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Failure distributions in multicomponent systems with imperfect repairs

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  • Richard Arnold
  • Stefanka Chukova
  • Yu Hayakawa

Abstract

We present a model for correlated failures in multicomponent systems where failed components are repaired. Due to these repairs multiple failures of each component are observable. Repair is instantaneous, but imperfect: in general the component is not returned to the good-as-new condition. Correlation amongst failures and the overall ageing of the system are modelled by treating each component failure as a shock which damages the other components in the system. We construct the likelihood for observations generated by such a system, and show how to simulate from this model. We demonstrate inference of the model parameters with simulated data and two real-world examples.

Suggested Citation

  • Richard Arnold & Stefanka Chukova & Yu Hayakawa, 2016. "Failure distributions in multicomponent systems with imperfect repairs," Journal of Risk and Reliability, , vol. 230(1), pages 4-17, February.
    • Handle: RePEc:sae:risrel:v:230:y:2016:i:1:p:4-17
    DOI: 10.1177/1748006X15584853
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    References listed on IDEAS

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    1. Simon M. S. Lo & Ralf A. Wilke, 2010. "A copula model for dependent competing risks," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 359-376, March.
    2. Pham, Hoang & Wang, Hongzhou, 1996. "Imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 94(3), pages 425-438, November.
    3. Moshe Shaked & J. George Shanthikumar, 1986. "Multivariate Imperfect Repair," Operations Research, INFORMS, vol. 34(3), pages 437-448, June.
    4. Jaap H. Abbring & Gerard J. Van Den Berg, 2003. "The identifiability of the mixed proportional hazards competing risks model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 701-710, August.
    5. Karen Bandeen-Roche, 2002. "Modelling multivariate failure time associations in the presence of a competing risk," Biometrika, Biometrika Trust, vol. 89(2), pages 299-314, June.
    6. Chukova, S. & Arnold, R. & Wang, Dong Q., 2004. "Warranty analysis: An approach to modeling imperfect repairs," International Journal of Production Economics, Elsevier, vol. 89(1), pages 57-68, May.
    7. Murthy, D. N. P. & Nguyen, D. G., 1985. "Study of a multi-component system with failure interaction," European Journal of Operational Research, Elsevier, vol. 21(3), pages 330-338, September.
    8. Wang, Wenbin & Banjevic, Dragan & Pecht, Michael, 2010. "A multi-component and multi-failure mode inspection model based on the delay time concept," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 912-920.
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