A mixed inspection policy for CSP-2 and precise inspection under inspection errors and return cost

Abstract

This article deals with a mixed policy between precise inspection and continuous sampling plan-2 (CSP-2) with inspection errors (Types I and II) and return cost. The optimal mixed inspection policy is determined by using the criterion of maximizing the unit net profit. Specifically, 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-2 and (2) the optimal proportions for which precise inspection should be performed for the non-inspected items in the procedure of CSP-2, the non-defective items, and the defective items identified by CSP-2. Overall, the analytical results indicate that, depending on the nine parameters (the process defective fraction, Type I error, Type II error, the selling price of an item, the unit repair cost, the unit return cost, the unit opportunity cost, the unit inspection cost, and the unit cost of precise inspection), both non-repairable and repairable products have two main optimal inspection policies for CSP-2: “do not inspect” and “do 100% inspection”; also, for the non-inspected items, the non-defective items, and the defective items identified in CSP-2, there are two main proportions on which precise inspection should be performed: 100% and 0%. A numerical example is provided to illustrate the proposed method. Besides, a comparison with CSP-2 is also made to evaluate the effectiveness of the proposed model.