對於功能多樣化的產品，製造商需要以各種不同的機器設備來生產多功能產品。然而，機器設備的維修與保養需要特殊專業的維修技術人員，因此製造商需要花費相當多的時間與成本來訓練特殊專業的維修技術人員。為了節省成本，製造商傾向於租賃機器設備來取代購買，在這情況下便有了租賃公司的衍生。對於租賃設備，租賃公司與製造商會針對設備的故障率/年齡特性來擬定租賃契約。而契約的內容包含了租賃期限、保養時間、故障維修的容忍時間及維修逾時的懲罰成本等等。為了降低租賃公司的維修成本及製造商因設備故障所帶來生產成本上的損失，本論文提出當設備的故障率或年齡到達一門檻值時，則進行預防保養的維修策略。我們利用預防保養之年齡回溯法與故障率降低法的維修策略來減少設備發生故障並且維持設備的正常運作，以製造出品質良好的產品。因此，對於租賃設備的故障率/年齡特性與租賃期的長短，本論文提出以下四個主題來研究租賃設備在租賃期內最佳的預防保養策略: (i) 年齡回溯法下，單一租賃期之預防保養策略; (ii) 年齡回溯法下，雙租賃期之預防保養策略; (iii) 故障率降低法下，單一租賃期之預防保養策略; (iv)故障率降低法下，雙租賃期之預防保養策略。

For multi-function products, manufacturers may need different types of machine
equipment to produce them. However, the maintenance of machine equipment usually requires special professional technicians, which is not economical for manufacturers to own a professional maintenance group. For cost reduction, manufacturers tend to lease machine equipment instead of buying them. Therefore, the lease companies have been developed. For the failure-rate/age feature of the leased equipment/goods, the lease company and manufacturers may sing a lease contract which includes the leased period, preventive maintenance (PM) time, tolerance time of repair and penalty cost. This thesis proposes that the lease company performs PM actions when the failure rate/age of equipment reaches a threshold value in order to reduce the lease company's maintenance cost and the manufacturer's production cost caused by equipment failures. The age-reduction and failure-rate-reduction methods of PM are adopted to prevent equipment failure and maintain the operational state of the equipment in order to produce the products with good quality. For the failure rate and age characteristic of the leased equipment and the length of lease period, this thesis proposes four major topics to investigate the optimal PM policy for the leased equipment within the lease period: (i) single-phase model under age-reduction method (ARM), (ii) two-phase model under ARM, (iii) single-phase model under failure-rate-reduction method (FRRM) and (iv) two-phase model under FRRM.

[1] Adachi, K. and Kodama, M., “Inspection policy for two-unit parallel redundant system”, Microelectronics and Reliability 20, 603-612 (1980).
[2] Anis, C. and Daoud, A.K., “An optimal inspection strategy for randomly failing equipment”, Reliability Engineering & System Safety 63, 127-131 (1999).
[3] Baohe, S., “An optimal inspection and diagnosis policy for a multi-mode system”, Reliability Engineering & System Safety 76, 181-188 (2002).
[4] Barlow, R.E. and Hunter, L.C., “Optimum preventive maintenance policies”,
Operations Research 8, 90-100, (1960).
[5] Barlow, R.E., Hunter, L.C., and Proschan, F., “Optimum checking procedures”,Journal of the Society for Industrial and Applied Mathematics 4, 1078-1095 (1963).
[6] Berg, M. and Epstein, B., “Comparison of age, block and failure replacement policies”, IEEE Transaction on Reliability 27-1, 25-29 (1978).
[7] Bhattacharjee, M.C., “Aging renewal process characterizations of exponential distributions”, Microelectronics and Reliability 33, 2143-2147 (1993).
[8] Biswas, A. and Sarkar, J., “Availability of a system maintained through several imperfect repairs before a replacement or a perfect repair”, Statistics & Probability Letters 50, 105-114 (2000).
[9] Blischke, W.R., “Mathematical models for analysis of warranty policies”,
Mathematical and Computer Modelling 13 1-16 (1990).
[10] Block, H.W., Borges, W.S. and Savits, T. H., “A general age replacement model with minimal repair”, Naval Research Logistics 35, 365-372 (1988).
[11] Boland, P.J. and Proschan, F., “Periodic replacement with increasing minimal repair costs at failure”, Operations Research 30, 1183-1189 (1982).
[12] Boland, P.J. and El-Neweihi, E., “Expected cost comparisons for inspection and repair policies”, Computers & Operations Research 22, 383-390 (1995).
[13] Brown, M. and Proschan, F., “Imperfect repair,” Journal of Applied Probability 20, 851–859 (1983).
[14] Cassandras, C.G. and Han, Y., “Optimal inspection policies for a manufacturing station”, European Journal of Operational Research 63, 35-53 (1992).
[15] Chan, J.K. and Shaw, L., “Modeling repairable systems with failure rates dependent on age and maintenance”, IEEE Transactions on Reliability 42, 566-570 (1993).
[16] 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).
[17] Chen, C.T., Chen, Y.W., and Yuan, J., “On a dynamic preventive maintenance policy for a system under inspection”, Reliability Engineering & System Safety 80, 41-47 (2003).
[18] Christer, A.H. and Waller, W.M., “Delay time models of industrial inspection maintenance problems”, Journal of the Operational Research Society 35, 401-406 (1984).
[19] Chun, Y.H., “Optimum number of periodic preventive maintenance operations under warranty”, Reliability Engineering and System Safety 37, 223-225 (1992).
[20] 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).
[21] Chung, K.J., “An approximation optimal inspection policy”, Microelectronics and Reliability 34, 1485-1488 (1994).
[22] Cui, L.R., Loh, H.T. and Xie, M., “Sequential inspection strategy for multiple systems under availability requirement”, European Journal of Operational Research 155, 170-177 (2004).
[23] Doyen, L. and Gaudoin, O., “Classes of imperfect repair models based on reduction of failure intensity or virtual age”, Reliability Engineering & System Safety 84, 45-56 (2004).
[24] Goel, L.R., Sharma, G.C. and Gupta, P., “Reliability analysis of a system with preventive maintenance, inspection and two types of repair”, Microelectronics and Reliability 26, 429-433 (1986).
[25] Gu, H.Y., “Studies on optimum preventive maintenance policies for general repair result”, Reliability Engineering & System Safety 41, 197-201 (1993).
[26] Jack, N. and Dagpunar, J.S., “An optimal imperfect maintenance policy over a warranty period”, Microelectronics and reliability 34, 529-534, (1994).
[27] Jack, N. and Schouten, F.V.D., “Optimal repair–replace strategies for a warranted product”, International Journal of Production Economics 67, 95-100 (2000).
[28] Jayabalan, V. and Chaudhuri, D., “Optimal maintenance and replacement policy for a deteriorating system with increased mean downtime”, Naval Research Logistics 39, 67-78 (1992a).
[29] Jayabalan, V. and Chaudhuri, D., “Optimal maintenance－Replacement policy under imperfect maintenance”, Reliability Engineering and System Safety 36(2), 165-169 (1992d).
[30] Jayabalan, V. and Chaudhuri, D., “Replacement policies: A near optimal algorithm”, IIE Transactions 27, 784-788 (1995).
[31] Kijima, M., Morimura, H. and Suzuki, Y., “Periodical replacement problem without assuming minimal repair”, European Journal of Operational Research 37(2), 194-203 (1988).
[32] Kijima, M. and Nakagawa, T., “Accumulative damage shock model with imperfect preventive maintenance”, Naval Research Logistics 38, 145-156 (1991).
[33] Kijima, M. and Nakagawa, T., “Replacement policies of a shock model with
imperfect preventive maintenance”, European Journal of Operational Research 57, 100-110 (1992).
[34] Lee, H.L. and Moinzadeh, K., “A repairable item inventory system with diagnostic and repair service”, European Journal of Operational Research 40, 210-221 (1989).
[35] Levitin, G. and Lisnianski, A., “Optimization of imperfect preventive maintenance for multi-state systems”, Reliability Engineering & System Safety 67, 193-203 (2000).
[36] Lie, C.H. and Chun, Y.H., “An algorithm for preventive maintenance policy”, IEEE Transactions on Reliability R-35(1), 71-75 (1986)
[37] Lin, D., Zuo, M.J. and Yam, R.C.M., “Sequential imperfect preventive maintenance models with two categories of failure modes”, Naval Research Logistics 48, 172-183 (2001).
[38] Makis, V. and Jardine, A.K.S., “Optimal replacement of a system with imperfect repair”, Microelectronics and Reliability 31, 381-388 (1991).
[39] Malik, M.A.K., “Reliable preventive maintenance policy”, AIIE Transactions 11(3), 221-228 (1979).
[40] Menipaz, E., “Optimization of stochastic maintenance policies”, European Journal of Operational Research 2, 97-106 (1978).
[41] Menipaz, E., “Cost Optimization of Some Stochastic Maintenance Policies”, IEEE Transactions on Reliability R-28, 133-136 (1979).
[42] Mohandas, K., Chaudhuri, D. and Rao, B.V.A., “Optimal periodic replacement with inspection and minimal repair for a system which is inoperable during inspection periods”, Microelectronics and Reliability 32, 509-513 (1992).
[43] Murthy, D.N.P. and Nguyen, D.G., “Optimal age policy with imperfect preventive maintenance,” IEE Transactions on Reliability R-30, 80-81 (1981).
[44] Nakagawa, T., “Imperfect preventive-maintenance,” Journal of the Operations Research Society of Japan 24, 213-227 (1979).
[45] Nakagawa, T., “Replacement models with inspection and preventive maintenance”, Microelectronics and Reliability 20, 427-433 (1980).
[46] Nakagawa, T., “A summary of periodic replacement with minimal repair at failure”, Journal of the Operational Research Society of Japan 24(3), 213-227 (1981).
[47] 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).
[48] Nakagawa, T., “Sequential imperfect preventive maintenance policies”, IEEE Transactions on Reliability 37(3), 295-298 (1988).
[49] Nguyen, D.G. and Murthy, D.N.P., “Optimal preventive maintenance policies for repairable systems”, Operations Research 29, 1181-1194 (1981).
[50] Osaki, S. and Nakagawa, T., “A note on age replacement”, IEEE Transactions on Reliability 24-1, 92-94 (1975).
[51] Osaki, S., Applied Stochastic System Modeling, Springer, New York (1993).
[52] Pham, H. and Wang, H., “Invited review－Imperfect Maintenance”, European
Journal of Operational Research 94, 425-438 (1996).
[53] Phillips, M.J., “A preventive maintenance plan for a system subject to revealed and unrevealed faults”, Reliability Engineering 2, 221-231 (1981).
[54] Qian, C., Nakamura, S. and Nakagawa, T., “Replacement and minimal repair policies for a cumulative damage model with maintenance”, Computers & Mathematics with Applications 46, 1111-1118 (2003).
[55] Scarsini, M. and Shaked, M., “On the value of an item subject to general repair or maintenance”, European Journal of Operational Research 122, 625-637 (2000).
[56] Seo, J.H. and Bai, D.S., “An optimal maintenance policy for a system under periodic overhaul”, Mathematical and Computer Modelling 39, 373-380 (2004).
[57] Sheu S.H., “Periodic replacement with minimal repair at failure and general random repair cost for a multi-unit system,” Microelectronics and Reliability, 31, 1019-1025 (1991).
[58] Sheu, S.H. and Liou, C.T., “An age replacement policy with minimal repair and general random repair cost”, Microelectronics and Reliability 32, 1283-1289 (1992).
[59] Sheu, S.H., Griffith, W.S. and Nakagawa, T., “Extended optimal replacement model with random minimal repair costs”, European Journal of Operational Research 85, 636-649 (1995).
[60] Sheu, S.H., “Extended block replacement policy of system subject to shocks”, IEEE Transactions on Reliability 46-3, 375-382 (1997).
[61] Sheu, S.H. and Yu, S.L., “Warranty strategy accounts for bathtub failure rate and random minimal repair Cost”, Computers & Mathematics with Applications 49, 1233-1242 (2005).
[62] Sim, S.H. and Endrenyi, J., “A failure-repair model with minimal and major maintenance”, IEEE Transactions on Reliability 42, 134-140 (1993).
[63] Stadje, W. and Zuckerman, D., “Optimal repair policies with general degree of repair in two maintenance models”, Operations Research Letters 11, 77-80 (1992).
[64] Teramoto, K., Nakagawa, T. and Motoori, M., “Optimal inspection policy for a parallel redundant system,” Microelectronics and Reliability 30, 151-155 (1990).
[65] Tilquin, C. and Cléroux, R., “Block replacement policies with general cost structures”, Technometrics 17-3, 291-298 (1975a).
[66] Tilquin, C. and Cleroux, R., “Periodic Replacement with minimal repair at failure and general cost function”, Journal of Statistical Computing and Simulation 4(1), 63-67 (1975b).
[67] Wang, H. and Pham, H., “Optimal age-dependent preventive maintenance policies with imperfect maintenance”, International Journal of Reliability, Quality and Safety Engineering 3, 119-135 (1996b).
[68] Yeh, R.H. and Lo, H.C., “Optimal preventive-maintenance warranty policy for repairable products”, European Journal of Operational Research 134, 59-69 (2001).
[69] Yun, W.Y., “An age replacement policy with increasing minimal repair cost”, Microelectronics and Reliability 29, 153-157 (1989).