Abstract
This article concerns repair-limit replacement problems and review the existing stochastic models in which repair times are random variables. If a system fails, we should decide whether we repair the failed system (repair option) or replace it by new one (replacement option with a lead time). We classify the existing repair-time limit models based on available information amount of repair times (perfect, partial, and no information), repair type (perfect and imperfect repair), and objective functions (expected cost and profit with and without discounting). We summarize the modeling assumptions and explain how to obtain the optimal repair-limit replacement policies. Finally, we propose some interesting topics for future studies.
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Dohi T, Aoki T, Kaio N, Osaki S (1998) Non-parametric preventive maintenance optimization models under earning rate criteria. IIE Trans 30:1099–1108
Dohi T, Aoki T, Kaio N, Osaki S (2001) Optimization the repair time limit replacement schedule with discounting and imperfect repair. J Qual Maintenance Eng 7:71–84
Dohi T, Aoki T, Kaio N, Osaki S (2003) The optimal repair-time limit replacement policy with imperfect repair: Lorenz transform approach. Math Comput Modell 38:1169–1176
Dohi T, Aoki T, Kaio N, Osaki S (2006) Statistical estimation algorithms for some repair-limit replacement scheduling problems under earning rate criteria. Comput Math Appl 51:345–356
Dohi T, Kaio N (2005) Repair-limit replacement program in industrial maintenance-renewal reward process modeling. In: Tokimasa T, Hiraki S, Kaio N (eds) Applied economic informatics and systems sciences. Kyushu University Press, Fukuoka, pp 157–172
Dohi T, Kaio N, Osaki S (1995) Solution procedure for a repair limit problem using the TTT concept. IMA J Math Appl Bus Ind 6:101–111
Dohi T, Kaio N, Osaki S (1998) On the optimal ordering policies in maintenance theory-survey and applications. Appl Stochast Models Data Anal 14:309–321
Dohi T, Kaio N, Osaki S (2000) A graphical method to repair cost limit replacement policies with imperfect repair. Math Comput Modell 31:99–106
Dohi T, Kaio N, Osaki S (2001) Determination of optimal repair-cost limit on the Lorenz curve. J Oper Res Soc Jpn 44:207–219
Dohi T, Kaio N, Osaki S (2003) A new graphical method to estimate the optimal repair-time limit with incomplete repair and discounting. Comput Math Appl 46:999–1007
Dohi T, Kaio N, Osaki S (2003) Preventive maintenance models: replacement, repair, ordering and inspection. In: Pham H (ed) Springer handbook of reliability. Springer, London, pp 349–366
Dohi T, Kaio N, Osaki S (2007) Stochastic profit models under repair-limit replacement program. In: Proceedings of international workshop on recent advances in stochastic, operations research II:27–34
Dohi, T. Kaio, N. and Osaki, S. (2010), A stochastic profit model under repair-limit replacement program with imperfect repair. In: Proceedings of 4th Asia-Pacific, International Symposium(APARM 2010), pp 153–160
Dohi T, Koshimae H, Kaio N, Osaki S (1997) Geometrical interpretations of repair cost limit replacement policies. Int J Reliab Qual Safe Eng 4:309–333
Dohi T, Matsushima N, Kaio N, Osaki S (1996) Nonparametric repair limit replacement policies with imperfect repair. Eur J Oper Res 96:260–273
Dohi H, Okamura H, Osaki S (1999) Optimal order-limit policies for an (r, Q) inventory system. IMA J Math Appl Bus Ind 10:127–145
Dohi T, Takeita K, Osaki S (2000) Graphical methods for determining/estimating optimal repair-limit replacement policies. Int J Reliab Qual Safe Eng 7:43–60
Drinkwater RW, Hastings NAJ (1967) An economical replacement model. Oper Res Q 18:121–138
Hastings NAJ (1968) Some notes on dynamic programming and replacement. Oper Res Q 19:453–464
Hastings NAJ (1969) The repair limit replacement method. Oper Res Q 20:337–349
Hastings NAJ (1970) Equipment replacement and the repair limit method. In: Jardine AKS (ed) Operational research in maintenance. Manchester University Press, Barnes & Noble Inc., New York, pp 100–118
Jiang X, Cheng K, Makis V (1998) On the optimality of repair-cost-limit polices. J Appl Probab 35:936–949
Jiang X, Makis V, Jardine AKS (2001) Optimal repair/replacement policy for a general repair model. Adv Appl Probab 33:206–222
Kaio N (1981) Optimum repair limit policies with cost constraint. Microelectron Reliab 21:597–599
Kaio N, Osaki S (1982) Optimum repair limit policies with a time constraint. Int J Syst Sci 13:1345–1350
Kaio N, Dohi T, Osaki S (2002) Classical replacement models. In: Osaki S (ed) Stochastic models in reliability and maintenance. Springer, Berlin, pp 65–87
Kapil DVS, Sinha SM (1978) Repair limit suspension policies for a 2-unit redundant system with 2-phase repairs. IEEE Trans Reliab R- 30:90
Kapur PK, Kapoor KR (1978) A note on repair limit suspension policies for a 2-unit standby redundant system with two phase repairs. Microelectron Reliab 17:591–592
Kapur PK, Kapoor KR, Kapil DVS (1980) Joint optimum preventive-maintenance and repair-limit replacement policies. IEEE Trans Reliab R-29:276–279
Kapur PK, Garg RB, Butani NL (1989) Some replacement policies with minimal repairs and repair cost limit. Int J Syst Sci 20:267–279
Kim HG, Yun WY (2010) A repair time limit replacement policy with estimation error. Commun Stat Theory Methods 39:1–14
Koshimae H, Dohi T, Kaio N, Osaki S (1996) Graphical/statistical approach to repair limit replacement problem. J Oper Res Soc Jpn 39:230–246
Lambe TA (1974) The decision to repair or scrap a machine. Oper Res Q 25:99–110
L’Ecuyer P, Haurie A (1987) The repair vs replacement problem: a stochastic control approach. Optimal Control Appl Methods 8:219–230
Love CE, Rodger R, Blazenko G (1982) Repair limit policies for vehicle replacement. INFOR 20:226–237
Love CE, Guo R (1996) Utilizing Weibull failure rates in repair limit analysis for equipment replacement/preventive maintenance decisions. J Oper Res Soc 47:1366–1376
Muth EJ (1977) An optimal decision rule for repair vs replacement. IEEE Trans Reliab R-26:179–181
Nakagawa T (2006) Maintenance theory of reliability. Springer, Berlin
Nakagawa T, Mizutani S (2009) A summary of maintenance policies for a finite interval. Reliab Eng Syst Safe 94:89–96
Nakagawa T, Osaki S (1974) The optimum repair limit replacement policies. Oper Res Q 25:311–317
Nguyen DG, Murthy DNP (1980) A note on the repair limit replacement policy. J Oper Res Soc 31:1103–1104
Nguyen DG, Murthy DNP (1981) Optimal repair limit replacement policies with imperfect repair. J Oper Res Soc 32:409–416
Osaki S, Okumoto K (1977) Repair limit suspension policies for a two unit standby redundant system with two phase repairs. Microelectron Reliab 16:41–45
Segawa Y, Ohnishi M (2000) The average optimality of a repair-limit replacement policy. Math Comput Modell 31:327–334
Thomas LC, Osaki S (1978) An optimal ordering policy for a spare unit with lead time. Eur J Oper Res 2:409–419
Wang H, Pham H (2005) Reliability and optimal maintenance. Springer, Berlin
White DJ (1989) Repair limit replacement. OR Spektrum 11:143–149
Acknowledgments
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No.2010-0025084). The authors are grateful to Professor S. Osaki who stimulated their interest in maintenance optimization area through many papers and edited books in reliability and maintenance.
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Yun, W.Y., Kaio, N. (2013). Repair-Time Limit Replacement Policies. In: Dohi, T., Nakagawa, T. (eds) Stochastic Reliability and Maintenance Modeling. Springer Series in Reliability Engineering, vol 9. Springer, London. https://doi.org/10.1007/978-1-4471-4971-2_5
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DOI: https://doi.org/10.1007/978-1-4471-4971-2_5
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