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Renewal Redundant Systems Under the Marshall–Olkin Failure Model. A Probability Analysis

Author

Listed:
  • Boyan Dimitrov

    (Department of Mathematics, Kettering University, Flint, MI 48504, USA)

  • Vladimir Rykov

    (Department of Applied Mathematics and Computer Modeling, Gubkin Russian State Oil and Gas University (Gubkin University), 119991 Moscow, Russia
    Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia)

  • Tatiana Milovanova

    (Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia)

Abstract

In this paper a two component redundant renewable system operating under the Marshall–Olkin failure model is considered. The purpose of the study is to find analytical expressions for the time dependent and the steady state characteristics of the system. The system cycle process characteristics are analyzed by the use of probability interpretation of the Laplace–Stieltjes transformations (LSTs), and of probability generating functions (PGFs). In this way the long mathematical analytic derivations are avoid. As results of the investigations, the main reliability characteristics of the system—the reliability function and the steady state probabilities—have been found in analytical form. Our approach can be used in the studies of various applications of systems with dependent failures between their elements.

Suggested Citation

  • Boyan Dimitrov & Vladimir Rykov & Tatiana Milovanova, 2020. "Renewal Redundant Systems Under the Marshall–Olkin Failure Model. A Probability Analysis," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:459-:d:336586
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    References listed on IDEAS

    as
    1. Omey, E. & Willekens, E., 1989. "Abelian and Tauberian theorems for the Laplace transform of functions in several variables," Journal of Multivariate Analysis, Elsevier, vol. 30(2), pages 292-306, August.
    2. Li, Xiaohu & Pellerey, Franco, 2011. "Generalized Marshall-Olkin distributions and related bivariate aging properties," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1399-1409, November.
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