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Some Stochastic Properties of a Compound-Renewal Damage Model

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  • Richard C. Morey

    (Institute for Defense Analyses, Arlington, Virginia)

Abstract

The compound-renewal process is investigated as a model of cumulative damage. The component is assumed to function until the cumulative wear exceeds some critical threshold, in general a random variable, at which time the component is assumed useless. It is this first passage time until breakdown which is of prime interest. Rather than focusing the attention on a certain selected compound-renewal process governed by mathematically convenient distributions, a class of compound-renewal processes involving the nonparametric, physically appealing assumption of a monotone failure rate is studied. Since the assumptions are nonparametric, the results for the most part manifest themselves in the form of useful bounds.

Suggested Citation

  • Richard C. Morey, 1966. "Some Stochastic Properties of a Compound-Renewal Damage Model," Operations Research, INFORMS, vol. 14(5), pages 902-908, October.
    • Handle: RePEc:inm:oropre:v:14:y:1966:i:5:p:902-908
    DOI: 10.1287/opre.14.5.902
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    Cited by:

    1. Jonathan E. Helm & Mariel S. Lavieri & Mark P. Van Oyen & Joshua D. Stein & David C. Musch, 2015. "Dynamic Forecasting and Control Algorithms of Glaucoma Progression for Clinician Decision Support," Operations Research, INFORMS, vol. 63(5), pages 979-999, October.
    2. van der Weide, J.A.M. & Pandey, M.D. & van Noortwijk, J.M., 2010. "Discounted cost model for condition-based maintenance optimization," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 236-246.
    3. Ching, Jianye & Leu, Sou-Sen, 2009. "Bayesian updating of reliability of civil infrastructure facilities based on condition-state data and fault-tree model," Reliability Engineering and System Safety, Elsevier, vol. 94(12), pages 1962-1974.

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