A note on a mixed inspection policy for CSP-T and precise inspection under inspection errors and return cost

Abstract

CSP-T is a three-level continuous sampling plan (CSP). Yu, Yu, and Wu investigated a mixed policy between precise inspection and CSP-T with inspection errors (Types I and II) and return cost. With respect to non-repairable and repairable products, the following decision variables are determined such that the unit net profit is maximal: (1) the optimal sampling plan for CSP-T and (2) the optimal proportions on which precise inspections should be performed for the non-inspected items, the non-defectives, and the defectives identified in the procedure of CSP-T. For both non-repairable and repairable products, there are two main optimal inspection policies for CSP-T: “Do 100% inspection consecutively” and “Stop inspection after 100% inspection”. This note will extend the work of Yu, Yu, and Wu to a generalized case with an n-level sampling inspection process. Differing from the work of Yu, Yu, and Wu, this note finds that the number of sampling inspection levels is a decision variable, and that for both of non-repairable and repairable products, there are three main optimal inspection policies for the generalized CSP: “Do 100% inspection consecutively”, “Stop inspection after 100% inspection”, and “Set the number of sampling inspection levels to be infinity”.