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On the Brown–Proschan model when repair effects are unknown

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  • Laurent Doyen

Abstract

A device is repaired after failure. The Brown–Proschan (BP) model assumes that the repair is perfect with probability p and minimal with probability (1−p). Theoretical results usually suppose that each repair effect (perfect or minimal repair) is known. However, this is not generally the case in practice. In this paper, we study the behavior of the BP model when repair effects are unknown. In this context, the main features of the failure process are derived: distribution functions of times between failures, failure intensity, likelihood function, etc. We propose to estimate the repair efficiency parameter p and the parameters of the first time to failure distribution with the likelihood function or equivalently the EM algorithm. We also propose to combine a moment estimation of the scale parameter and a maximum likelihood estimation of other parameters. Copyright © 2010 John Wiley & Sons, Ltd.

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  • Laurent Doyen, 2011. "On the Brown–Proschan model when repair effects are unknown," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 27(6), pages 600-618, November.
    • Handle: RePEc:wly:apsmbi:v:27:y:2011:i:6:p:600-618
    DOI: 10.1002/asmb.869
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    Cited by:

    1. Liu, Xingheng & Finkelstein, Maxim & Vatn, Jørn & Dijoux, Yann, 2020. "Steady-state imperfect repair models," European Journal of Operational Research, Elsevier, vol. 286(2), pages 538-546.

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