A sequential Bayesian Cumulative Conformance Count approach to deterioration detection in high yield processes

Abstract

Cumulative conformance count (CCC) control chart is a powerful alternative to the traditional p-control chart, particularly in monitoring high yield processes with extremely low proportions of nonconformance. However, a prevalent limitation of the CCC control chart is its inability to detect small process deterioration. A sequential Bayesian CCC approach capable of detecting small process deterioration is proposed in this paper. The new approach outperforms the traditional CCC chart in that it does not require a large sample of initial observations of the process, which may be difficult, if not impossible to obtain in practice. Moreover, the approach is self-starting, and thus may be used in short production runs. A Bayesian updating procedure is developed, which allows for the determination of initial control limits based on only three initial observations or some prior knowledge about the proportion of nonconformance of the process. Values of proportions of nonconformance, ranging from 0.1 to 0.00001, are tested to demonstrate the deterioration detection capability of the new approach in conjunction with the proposed deterioration detection rules.