Markovian Decision Models for the Evaluation of a Large Class of Continuous Sampling Inspection Plans

Abstract

The purpose of this article is to present a uniform method for the evaluation of a large class $S_D$ of Dodge-type continuous sampling inspection plans. The class of Dodge-type plans includes, among others, CSP-1, 2, 3, 4, and 5, MLP-1, $r$, and $T$, and H-106 plans. The evaluation of any plan $S \varepsilon S_D$ is in terms of its average outgoing quality limit (AOQL). The AOQL for $S$ may be defined as an upper bound to the long run proportion of defective items that remains in the output after inspection, given certain assumptions about Nature's (the processes') ability to control process quality. In particular, a specific method of evaluation involving linear programming as its computational tool is developed for the case where Nature is assumed to be unrestricted in her ability to produce and submit defectives. The problem of determining unrestricted AOQL's for the plans in $S_D$ is viewed in terms of two Markovian decision models where Nature is taken to be the decision maker. These decision models are abstractly described in Section 2. Their relation to the problem of evaluating continuous sampling plans is specified in Section 3. The linear programs corresponding to the two decision models are derived in Sections 4 and 5. In Section 6 the linear programming approach is illustrated with an example, and in the last section a row reduction theorem is given for one of the linear programs.