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Estimation of G-renewal process parameters as an ill-posed inverse problem

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  • Krivtsov, V.
  • Yevkin, O.

Abstract

Statistical estimation of G-renewal process parameters is an important estimation problem, which has been considered by many authors. We view this problem from the standpoint of a mathematically ill-posed, inverse problem (the solution is not unique and/or is sensitive to statistical error) and propose a regularization approach specifically suited to the G-renewal process. Regardless of the estimation method, the respective objective function usually involves parameters of the underlying life-time distribution and simultaneously the restoration parameter. In this paper, we propose to regularize the problem by decoupling the estimation of the aforementioned parameters. Using a simulation study, we show that the resulting estimation/extrapolation accuracy of the proposed method is considerably higher than that of the existing methods.

Suggested Citation

  • Krivtsov, V. & Yevkin, O., 2013. "Estimation of G-renewal process parameters as an ill-posed inverse problem," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 10-18.
    • Handle: RePEc:eee:reensy:v:115:y:2013:i:c:p:10-18
    DOI: 10.1016/j.ress.2013.02.005
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    1. Makis, Viliam & Jardine, Andrew K. S., 1993. "A note on optimal replacement policy under general repair," European Journal of Operational Research, Elsevier, vol. 69(1), pages 75-82, August.
    2. Kahle, Waltraud, 2007. "Optimal maintenance policies in incomplete repair models," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 563-565.
    3. Krivtsov, Vasiliy V., 2007. "Practical extensions to NHPP application in repairable system reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 560-562.
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    2. Hu, Wei & Westerlund, Per & Hilber, Patrik & Chen, Chuanhai & Yang, Zhaojun, 2022. "A general model, estimation, and procedure for modeling recurrent failure process of high-voltage circuit breakers considering multivariate impacts," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    3. Serguei Maximov & Consuelo de J. Cortes-Penagos, 2020. "A long-time asymptotic solution to the g-renewal equation for underlying distributions with nondecreasing hazard functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(2), pages 311-341, October.
    4. 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.
    5. Hu, Wei & Yang, Zhaojun & Chen, Chuanhai & Wu, Yue & Xie, Qunya, 2021. "A Weibull-based recurrent regression model for repairable systems considering double effects of operation and maintenance: A case study of machine tools," Reliability Engineering and System Safety, Elsevier, vol. 213(C).

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