On parameter design of binary-input-and-binary-output dynamic systems

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 leveling factor is adjusted to achieve the desired proportion of misclassification probabilities. The standardized SN ratio ηs is calculated assuming that leveling is conducted to make both misclassification probabilities equal. In this paper, we first show that using ηs in the Taguchi approach can be justified even for the case where α 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 also be justified with respect to this criterion if a certain set of assumptions is satisfied. The appropriate value of α is also determined.