Statistical testing procedure for the interaction effects of several controllable factors in two-valued input-output systems

TL;DR

This paper introduces a new statistical testing procedure for analyzing interaction effects among controllable factors in two-valued input-output systems, addressing limitations of traditional methods like Taguchi's approach.

Contribution

It proposes a general testing framework based on contingency table analysis for main and interaction effects, improving reliability over existing methods.

Findings

The proposed method effectively detects interaction effects.

It handles unbalanced standard errors in SN ratios.

The approach is applicable to factorial design data.

Abstract

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.