Quality & Quantity 35: 265–276, 2001.
© 2001 Kluwer Academic Publishers. Printed in the Netherlands.
Trade-off between Quality and Cost
Industries and Regional Development Center, National Kaohsiung University of Applied Sciences,
415 Chien-Kung Road, Kaohsiung 807 Taiwan, R.O.C.
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Abstract. This paper proposed a new model that takes both quality and cost into account. This
model is a natural extension of the classical Taguchi quality model where only quality is controlled.
This paper also gives a number of numerical examples for illustration.
Key words: cost, quality, trade-off
Given the input characteristic x, the output characteristic y in the Taguchi (1987)
quality selection model is determined by
y = g(x).
Suppose that the input x is a normally distributed random variable with mean µ and
while the target value for the output is y
. So the output y is a random
variable as well. From the quality point of view, the nearer the better for y to
distribute around the target y
. Taguchi (Belavendram, 1995) therefore introduced
his loss function
= kE(y − y
to measure the loss of quality, where K>0 is the coefﬁcient of the Taguchi loss
function (Taguchi, 1986).
If one only aims to improve quality, he should control both the mean µ and
of the input variable x in order to minimize the loss function. For
example, if the output is a linear function of the input, namely
y = bx + c,
it can be easily shown that
+ (bµ + c − y