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Optimal replacement policy based on maximum repair time for a random shock and wear model

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  • Miaomiao Yu

    (Sichuan University of Science and Engineering)

  • Yinghui Tang

    (Sichuan Normal University)

Abstract

We study a $$\delta $$ δ shock and wear model in which the system can fail due to the frequency of the shocks caused by external conditions, or aging and accumulated wear caused by intrinsic factors. The external shocks occur according to a Bernoulli process, i.e., the inter-arrival times between two consecutive shocks follow a geometric distribution. Once the system fails, it can be repaired immediately. If the system is not repairable in a pre-specific time D, it can be replaced by a new one to avoid the unnecessary expanses on repair. On the other hand, the system can also be replaced whenever its number of repairs exceeds N. Given that infinite operating and repair times are not commonly encountered in practical situations, both of these two random variables are supposed to obey general discrete distribution with finite support. Replacing the finite support renewal distributions with appropriate phase-type (PH) distributions and using the closure property associated with PH distribution, we formulate the maximum repair time replacement policy and obtain analytically the long-run average cost rate. Meanwhile, the optimal replacement policy is also numerically determined by implementing a two-dimensional-search process.

Suggested Citation

  • Miaomiao Yu & Yinghui Tang, 2017. "Optimal replacement policy based on maximum repair time for a random shock and wear model," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 80-94, April.
    • Handle: RePEc:spr:topjnl:v:25:y:2017:i:1:d:10.1007_s11750-016-0417-0
    DOI: 10.1007/s11750-016-0417-0
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    References listed on IDEAS

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    1. Castro, I.T. & Pérez-Ocón, R., 2006. "Reward optimization of a repairable system," Reliability Engineering and System Safety, Elsevier, vol. 91(3), pages 311-319.
    2. Yu, Miaomiao & Tang, Yinghui & Liu, Liping & Cheng, Jiang, 2013. "A phase-type geometric process repair model with spare device procurement and repairman’s multiple vacations," European Journal of Operational Research, Elsevier, vol. 225(2), pages 310-323.
    3. Hongzhou Wang & Hoang Pham, 2006. "Reliability and Optimal Maintenance," Springer Series in Reliability Engineering, Springer, number 978-1-84628-325-3, June.
    4. Chien, Yu-Hung, 2012. "The effects of a free-repair warranty on the discrete-time periodic replacement policy," International Journal of Production Economics, Elsevier, vol. 135(2), pages 832-839.
    5. Yeh, Ruey Huei & Chen, Ming-Yuh & Lin, Chen-Yi, 2007. "Optimal periodic replacement policy for repairable products under free-repair warranty," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1678-1686, February.
    6. Zhang, Yuan Lin & Wang, Guan Jun, 2009. "A geometric process repair model for a repairable cold standby system with priority in use and repair," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1782-1787.
    7. Sheu, Shey-Huei & Chien, Yu-Hung, 2004. "Optimal age-replacement policy of a system subject to shocks with random lead-time," European Journal of Operational Research, Elsevier, vol. 159(1), pages 132-144, November.
    8. Philip J. Boland & Frank Proschan, 1982. "Periodic Replacement with Increasing Minimal Repair Costs at Failure," Operations Research, INFORMS, vol. 30(6), pages 1183-1189, December.
    9. Li, Zehui & Kong, Xinbing, 2007. "Life behavior of [delta]-shock model," Statistics & Probability Letters, Elsevier, vol. 77(6), pages 577-587, March.
    10. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    11. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, June.
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    Cited by:

    1. Maxim Finkelstein & Ji Hwan Cha & Shyamal Ghosh, 2021. "Optimal inspection for missions with a possibility of abortion or switching to a lighter regime," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 722-740, October.
    2. Cihangir Kan & Serkan Eryilmaz, 2021. "Reliability assessment of a discrete time cold standby repairable system," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 613-628, October.
    3. Miaomiao Yu & Yinghui Tang, 2024. "Analyze periodic inspection and replacement policy of a shock and wear model with phase-type inter-shock arrival times using roots method," Journal of Risk and Reliability, , vol. 238(2), pages 233-246, April.
    4. Ji Hwan Cha & Maxim Finkelstein, 2019. "Optimal preventive maintenance for systems having a continuous output and operating in a random environment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 327-350, July.

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