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Repair-Time Limit Replacement Policies

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Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY,volume 9))

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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References

  1. Dohi T, Aoki T, Kaio N, Osaki S (1998) Non-parametric preventive maintenance optimization models under earning rate criteria. IIE Trans 30:1099–1108

    Google Scholar 

  2. 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

    Article  Google Scholar 

  3. 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

    Article  MATH  Google Scholar 

  4. 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

    Article  MathSciNet  MATH  Google Scholar 

  5. 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

    Google Scholar 

  6. 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

    MathSciNet  MATH  Google Scholar 

  7. 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

    Article  MathSciNet  MATH  Google Scholar 

  8. 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

    Article  MathSciNet  MATH  Google Scholar 

  9. 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

    MathSciNet  MATH  Google Scholar 

  10. 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

    Article  MathSciNet  MATH  Google Scholar 

  11. 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

    Chapter  Google Scholar 

  12. 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

    Google Scholar 

  13. 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

    Google Scholar 

  14. 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

    Article  Google Scholar 

  15. Dohi T, Matsushima N, Kaio N, Osaki S (1996) Nonparametric repair limit replacement policies with imperfect repair. Eur J Oper Res 96:260–273

    Article  Google Scholar 

  16. 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

    MathSciNet  MATH  Google Scholar 

  17. 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

    Article  Google Scholar 

  18. Drinkwater RW, Hastings NAJ (1967) An economical replacement model. Oper Res Q 18:121–138

    Article  Google Scholar 

  19. Hastings NAJ (1968) Some notes on dynamic programming and replacement. Oper Res Q 19:453–464

    Article  MathSciNet  Google Scholar 

  20. Hastings NAJ (1969) The repair limit replacement method. Oper Res Q 20:337–349

    Article  Google Scholar 

  21. 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

    Google Scholar 

  22. Jiang X, Cheng K, Makis V (1998) On the optimality of repair-cost-limit polices. J Appl Probab 35:936–949

    Article  MathSciNet  MATH  Google Scholar 

  23. Jiang X, Makis V, Jardine AKS (2001) Optimal repair/replacement policy for a general repair model. Adv Appl Probab 33:206–222

    Article  MathSciNet  MATH  Google Scholar 

  24. Kaio N (1981) Optimum repair limit policies with cost constraint. Microelectron Reliab 21:597–599

    Article  Google Scholar 

  25. Kaio N, Osaki S (1982) Optimum repair limit policies with a time constraint. Int J Syst Sci 13:1345–1350

    Article  MATH  Google Scholar 

  26. 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

    Chapter  Google Scholar 

  27. 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

    Article  Google Scholar 

  28. 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

    Article  Google Scholar 

  29. Kapur PK, Kapoor KR, Kapil DVS (1980) Joint optimum preventive-maintenance and repair-limit replacement policies. IEEE Trans Reliab R-29:276–279

    Google Scholar 

  30. Kapur PK, Garg RB, Butani NL (1989) Some replacement policies with minimal repairs and repair cost limit. Int J Syst Sci 20:267–279

    Article  MathSciNet  MATH  Google Scholar 

  31. Kim HG, Yun WY (2010) A repair time limit replacement policy with estimation error. Commun Stat Theory Methods 39:1–14

    MathSciNet  Google Scholar 

  32. 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

    MathSciNet  MATH  Google Scholar 

  33. Lambe TA (1974) The decision to repair or scrap a machine. Oper Res Q 25:99–110

    Article  MATH  Google Scholar 

  34. L’Ecuyer P, Haurie A (1987) The repair vs replacement problem: a stochastic control approach. Optimal Control Appl Methods 8:219–230

    Article  MathSciNet  MATH  Google Scholar 

  35. Love CE, Rodger R, Blazenko G (1982) Repair limit policies for vehicle replacement. INFOR 20:226–237

    MATH  Google Scholar 

  36. 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

    MATH  Google Scholar 

  37. Muth EJ (1977) An optimal decision rule for repair vs replacement. IEEE Trans Reliab R-26:179–181

    Google Scholar 

  38. Nakagawa T (2006) Maintenance theory of reliability. Springer, Berlin

    Google Scholar 

  39. Nakagawa T, Mizutani S (2009) A summary of maintenance policies for a finite interval. Reliab Eng Syst Safe 94:89–96

    Article  Google Scholar 

  40. Nakagawa T, Osaki S (1974) The optimum repair limit replacement policies. Oper Res Q 25:311–317

    Article  MathSciNet  MATH  Google Scholar 

  41. Nguyen DG, Murthy DNP (1980) A note on the repair limit replacement policy. J Oper Res Soc 31:1103–1104

    MathSciNet  MATH  Google Scholar 

  42. Nguyen DG, Murthy DNP (1981) Optimal repair limit replacement policies with imperfect repair. J Oper Res Soc 32:409–416

    MathSciNet  MATH  Google Scholar 

  43. 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

    Article  Google Scholar 

  44. Segawa Y, Ohnishi M (2000) The average optimality of a repair-limit replacement policy. Math Comput Modell 31:327–334

    Article  MathSciNet  MATH  Google Scholar 

  45. Thomas LC, Osaki S (1978) An optimal ordering policy for a spare unit with lead time. Eur J Oper Res 2:409–419

    Article  MathSciNet  MATH  Google Scholar 

  46. Wang H, Pham H (2005) Reliability and optimal maintenance. Springer, Berlin

    Google Scholar 

  47. White DJ (1989) Repair limit replacement. OR Spektrum 11:143–149

    Article  MATH  Google Scholar 

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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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Correspondence to Won Young Yun .

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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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  • Online ISBN: 978-1-4471-4971-2

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