑ � � = 1��#� ,
� ≥ 0, � � ≥ 0, j,k= 1,....,s
Where Bj is of size % × & and determined by Equation (2):
! = '��(�)�(� )��(�)�(� )⋮��(�)�(� )) (2)
Thus, three 3×17 matrices *�, *�, *� are formed and three LP models are solved to
produce the values of � �.
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(Step-9) Building the MMC models: The MMC models for the categorical data
sequences are given by Equation (3):
+,-� ≡/01+,-�(�)+,-�(�)⋮+,-�(�) 2
34 =/01+,(�)+,(�)⋮+,(�)2
345
/1����(��) ����(��) ⋯ ����(��)����(��)⋮����(��)
����(��) ⋯ ����(��)⋮ ⋮ ⋮����(��) ⋯ ����(��)24 (3)
Where �,(�) is the state vector of the sth
categorical data sequence at time n.
More specifically, the MMC models for the categorical data sequences S1, S2, S3 are
obtained from Equation (4):
+6-�(�) = λ11�,(�)P (11) + λ12�,(�)P (21) + λ13�,(�)P (31)
+6-�(�) = λ21�,(�) P (12) + λ22�,(�)P (22) + λ23�,(�)P (32) (4)
+6-�(�) = λ31�,(�) P (13) + λ32�,(�)P (23) + λ33�,(�)P (33)
By employing all possible (alternative) optimal solutions of the respective LP models,
the following MMC models are derived from Equation (4):
+6-�(�) = �,(�)P (11) +6-�(�)
= �,(�) P (11)
(a) +6-�(�) = �,(�)P (22) (b) +6-�(�)
= �,(�)P (22) +6-�(�)
= �,(�) P (13) +6-�(�) = �,(�)P (23)
(5) +6-�(�) = �,(�)P (21) +6-�(�)
= �,(�)P (21)
(c) +6-�(�) = �,(�)P (22)
(d) +6-�(�) = �,(�)P (22) +6-�(�)
= �,(�)P (13) +6-�(�) = �,(�)P (23)
The resulting MMC model for n=12 is given by expression (6). The vectors represent
the steady-state probabilities of each categorical data sequence:
+��(�) = 70 0 0 0 0 0 0 0 0 0 0 0 0.6667 0 0.3333 0 0;
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+��(�) = 70 0 0 0 0 0 0 0 0 0 0.5000 0 0 0 0.5000 0 0; (6) +��(�) = 70 0 0 0 0 0 0 0 0 0 0.6667 0 0 0.3333 0 0 0;
(Step-10) Determining the value of each categorical data sequence at the steady-state:
To predict the values of the categorical data sequences we multiply successively each
vector of the Multivariate Markov Chain model by the matrix whose elements are the
crisp number sets of the AHP scale. Hence, the following predicted values correspond
to the crisp numerical intensity of the AHP scale that will be assigned to each pairwise
comparison at a later stage (steady-state).
+��(�) ∗[1/9 1/8 1/7 1/6 1/5 1/4 1/3 1/2 1 2 3 4 5 6 7 8 9;> = 5.6666
+��(�) ∗[1/9 1/8 1/7 1/6 1/5 1/4 1/3 1/2 1 2 3 4 5 6 7 8 9;> = 5.0000 (7) +��(�) ∗[1/9 1/8 1/7 1/6 1/5 1/4 1/3 1/2 1 2 3 4 5 6 7 8 9;> = 4.0000
(Step-11) Employing the Fuzzy AHP scale and fuzzifying the predicted preferences to
overcome subjectivity: the triangular fuzzy numbers (TFNs) take turn. The TFN (���?(�),
���@(�), ���A(�)
) represents the future customer preference at the steady-state, where ���?(�)
and ���A(�) represent the lower and upper predicted values and ���@(�)
the predicted modal
value. Using Table 1 the predicted crisp preferences are converted into fuzzy
preferences (TFNs). More specifically, the numerical values of the AHP scale
correspond to the modal values of the Fuzzy AHP scale. Thus, the predicted preferences
+��(�) provided by expression (7), are the modal values ���@(�) of the predicted fuzzy
preferences. To find the lower and upper values of the predicted fuzzy preferences each
vector of the MMC model is multiplied by a matrix whose elements are the lower and
upper values of the Fuzzy AHP scale, respectively. For example, the lower bound ���?(�)
of the predicted fuzzy preferences is calculated as follows:
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���?(�) = +��(�) ∗[1/10 1/9 1/8 1/7 1/6 1/5 1/4 1/3 1 1 2 3 4 5 6 7 8;>= 4.6667
���?(�) = +��(�) ∗[1/10 1/9 1/8 1/7 1/6 1/5 1/4 1/3 1 1 2 3 4 5 6 7 8;> = 4.0000 (8) ���?(�) = +��(�) ∗[1/10 1/9 1/8 1/7 1/6 1/5 1/4 1/3 1 1 2 3 4 5 6 7 8;> = 3.0000
Accordingly, the upper bound ���A(�) of the predicted fuzzy preferences is computed as
follows:
���A(�) = +��(�) ∗[1/8 1/7 1/6 1/5 1/4 1/3 1/2 1 1 3 4 5 6 7 8 9 10;> = 6.6667
���A(�) = +��(�) ∗[1/8 1/7 1/6 1/5 1/4 1/3 1/2 1 1 3 4 5 6 7 8 9 10;> = 6.0000 (9) ���A(�) = +��(�) ∗[1/8 1/7 1/6 1/5 1/4 1/3 1/2 1 1 3 4 5 6 7 8 9 10;> = 5.0000
(Step-12) Constructing the fuzzy pairwise comparison matrices:
The computed fuzzy preferences form the fuzzy pairwise comparison matrix (Table 2)
and are used to extract the relative weights of technical specifications. Each row and
column of the pairwise comparison matrix corresponds to a technical specification.
---------------------
Table 2 ---------------------
(Step-13) Estimating the index of optimism:
The subjective preferences of the fuzzy pairwise comparison matrices are converted to
crisp values by estimating the degree of optimism of the respondents (Kwong and Bai,
2002; Promentilla et al., 2008). The index of optimism µ, provided by the following
convex combination, measures the degree of optimism (Hsu and Lin, 2006; Lee, 1999):
B�� C = DB� AC + (1 − D)B� ?C , ∀D ∈ 70,1; (10)
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Setting µ = 0.5, indicates a moderate degree of optimism and using Equation (10) the
fuzzy comparison matrices are transformed to the following crisp (Table 3).
---------------------
Table 3 ---------------------
(Step-14) Utilizing the LP method LP-GW-AHP to estimate the relative weights of the
decision elements:
The LP-GW-AHP method of Hosseinian et al. (2012) is used to derive the relative
importances of technical specifications. The LP model that derives the relative weights
from the pairwise comparison matrix is:
�H�I (11.1)
JKLMNOPPQ �� ≥ I,� = 1, … , % (11.2)
RH� S − �� = 0,� #� � = 1,… , %(11.3)
R��� #� = 1(11.4)
S� − �T �� ≥ 0,� = 1,… , % (11.5)
S� − �� �� ≤ 0,� = 1,… , % (11.6) �� ≥ 0;S ≥ 0,� = 1,… , %H�W M = 1,… , % (11.7)
where xi are the relative weights for technical specifications, yj are the outputs weights
which are determined by the LP model and aij (i, j = 1,..., s) are the elements of the
pairwise comparison matrix. Constraints (11.5) and (11.6) denote assurance regions,
(Wang et al., 2008), and b is determined by Equation (12):
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X = &�� Ymax� ]1̂� RH� ̂
� #� _ ,max� ]1O� RH� O �
#� _` (12)
where r1,…,rs and c1,…,cs are the row and column sums of the comparison matrix.
(Step-15) Obtaining overall weights:
The same procedure is followed to predict the relative weights of the technical
specifications with respect to second customer requirement. The relative weights of
each technical specification along with the weighting factor of each customer
requirement are used to calculate the final weights of technical specifications. The final
weights are provided in the last row of the HOQ (Table 4).
---------------------
Table 4
---------------------
To produce the overall weights of technical specifications the described methodological
steps are performed for all decision-makers. Finally, the geometric mean is employed to
calculate the overall weights of the HOQs.
CONCLUDING REMARKS AND FURTHER RESEARCH
The principal goal of this research was to address the dynamic nature of the
“Voice of the Customer” and prevent a series of potential managerial problems that may
stem from a failure to acknowledge it. In this direction, a robust QFD framework was
developed to capture the true “Voice of the Customer”, describe the pattern of customer
preference trends, translate them into design decisions, and reliably prioritize the related
design actions. For the development of this enhanced QFD methodological framework,
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a first-order Multivariate Markov Chain model (Ching et al., 2002) was embedded for
the first time into the extended QFD framework, QFD-LP-GW- Fuzzy AHP (Kamvysi
et al., 2014). QFD-LP-GW-Fuzzy AHP addresses the need for capturing and accurately
translating the actual “Voice of the Customer” into design decisions, while MMC
models are employed to feed the framework with the predicted customers’ preferences.
Based on the assumption that each set of preferences expressed by a respondent for a
given pairwise comparison in n successive time periods is a categorical data sequence,
the MMC models satisfied the need for determing the patterns of change in the “Voice
of the Customer”. Also, since the pairwise comparisons are conducted with respect to a
common parent decision element, the adoption of the MMC models is prompted by the
assumed correlation among the categorical data sequences.
The proposed Multivariate Markov Chain-QFD-LP-GW-Fuzzy AHP framework
is described in full detail and its implementation steps are presented through an
illustrative example, verifying its applicability. It enables design engineers to anticipate
customer preferences and identify emerging features that will make future products
attractive and desirable or identify obsolete features that should be excluded from future
designs. Furthermore, it helps to overcome a major challenge of the product design and
development process: the availability of large scale, realistic customer data.
Determining and meeting future customer expectations provides strong competitive
edge given that organizations gain a broader and deeper understanding of evolving
customers’ needs. Getting this valuable insight helps in creating and building long-term
relationships with customers, designing products and deploying strategies to be ahead of
competition in satisfying customers’ expectations. Finally, despite the inherent
difficulties in acquiring appropriate data, future research might consider utilizing
higher-order Multivariate Markov Chains expecting to improve prediction accuracy of
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the proposed framework. In addition, since customer wants often present a surrogate
nature hidden Markov chains along with MMCs might provide better prediction
platforms for designers.
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Table 1: Crisp and Fuzzy AHP scales
Linguistic variables AHP scale Fuzzy AHP scale
TFNs Reciprocal TFNs
Equally important 1 (1,1,1) (1,1,1)
Intermediate 2 (1,2,3) (1/3,1/2,1)
Moderately more
important 3 (2,3,4) (1/4,1/3,1/2)
Intermediate 4 (3,4,5) (1/5,1/4,1/3)
Strongly more important 5 (4,5,6) (1/6,1/5,1/4)
Intermediate 6 (5,6,7) (1/7,1/6,1/5)
Very strongly more
important 7 (6,7,8) (1/8,1/7,1/6)
Intermediate 8 (7,8,9) (1/9,1/8,1/7)
Extremely more important 9 (8,9,10) (1/10,1/9,1/8)
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Table 2: The fuzzy comparison matrix
CR1 TS1 TS2 TS3
TS1 (1, 1, 1) (4.6667, 5.6666, 6.6667) (4, 5, 6)
TS2 (1/6.6667, 1/5.6666, 1/4.6667) (1, 1, 1) (3, 4, 5)
TS3 (1/6, 1/5, 1/4) (1/5, 1/4,1/3) (1, 1, 1)
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Table 3: The crisp comparison matrix
CR1 TS1 TS2 TS3
TS1 1.0000 5.6667 5.0000
TS2 0.1821 1.0000 4.0000
TS3 0.2083 0.2667 1.0000
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Table 4: The House of Quality (Multivariate Markov Chain-QFD-LP-GW-Fuzzy AHP
framework)
HOWs
Weighting
factor TS 1 TS 2 TS 3
WHATs CR 1 α1 0.6877 0.2193 0.0930
CR 2 α2 0.5156 0.3643 0.1201
Final weights α 1×0.6877+α 2× 0.5156 α 1×0.2193+α 2× 0.3643 α 1×0.0930+α 2× 0.1201
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Figure 1: The steps of the methodological framework
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