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A bathtub pattern for repairable systems: From better-than-minimal to minimal and worse-than-minimal repairs

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  • Amy Langston
  • Maxim Finkelstein
  • Ji Hwan Cha

Abstract

We introduce a new combined repair process to describe repairs that are initially better-than-minimal, then become minimal, before finally becoming worse-than-minimal. The extended generalized Polya process (EGPP), non-homogeneous Poisson process (NHPP), and generalized Polya process (GPP) are used to describe this repair pattern, respectively. Several useful properties are derived for the combined process under two settings: change in repair type after a specified time and change in repair type after a specified number of failures/repairs. As an application, the optimal age replacement problem is defined and its optimal solution is analyzed. Detailed numerical examples support our findings.

Suggested Citation

  • Amy Langston & Maxim Finkelstein & Ji Hwan Cha, 2025. "A bathtub pattern for repairable systems: From better-than-minimal to minimal and worse-than-minimal repairs," Journal of Risk and Reliability, , vol. 239(5), pages 1000-1015, October.
    • Handle: RePEc:sae:risrel:v:239:y:2025:i:5:p:1000-1015
    DOI: 10.1177/1748006X241306853
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    References listed on IDEAS

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    1. Tanwar, Monika & Rai, Rajiv N. & Bolia, Nomesh, 2014. "Imperfect repair modeling using Kijima type generalized renewal process," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 24-31.
    2. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, March.
    3. Pham, Hoang & Wang, Hongzhou, 1996. "Imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 94(3), pages 425-438, November.
    4. Mohamed-Salah Ouali & Lotfi Tadj & Soumaya Yacout & Daoud Ait-Kadi, 2011. "A Survey of Replacement Models with Minimal Repair," Springer Series in Reliability Engineering, in: Lotfi Tadj & M.-Salah Ouali & Soumaya Yacout & Daoud Ait-Kadi (ed.), Replacement Models with Minimal Repair, pages 3-100, Springer.
    5. Amy Langston & Maxim Finkelstein & Ji Hwan Cha, 2024. "On the point process with finite memory and its application to optimal age replacement," Journal of Risk and Reliability, , vol. 238(6), pages 1184-1194, December.
    6. Ji Hwan Cha & Maxim Finkelstein, 2018. "Point Processes for Reliability Analysis," Springer Series in Reliability Engineering, Springer, number 978-3-319-73540-5, March.
    7. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    8. Badía, F.G. & Berrade, M.D. & Cha, Ji Hwan & Lee, Hyunju, 2018. "Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 362-372.
    9. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, March.
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    Cited by:

    1. Dong, Wenjie & Zhang, Meixuan & Xie, Naiming & Kujawińska, Agnieszka & Sheu, Shey-Huei, 2026. "Bivariate periodic replacement policies for systems with multi-attempt minimal repair," Reliability Engineering and System Safety, Elsevier, vol. 268(C).

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