Statistical Testing Procedure for the Interaction Effects of Several Controllable Factors in Two-Valued Input–Output Systems

Abstract

Suppose several two-valued input–output systems are designed by setting the levels of several controllable factors. For this situation, the Taguchi method has proposed assigning the controllable factors to the orthogonal array and using analysis of variance (ANOVA) for the standardized signal–noise (SN) ratio, which is a natural measure for evaluating the performance of each input–output system. Though this procedure is simple and useful in application indeed, the result can be unreliable when the estimated standard errors of the standardized SN ratios are unbalanced. In this article, we treat the data arising from the full factorial or fractional factorial designs of several controllable factors as the frequencies of high-dimensional contingency tables, and propose a general testing procedure for the main effects or the interaction effects of the controllable factors.

AMS Subject Classification:

• 62K15

Keywords:

• Confoundings
• Contingency tables
• Controllable factors
• Covariate matrix
• Generalized linear models
• Hierarchical models
• Fractional factorial designs
• Full factorial designs
• Standardized SN ratio
• Sufficient statistics
• Two-valued input–output systems