本論文針對可維修產品，探討有限區間下免費小修保固對產品置換時間的影響。當產品以附加免費小修保固銷售時，賣方須負擔保固期產品失效之修理與費用，而買方雖不必負擔小修費用但需負擔產品因失效所帶來的當機成本。本論文以買方觀點，分別建構了四種產品保固長度與產品使用時間關係之成本模式，並推導出這四種模式之期望總成本最低之最佳置換時間。在產品失效率隨時間遞增的情況下，本論文進一步獲得最佳置換時間之特性，藉此發展尋求最佳置換時間之演算法。最後，透過數值範例說明附免費小修保固的產品在有限區間下對最佳置換時間之影響。

In this thesis, we investigate the effects of repairable products’ single-replacement on a free minimal repair warranty under a finite horizon. When a product is being sold with a free minimal repair warranty, the vendor is responsible for the reparation and the related cost, while despite the vendee is free from the repairing cost, they still need to afford for the downtime cost. The research develops four cost models which are related to product warranty period and product usage period. And derived from the model, we obtain the corresponding optimal single-replacement time so that the expected total cost is minimized. Under the case of product failure rate is increased with time, the research further obtain the characteristic about the optimal single-replacement time, and an algorithm is developed to derive the optimal single-replacement time. Finally, the impact of repairable products’ single-replacement with a free minimal repair warranty under a finite horizon is illustrated through a numerical example.

[1]葉瑞徽, 「產品保證對最佳維修策略之影響」, 國科會研究計畫 NSC-91-2213-E-011-091, 2002.
[2]方正中，高子傑，郭輝明，蕭瑞民，2006第六版，「工程經濟」，滄海書局。
[3]Blischke, W R., “Mathematical models for analysis of warrwnty policies”, Mathematical Computational Modeling, 13, 1-16 (1990)
[4]Chen, M. and Feldman, R.M., “Optimal replacement policies with minimal repair and age-dependent costs”, European Journal of Operational Research 98, 75-84 (1997).
[5]Chukova, S. and Johnston, M.R., “Two-dimensional warranty repair strategy based on minimal and complete repairs”, Mathematical and Computer Modelling 44, 1133-1143 (2006).
[6]Jaturonnatee, J., Murthy, D.N.P., and Boondiskulchok, R.“Optimal preventive maintenance of leased equipment with corrective minimal repairs”, European Journal of Operational Research 174, 201-215 (2006).
[7]Murthy, D.N.P. and Djamaludin, “New product warranty: A literature review”, International Journal of Production Economics, 79, 231-260 (2002).
[8]Nakagawa, T., “A summary of periodic replacement with minimal repair at fialure”, Journal of the Operational Research Society of Japan 24(3), 231-227(1981).
[9]Nakagawa, T., and Kowada, M., “Analysis of a system with minimal repair and its application to replacement policy”, European Journal of Operational Research 12, 176-182 (1983).
[10]Osaki, S. and Nakagawa, T., “A note on age replacement”, IEEE Transactions on Reliability 24-1, 92-94 (1975).
[11]Osaki, S., Applied Stochastic System Modeling, Springer, New York (1993).
[12]Polatoglu, H. and I. Sahin,“Probability distribution of cost, revenue and profit over a warranty cycle,” European Journal of Operational Research, 108, 170-183 (1998).
[13]Sheu, J.H., “Periodic replacement with minimal repair at failure and general random repair cost for a multi-unit system”, Microelectronics and Reliability 31, 1019-1025 (1992).
[14]Sheu, S.H., “Extended block replacement policy of system subject to shocks”, IEEE Transactions on Reliability 46-3, 375-382 (1997).