A Proposal on Sequential Experiments Method for Plual Quality Characteristics with Requirements

Abstract

In cases where plural quality characteristics and their respective requirements exist and when the operating conditions that satisfy all the requirements are explored - with a set of given data in an experimental region from which the data have been collected -, there may be no operating condition explored. In such an instance, we have a problem of where to move the experimental region in order to explore the operating conditions which satisfy the requirements. While for a single quality characteristic this problem has been well investigated in the field of sequential experiments methodology, for plural quality characteristics it is necessary to solve this problem by finding an appropriate response variable as a function of operating conditions. This paper shows that the probability that quality characteristics simultaneously satisfy the requirements is derived as a function of operating conditions, and that the steepest ascent method, which is known as a sequential experiments method for a single response variable, can be also applied to the case for plural quality characteristics by treating the probability as a response variable. Specifically, it shows how to derive favorable estimates for that probability and its steepest ascent direction and discusses the properties of those estimators. In addition, a practical application of this method is discussed.