Design of control and monitoring rules for state dependent processes

Most statistical process control (SPC) methods assume that faulty products are the result of independent and identically distributed error modes in the production system. This paper proposes a general framework for extending SPC methods to autocorrelated and state dependent processes. The suggested methodology does not require an α-priori knowledge of the process distribution. A context identification model is used to estimate the probabilities of different process outputs based on the contexts in which they appear. The Kullback-Leibler measure for the discrimination between distributions is adapted for dealing with distribution that can be described with context models. It is demonstrated that the Kullback-Leibler statistic is approximately Chi-square distributed with the number of degrees of freedom depending on the number of contexts and symbol types. Control limits are developed for the dependent processes, and numerical examples are presented.