A mixed inspection policy for CSP-1 and precise inspection under inspection errors and return cost

This paper is to deal with a mixed policy between precise inspection and CSP-1 with inspection errors (Types I and II) and return cost. First, the concept of a renewal reward process is employed to obtain the long-term net profit of the mixed inspection policy. Then, with respect to non-repairable and repairable products, we determine the following four decision variables such that the unit net profit is maximal: (1) the optimal clearance number, (2) the optimal sampling frequency, and (3) the proportions which should be taken precise inspection for the non-inspected items in the procedure of CSP-1 and the non-defectives identified by CSP-1. Overall, the analytical results indicate that depending on seven parameters (Type I error, Type II error, the selling price of an item, the unit repair cost, the unit return cost, the unit cost of precise inspection, and the process defective fraction), there are three possible optimal inspection policies for CSP-1: “Do not inspect”, “Do 100% inspection”, or any setting for (i, s); for both of the non-defectives identified in CSP-1 and the non-inspected items, there are three possible proportions which should be performed a precise inspection: all, none, or any proportion.