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Optimal replacement under additive damage in randomly varying environments

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  • K.‐H. Waldmann

Abstract

A system is subject to a sequence of randomly occurring shocks. Each shock causes a random amount of damage which accumulates additively. Any of the shocks might cause the system to fail. The shock process is in some sense related to an environmental process in order to describe randomly varying external factors of an economical and/or technical nature as well as internal factors of a statistical nature. A discrete time formulation of the problem is given. Sufficient conditions are found for optimality of a generalized control‐limit rule with respect to the total cost criterion: Whenever the accumulated damage s is not less than a specified critical number t(i), depending on the environmental state i, replace the system by a new one; otherwise do not replace it. Moreover, bounds are given for these critical numbers.

Suggested Citation

  • K.‐H. Waldmann, 1983. "Optimal replacement under additive damage in randomly varying environments," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(3), pages 377-386, September.
    • Handle: RePEc:wly:navlog:v:30:y:1983:i:3:p:377-386
    DOI: 10.1002/nav.3800300302
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    Cited by:

    1. John A. Flory & Jeffrey P. Kharoufeh & David T. Abdul‐Malak, 2015. "Optimal replacement of continuously degrading systems in partially observed environments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(5), pages 395-415, August.

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