On Parameter Design of Binary-Input-and-Binary-Output Dynamic Systems

Abstract

This paper deals with the binary-input-and-binary-output (BIBO) dynamic parameter design problem. In the Taguchi two-step procedure, the settings of control factors are first determined such that the so-called standardized SN ratio is maximized, and then the levelling factor is adjusted to achieve the desired proportion of misclassification probabilities. The standardized SN ratio ηs is calculated assuming that levelling is conducted to make both misclassification probabilities equal. Then, a question arises whether or not ηs is still a valid measure for comparing different designs when the desired ratio of the two misclassification probabilities is not 1 (as in some chemical or metallurgical separations). In addition, Taguchi did not explain what the optimization criterion is in the above two-step procedure. In this paper, we first show that using ηs in the Taguchi approach can be justified even for the case where is not 1. Then, we formulate the BIBO parameter design problem in terms of minimizing expected quadratic loss, and show that the Taguchi two-step procedure can be also justified with respect to this criterion if a certain set of assumptions is satisfied. The appropriate value of is also determined.