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On Reliability of a Double Redundant Renewable System with a Generally Distributed Life and Repair Times
Open AccessArticle

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

1
Department of Mathematics, Kettering University, Flint, MI 48504, USA
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Department of Applied Mathematics and Computer Modeling, Gubkin Russian State Oil and Gas University (Gubkin University), 119991 Moscow, Russia
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Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 459; https://doi.org/10.3390/math8030459 (registering DOI)
Received: 24 February 2020 / Revised: 13 March 2020 / Accepted: 13 March 2020 / Published: 24 March 2020
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. View Full-Text
Keywords: LST and PGF probability interpretation; Marshall–Olkin reliability model; reliability analysis; stationary probabilities; system with component-dependent failures LST and PGF probability interpretation; Marshall–Olkin reliability model; reliability analysis; stationary probabilities; system with component-dependent failures
MDPI and ACS Style

Dimitrov, B.; Rykov, V.; Milovanova, T. Renewal Redundant Systems Under the Marshall–Olkin Failure Model. A Probability Analysis. Mathematics 2020, 8, 459.

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