Evaluating and Implementing 3-Level Control Charts

In some situations, an appropriate quality measure uses three or more discrete levels (rather than an attributes or a variables measure) to classify a product characteristic. In previous work, we refer to such a classification scheme as a multi-level product quality measure, and present a general methodology for the evaluation and implementation of 3-level (conforming, marginal, nonconforming) acceptance sampling plans. In this paper, we apply this classification scheme and methodology for the purpose of evaluating and implementing 3-level control charts. The OC and ARL functions are formulated and integrated into an approximate parameter selection method. Because of the approximation, a manufacturer must overstate their ARL expectations in order to obtain reasonable control chart performance.