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Imperfect repair in degradation processes: A Kijima‐type approach

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  • Waltraud Kahle

Abstract

We consider a Wiener process with linear drift for degradation modeling. Regularly, maintenance actions are carried out which produce a reduction of the degradation level. In this paper, we consider the influence of such maintenance actions to the further development of the degradation process and the resulting lifetime distribution. A connection between virtual age in Kijima‐type models and degradation level in the underlying degradation process is developed. Furthermore, estimators for the process parameters as well as for the degree of repair are developed.

Suggested Citation

  • Waltraud Kahle, 2019. "Imperfect repair in degradation processes: A Kijima‐type approach," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(2), pages 211-220, March.
    • Handle: RePEc:wly:apsmbi:v:35:y:2019:i:2:p:211-220
    DOI: 10.1002/asmb.2438
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    Cited by:

    1. Maxim Finkelstein & Ji Hwan Cha, 2021. "On degradation-based imperfect repair and induced generalized renewal processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 1026-1045, December.
    2. 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.
    3. Mosayebi Omshi, E. & Grall, A., 2021. "Replacement and imperfect repair of deteriorating system: Study of a CBM policy and impact of repair efficiency," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    4. Maxim Finkelstein & Ji Hwan Cha, 2022. "Reducing degradation and age of items in imperfect repair modeling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1058-1081, December.
    5. Huynh, K.T., 2021. "An adaptive predictive maintenance model for repairable deteriorating systems using inverse Gaussian degradation process," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    6. Khac Tuan Huynh & Antoine Grall, 2020. "A condition-based maintenance model with past-dependent imperfect preventive repairs for continuously deteriorating systems," Journal of Risk and Reliability, , vol. 234(2), pages 333-358, April.

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