A Joint Inspection Policy between CSP-1 and Precise Inspection for Non-repairable Products under Inspection Errors and Return Cost

Under the assumptions that inspections in CSP-1 are not perfect and each defective shipped to the buyer will be fined a return cost, this paper investigates a joint policy between precise inspection and CSP-1 for non-repairable products, where precise inspection is introduced to screen out the defectives for the products behind the procedure of CSP-1. By using the criterion of maximizing the unit net profit, the following five decision variables are determined: (1) the optimal clearance number, (2) the optimal sampling frequency, and (3) the proportions which should be taken precise inspection for the defectives identified by CSP-1, 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 opportunity cost, the unit return cost, the unit cost of precise inspection, and the process defective fraction), two main inspection policies for CSP-1 are ”Do not inspect” and ”Do 100% inspection.” Besides, for the defectives and the non-defectives identified in CSP-1 and the non-inspected items, two main proportions which should be performed precise inspection are: 100% and 0%.