Quality & Quantity 38: 75–79, 2004.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
Set the Optimum Process Parameters Based on
Asymmetric Quality Loss Function
Department of Industrial Management, Southern Taiwan University of Technology, 1 Nan-Tai
Street, Yung-Kang City, Tainan 710, Taiwan, Republic of China
Department of Industrial Engineering and Management, National Yunlin University of Science and
Technology, Touliu 640, Taiwan, Republic of China
Abstract. Recently, Huang has presented a trade-off problem of determining the optimum process
parameters for the product quality and process adjustment cost. About product quality, Huang adopts
the symmetric quadratic quality loss function for measuring the loss of proﬁt. However, he has
neglected other types of quality loss function in the model. In this paper, we will further propose
the modiﬁed Huang’s cost model with the linear and quadratic asymmetric quality loss function of
product for determining the optimum process parameters.
Key words: asymmetric quality loss function, trade-off problem, process mean, process standard
deviation, target value.
Taguchi (1986) has presented the quadratic quality loss function for minimizing
the total society losses to the producer and the customer. The classical Taguchi’s
(1986) quality model only considers the control of quality. However, the trade-off
problem between quality and cost is an important one. Recently, Huang (2001) has
presented a trade-off problem of determining the optimum process parameters for
the product quality and process adjustment cost. Huang (2001: 266) points out that
‘It costs to control the process variance, σ
, and, in general, the more it costs the
smaller the process variance is control. Moreover, it also costs to set the process
mean, µ, to a contain value. It is therefore unreasonable to aim higher quality
without the cost into account’.
About product quality, Huang (2001) adopts the symmetric quadratic quality
loss function for measuring the loss of proﬁt which is assumed to be proportional to
the loss of quality. However, he has neglected other types of quality loss function in
the model. The regular symmetric quadratic loss function is patently inappropriate
in some situations. Trietsch (1999: 69) remarks that ‘One such case occurs when
Author for correspondence.