Introducing Multivariate Markov Modelling within QFD to ...

International Journal of Quality & Reliability M

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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:

http://mc.manuscriptcentral.com/ijqrm

International Journal of Quality & Reliability Management


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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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