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Technical Note—Probabilistic Analysis of a Single-Server n -unit System with ( n − 1) Warm Standbys

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  • M. N. Gopalan

    (Indian Institute of Technology, Bombay, India)

Abstract

This paper deals with the availability and reliability of an n -unit system with ( n − 1) warm standbys and a single repair facility. The failure times of the operating unit and of a standby are assumed 1o be exponentially distributed with parameters λ 1 and λ 2 respectively. Initially, a unit is switched on and the other units are kept as warm standbys. The system breaks down when the last operating unit foils. This paper characterizes the system by the probabilities of its being in the up or the down state, sets up integral equations for these probabilities by identifying suitable regenerative stochastic processes, and employs the Laplace-transform technique to solve these equations. It obtains the mean down-time of the system during (0, t ) and the mean time to system failure explicitly. Finally it discusses the cases n = 2 and 3.

Suggested Citation

  • M. N. Gopalan, 1975. "Technical Note—Probabilistic Analysis of a Single-Server n -unit System with ( n − 1) Warm Standbys," Operations Research, INFORMS, vol. 23(3), pages 591-598, June.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:3:p:591-598
    DOI: 10.1287/opre.23.3.591
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    Cited by:

    1. R. K. Bhardwaj & Komaldeep Kaur & S. C. Malik, 2017. "Reliability indices of a redundant system with standby failure and arbitrary distribution for repair and replacement times," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 423-431, June.

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