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Suppose several two-valued input-output systems are designed by setting thelevels of several controllable factors. For this situation, Taguchi method hasproposed to assign the controllable factors to the orthogonal array and useANOVA model for the standardized SN ratio, which is a natural measure forevaluating the performance of each input-output system. Though this procedureis simple and useful in application indeed, the result can be unreliable whenthe estimated standard errors of the standardized SN ratios are unbalanced. Inthis paper, we treat the data arising from the full factorial or fractionalfactorial designs of several controllable factors as the frequencies ofhigh-dimensional contingency tables, and propose a general testing procedurefor the main effects or the interaction effects of the controllable factors.

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