John F. Kros and Christina M. Mastrangelo
Taguchi method; Nonquadratic loss functions; Experimental design; Signal-to-noise ratios.
Introduction
The Taguchi-style of off-line quality control is a methodology often referred to as robust design. Robust design systematically reduces variation in a product or process design by reducing the sensitivity of the design to noise factors. The technique of robust design involves the identification of product input parameters that minimize estimated expected loss. The expected loss increases as the value of a quality characteristic departs from its target value, and a basic quadratic loss function (LF) is typically used to model this loss.
The loss function is used to develop performance statistics which, in turn, become the criteria for comparing different input parameter levels. These performance statistics are signal-to- noise (S/N) ratios (see Refs. 1-4 for review). Numerous discussions of Taguchi's approach are available, and for an overview of these methods, the reader is referred to Refs. 5-17.
Taguchi-style experimentation assumes quadratic loss. However, the quadratic LF may only be an approximation of the actual LF, and the use of a quadratic LF as a surrogate for the true LF may not be adequate in many circumstances. For example, the losses for overfilling/ underfilling a container or over/underdosage effects of prescribed medicine are, in general, unequal (i.e., asymmetric loss).
It is generally agreed upon that improved measures of the actual LF will, in turn, produce improved designs (5,17-19). Several authors have considered different classes of LFs as well as modeling techniques (18-22).
For example, Kim and Liao (21) developed various forms of quality LF's to extend the usefulness of Taguchi's quality LF. An asymmetric class and an insensitive class of LFs were modeled. Stevens and Baker (22) generalized the quadratic LF and compared it to the traditional quadratic LF on five theoretical criteria. A simulation was used as the vehicle for comparison, and an empirical example was used to demonstrate the generalized LF. Furthermore, Leon and Wu (18) modeled general dispersion and off-target measures as functions of design factors with a series of nonquadratic loss ftinctions. They developed a two-step parameter design procedure for general LFs around these dispersion and target measures.
However, a comprehensive relationship among the LF, S/N ratios, -and the three general quality characteristics (smaller-the- better, large r- the-be tte r, and nominal-the -best) has not been developed. Maghsoodloo (23) reviewed
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c 1998 by Marcel Dekker, Inc.