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

不可維修品在考量檢驗誤差和退貨成本下之CSP-1和精密檢驗的最佳聯合檢驗

于鴻福(Hong-Fwu Yu)；游文清(Wen-Ching Yu)

CSP-1 ； 檢驗誤差 ； 退貨成本 ； 精密檢驗 ； CSP-1 ； inspection errors ； return cost ； precise inspection

品質學報

18卷1期（2011 / 03 / 01）

61 - 74

英文

本研究之目的是針對不可維修產品，在考量存在檢驗誤差和退貨成本下，探討CSP-1和精密檢驗的最佳聯合檢驗策略。本文以最大化長期之單位淨利爲目標，以決定(1)CSP-1之最佳檢驗計畫與(2)於CSP-1中未檢驗之產品、檢驗判定爲良品和判定爲不良品之產品需進行精密檢驗之比例。分析之結果顯示，取決於七個參數（包括：型Ⅰ誤差、型Ⅱ誤差、產品的售價、單位機會成本、單位退貨成本、單位精密檢驗成本和製程的不良率），最佳檢驗策略中針對CSP-1的部份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-1中未檢驗、檢驗判定爲良品和不良品之產品需進行精密檢驗之比例的部份，亦有兩種主要的比例：100%和0%。

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%.

1. Chen, C. H.,Chou, C. Y.(2004).Minimum average fraction inspected for modified CSP-1 plan.Pan-Pacific Management Review,7(1),35-43.
   連結：
2. Lin, T. Y.,Yu, H. F.(2009).An optimal policy for CSP-1 with inspection errors and return cost.Journal of Chinese Institute of Industrial Engineers,26(1),70-76.
   連結：
3. Dodge, H. F., 1943, A sampling inspection plan for continuous production, Annals of Mathematical Statistics, 14(3), 264-279.
4. Case, K. E.,Bennett, G. K.,Schmidt, J. W.(1973).The Dodge CSP-1 continuous sampling plan under inspection error.AIIE Transactions,5(2),193-202.
5. Chen, C. H.,Chou, C. Y(2002).Economic design of continuous sampling plan under linear inspection cost.Journal of Applied Statistics,29(7),1003-1009.
6. Endres, A. C.(1979).Minimum AFI plan designs for inspection error.Proceedings of ASQC Technical Conference Transaction-Houston
7. Govindaraju, K.,Kandasamy, C.(2000).Design of generalized CSP-C continuous sampling plan.Journal of Applied Statistics,27(7),829-841.
8. Haji, A.,Haji, R.(2004).The optimal policy for a sampling plan in continuous production in terms of the clearance number.Computers and Industrial Engineering,47(2),141-147.
9. Resnikoff, G. J.(1960).Minimum average fraction inspected for a continuous sampling plan.Journal of Industrial Engineering,11(2),208-209.
10. Ross, S. M.(1993).Introduction to probability models.New York:Academic Press, Inc..
11. Wang, R. C.,Chen, C. H.(1997).Minimum average fraction inspected for continuous sampling plan CSP-1 under inspection error.Journal of Applied Statistics,24(5),539-548.
12. Yu, H. F.,Yu, W. C.,Wu, W. P.(2009).A mixed inspection policy for CSP-1 and precise inspection under inspection errors and return cost.Computers and Industrial Engineering,57(3),652-659.

1. 陳亭彣、于鴻福(2013)。考量檢驗誤差和退貨成本下之MLP-2和精密檢驗的最適混合檢驗策略。品質學報，20(1)，115-136。
2. 謝雅惠,潘彥如,黃允成,張妤宣(2018)。根據更新過程理論建構複合式最適檢驗計畫之研究。技術學刊，33(2)，79-97。