  Suppose several two-valued input-output systems are designed by setting the
levels of several controllable factors. For this situation, Taguchi method has
proposed to assign the controllable factors to the orthogonal array and use
ANOVA model for the standardized 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 paper, 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.
