考量檢驗誤差與退貨成本下之CSP-1的最適抽樣策略

The optimal policy for CSP-1 with inspection errors and return cost

巫文萍(Wen-Ping Wu)

國立虎尾科技大學/管理學院/工業工程與管理研究所/碩士(2007年)

摘要

產品品質的良窳，不僅直接影響生產者獲利與市場佔有率，甚至會影響使用者生命、財產的安全，因此如何有效的篩選出不良產品以提昇產品品質，是生產者所要面對的課題。在連續製程中，CSP-1是最早用於監控製程、控制產品品質與消弭不良品的方法，惟CSP-1係假設檢驗誤差不存在且允許出貨有不良率。事實上，檢驗大多存在有檢驗誤差 ( 型Ⅰ和型Ⅱ誤差 )，且某些產品或設備之關鍵零組件是不允許不良品存在的 ( 如車輛的剎車系統與飛航之雷達導引系統等 )。本論文的目的即是要探討存在有檢驗誤差及不允許不良品存在下之CSP-1的最佳檢驗策略。更明確地說，本文以最大化單位淨利為目標，在每一件不良品皆課以高額的處罰 (或退貨) 成本，並針對檢驗中存在的型Ⅰ和型Ⅱ誤差，嘗試引進較高成本之精密檢驗方式，以提升檢驗效果的條件下，針對將CSP-1檢驗判定的不良品丟棄與否、CSP-1未檢驗之部分是否予以精密檢驗和CSP-1檢驗後之產品是否以固定比例施予精密檢驗，考慮十種不同的情境組合，以決定其最佳檢驗間隔數i (clearance number)、抽樣比率f (sampling frequency) 和最佳精密檢驗比率。

並列摘要

CSP-1 is the earliest method used to monitor and control the quality of products manufactured in a continuous production process. Two characteristics are involved in CSP-1: (1) Inspections are assumed to be perfect and (2) Defectives are permitted for the products shipped to the consumer. In practical applications, these characteristics are somewhat impractical. Because the inspection testing fails to be perfect and two types of errors (types I and II) can occur. The former will result in the necessity of producing additional items beyond the quantity ordered by the manufacturer; the latter results in that the products shipped to the consumer may not satisfy the quality requirement. Besides, defectives are strictly prohibited for some products and a great return cost will be fined for each defective. In such a situation, one of the effective methods to screen out the defectives is a precise inspection. However, precise inspection is usually costly. The purpose of this paper is to determine the optimal policy of CSP-1 with inspection errors and return cost. More specifically, by adopting a precise inspection to screen out the defectives for the products behind the procedure of CSP-1, a nonlinear programming problem is built to determine the optimal clearance number, sampling frequency and precise inspection proportion such that the unit net profit is maximal for each of the following three situations: (a) discarding the defectives identified by CSP-1, (b) except (a), taking precise inspection for a proportion of the products not inspected in the procedure of CSP-1, and (c) except (a) and (b), taking precise inspection for a proportion of the nondefective identified by CSP-1.

參考文獻

4.Chen, C. H. and Chou, C. Y. (2004). “Minimum average fraction inspected for modified CSP-1 plan”, Pan-Pacific Management Review 7, 35-43.

1.Banzhoof, R. A. and Brugger, R. M. (1970). “Reviews of standards and specifications-MIL-STD-1235 (ORD), single and multi-level continuous sampling procedures and tables for inspection by attributes”, Journal of Quality Technology 2(1), 41-53.

2.Case, K. E., Bennett, G. K. and Schmidt, J. W. (1973). “The Dodge CSP-1 continuous sampling plan under inspection error”, AIIE Transactions 5, 193-202.

3.Chen, C. H. and Chou, C. Y. (2002). “Economic design of continuous sampling plan under linear inspection cost”, Journal of Applied Statistics 29, 1003-1009.

5.Dodge, H. F. (1943). “A sampling inspection plan for continuous production”, Annals of Mathematical Statistics 14, 264-279.