A sequential monitoring Bayesian control scheme for attributes

Abstract

Classic approaches of Statistical Process Control (SPC) include the collection of samples from a production process and the computation of some output concerning a specific quality characteristic. This output, which is called chart statistic, is then compared against appropriately designed limits to decide whether an investigation for an assignable cause occurrence is needed. In recent years however, and especially in highly automated production processes, it is not unusual to have the ability of 100% inspection of the entire production. In such cases, the control procedure should be based on more appropriately designed SPC tools. This paper proposes a Bayesian model for production processes where all produced items are inspected. Each product may be conforming or nonconforming, and the output of the control procedure is the probability of out-of-control operation. This probability is compared against a critical probability to decide whether an intervention to the process is economically advisable. The case of inspection errors, namely, the case where a conforming item may be erroneously categorized as nonconforming and vice versa, is also investigated. Our numerical investigation reveals the economic superiority of the new scheme compared to simpler schemes that have been proposed over the years to tackle such problems.

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