A mixed inspection policy for csp-t and precise inspection under inspection errors and return cost

Abstract

This article deals with 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 taken for the non-inspected items, the non-defectives, and the defectives identified in the procedure of CSP-T. Overall, the analytical results indicate that depending on ten parameters (the process defective fraction, Type I error, Type II error, the selling price of an item, the unit formal repair cost, the unit informal repair cost, the unit return cost, the unit opportunity cost, the unit inspection cost, and the unit cost of precise inspection), both of non-repairable and repairable products have two main optimal inspection policies for CSP-T: “Do 100% inspection consecutively” and “Stop inspection after 100% inspection”; besides, for the non-inspected items, the non-defectives, and the defectives identified in the procedure of CSP-T, there are two main proportions on which precise inspection should be performed: 100% and 0%.

本研究之目的是在考量檢驗誤差（型I和型II）和退貨成本下 ， 探討CSP-T和精密檢驗的最佳混合檢驗策略。 明確地說 ， 針對不可維修和可維修兩種產品 ， 本文以最大化長期之單位淨利為目標 ， 以決定(1) CSP-T之最佳檢驗計畫與(2)於CSP-T中未檢驗之產品、 檢驗判定為良品和判定為不良品之產品需進行精密檢驗之比例。 分析之結果顯示 ， 取決於十個參數(製程的不良率、 型I誤差、 型II誤差、 產品售價、 正式的單位維修成本、 非正式的單位維修成本、 單位退貨成本、 單位機會成本、 單位檢驗成本和單位精密檢驗成本) ， 不可維修和可維修兩種產品之最佳混合檢驗策略中 ， CSP-T 有兩種主要的檢驗策略 ： 不執行任何檢驗與執行百分之百檢驗 ； 而對於在CSP-T中未檢驗、 檢驗判定為良品和不良品之產品需進行精密檢驗之比例的部份 ， 則亦有兩種主要的比例 ： 0%和100%。

（*聯絡人 ： [email protected]）

Keywords:

• CSP-T
• inspection errors
• return cost
• optimal mixed inspection policy

Keywords:

• 關鍵字 ： CSP-T ， 檢驗誤差 ， 退貨成本 ， 最佳混合檢驗策略

Notes

（*聯絡人 ： [email protected]）