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Statistica Sinica 2(1992), 335-358



R. V. León and C. F. J. Wu

AT&T Bell Laboratories and University of Waterloo

Abstract: Parameter design is a quality engineering method, popularized by Japan- ese quality expert G. Taguchi, that aims at reducing sensitivity to hard-to-control variation in products and manufacturing processes. The method finds the settings of design factors that minimize expected loss due to variation. To do the minimization Taguchi uses controversial two-step procedures involving quantities he calls signal-to-noise (SN) rations. To explain SN ration, León, Shoemarker and Kacker (1987) introduced Performance Measures Independent of Adjustment (PerMIAs) and showed that some of Taguchi's SN ratios are PerMIAs. In this paper we propose a theory to explain the roles of PerMIAs and adjustment factors in the two-step procedures for constrained minimization. We develop conditions for finding PerMIAs and two-step procedures. In the second part of the paper (Sections 6 and 7), we extend the modeling techniques for quadratic loss to general loss functions. For this purpose, general dispersion, location and off-target measures are introduced. Our results are illustrated with several examples involving quadratic and other loss functions. Most of Sections 6 and 7 can be read independently of Sections 2 to 4.

Key words and phrases: PerMIA, Taguchi's signal-to-noise ratio, parameter design, robust design, statistical quality control, loss function, dispersion measure, off-target measure.

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