ABSTRACT
The Taguchi method for analyzing quality improvement experiments has been much discussed. It first defines summarizing quantities called perfor mance measures (PMs) and then analyzes them using analysis of variance. PMs are defined as functions of the response y; however, we believe that they should be regarded as quantities of interest derived after analysis of the basic response and defined as functions of the fitted values or parameter estimates. One of Taguchi’s signal-to-noise ratios (SNRs) involves J^y~4. This is not a good estimate of £ 11-4, though J2 A* might be acceptable. However, as Box (1988) showed, Taguchi’s signal-to-noise ratios make sense only when the log of the response is normally distributed. The correct statistical procedure is (1) to analyze the basic responses using appropriate statistical models and then (2 ) to form quantities of interest and measures of their uncertainty. Taguchi’s procedure inverts this established process of statistical analysis by forming the PMs first and then analyzing them. However, most writers concentrate on the analysis of PMs, though they may use other than signal-to-noise ratios. Miller and Wu (1996) refer to the Taguchi approach as performance measure modeling (PMM) and the
established statistical approach as response function modeling (RFM). They, of course, recommend RFM. However, what they actually do seems to be closer to the PMM approach. The major difference is that they consider statistical models for responses before choosing PMs. Because of the initial data reduction to PMs, their primary tool for analysis is restricted to graphical tools such as the normal probability plot. Interpretation of such plots can be subjective. Because information on the adequacy of the model is in the residuals, analysis using PMs makes testing for lack of fit difficult or impossible.
