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Transient Analysis of a Two-Unit Standby System with Markovian Degrading Units

Author

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  • Frank A. Van der Duyn Schouten

    (CWI, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands and Faculty of Economics, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands)

  • Pieter Wartenhorst

    (McKinsey & Company, Amstel 344, 1017 AS Amsterdam, The Netherlands)

Abstract

A two-unit cold standby system with Markovian degrading units and one repair facility is considered. Two types of repair are possible: preventive and corrective, where the latter is supposed to be more time consuming than the first. The system is controlled by a repair policy of control limit type: a preventive repair on the working unit is carried out as soon as the state of this unit exceeds a certain threshold unless the repair facility is occupied by the other unit. In this paper we derive explicit expressions for the Laplace transforms of the up- and down-periods of this system, which provide insight in the availability of the system and which can be used to obtain approximations for the interval availability distribution. An iterative numerical procedure is presented for the special case of generalized Erlangian distributed repair times.

Suggested Citation

  • Frank A. Van der Duyn Schouten & Pieter Wartenhorst, 1994. "Transient Analysis of a Two-Unit Standby System with Markovian Degrading Units," Management Science, INFORMS, vol. 40(3), pages 418-428, March.
    • Handle: RePEc:inm:ormnsc:v:40:y:1994:i:3:p:418-428
    DOI: 10.1287/mnsc.40.3.418
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    Cited by:

    1. Montoro-Cazorla, Delia & Perez-Ocon, Rafael, 2006. "Replacement times and costs in a degrading system with several types of failure: The case of phase-type holding times," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1193-1209, December.
    2. Cocozza-Thivent, Christiane, 2007. "MUT of a one out of two system with preventive maintenance," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1203-1229, November.
    3. Smith, M. A. J. & Dekker, R., 1997. "Preventive maintenance in a 1 out of n system: The uptime, downtime and costs," European Journal of Operational Research, Elsevier, vol. 99(3), pages 565-583, June.
    4. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2006. "A deteriorating two-system with two repair modes and sojourn times phase-type distributed," Reliability Engineering and System Safety, Elsevier, vol. 91(1), pages 1-9.

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