A systematic approach to quality function deployment with a full ...

138 L.-K. Chan, M.-L. Wu / Omega 33 (2005) 119 – 139
in terms of a customer need Wm, then further improvement may not be urgently needed and thus a lower priority could
be assigned to Wm. At the other extreme, if C1 performs much worse than many other companies on Wm, then it may
be di cult for C1 to build a competitive advantage within a short period of time. In both cases, Wm could be assigned
a lower priority rating. However, if most companies perform quite similarly on Wm, not too much improvement e ort
from C1 may result in a better performance of its product and give C1 a unique competitive advantage. Thus a higher
priority could be assigned to Wm. In particular, if all companies’ performances on Wm are the same, it implies a great
market opportunity since any improvement would create a signi cant competitive advantage. So the highest priority could
be assigned to Wm. This basis of assigning priorities is interestingly related to the entropy concept in information theory.
Entropy is a measure for the amount of information (or uncertainty, variations) represented by a discrete probability
distribution, p1;p2;:::;pL:
L�
pl ln(pl); (A.1)
E(p1;p2;:::;pL)=− L
l=1
where L =1=ln(L) is a normalization constant to guarantee 0 6 E(p1;p2;:::;pL) 6 1. Larger entropy or E(p1;p2;:::;pL)
value implies smaller variations among the pl’s and hence less information contained in the distribution. For the mth row
of the customer comparison matrix X corresponding to the customer need Wm;xm1;xm2;:::;xmL, let xm = �L l=1 xml be the
total score with respect to Wm. Then according to (A.1), the normalized ratings pml = xml=xm for l =1; 2;:::;L can be
viewed as the “probability distribution” of Wm on the L companies with entropy as
L�
L�
(xml=xm)ln(xml=xm): (A.2)
E(Wm)=− L
l=1
pml ln(pml)=− L
l=1
It is clear that the larger the E(Wm) value, the less information contained in Wm or smaller variations among the pml’s
(or xml’s). If all companies’ performance ratings on Wm;xm1;xm2;:::;xmL, are the same, Wm has zero variations and E(Wm)
achieves its maximum of 1. So E(Wm) can be used to re ect the relative competitive advantage in terms of the customer
need Wm. All these E(Wm) values, after normalization:
�
M�
em = E(Wm) E(Wm); m=1; 2;:::;M (A.3)
m=1
can be considered as the customer competitive priority ratings for company C1 on the M customer needs, with a larger
em indicating higher competitive priority for the corresponding Wm.
For more on entropy and its applications, see Refs. [13,22,30–32].
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