Information theoretic framework for process control

This paper proposes a general framework for constructing control charts based on information theory. The potential applications include developing information charts, for monitoring moments and distributions of a process variable and process attributes. In information theoretic process control, process moments are mapped to process distributions at in-control and monitoring states, and then to a control function via constrained maximization of entropy and minimization of Kullback–Leibler function (cross-entropy). Variants of information charts can be developed without using distributional assumptions and based on a single criterion function, the information discrepancy between two distributions. An example of an information chart, Information mean-variance chart, IMV-chart, for monitoring process mean and variance is developed. The IMV-chart combines the standard {x^–}-chart and s²-chart, and provides an information theoretic explication of the traditional procedures. Based on a run-length study, it is found that the IMV-chart singly possesses certain advantages over the standard two-chart implementation of {x^–}-chart and s²-chart. Multivariate extension, monitoring counts and proportions, and monitoring distributional changes are briefly discussed.