Recognition of the Best Setting for the Target Value of an Industrial Process under Parametric Uncertainty

Abstract

Most stochastic models for determining the optimal target value for an industrial process are developed in the extensive literature under the assumptions that the parameter values of the underlying distributions are known with certainty. In actual practice, such is simply not the case. When these models are applied to solve real-world problems, the parameters are estimated and then treated as if they were the true values. The risk associated with using estimates rather than the true parameters is called estimation risk and is often ignored. When data are limited and (or) unreliable, estimation risk may be significant, and failure to incorporate it into the model design may lead to serious errors. Its explicit consideration is important since decision rules that are optimal in the absence of uncertainty need not even be approximately optimal in the presence of such uncertainty. The aim of the present paper is to show how the invariance principle may be employed in the particular case of finding, from the statistical data, the best setting for the target value of an industrial process. An example is given.