Application of Decomposable Semi-Regenerative Processes to the Study of k -out-of- n Systems

Vladimir Rykov, Nika Ivanova and Dmitry Kozyrev
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Vladimir Rykov: Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., 117197 Moscow, Russia
Nika Ivanova: Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., 117197 Moscow, Russia
Dmitry Kozyrev: Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., 117197 Moscow, Russia

Mathematics, 2021, vol. 9, issue 16, 1-23

Abstract: This paper aimed to demonstrate the capabilities of decomposable semi-regenerative processes for the investigation of the k -out-of- n system. Proposed in 1955 by W. Smith, the regeneration idea has come a long way in terms of development and has found widespread applications. First, we briefly recall the history of the development of the regeneration idea and the main results of the theory of regenerative, semi-regenerative, and decomposable semi-regenerative processes. Then, the methods of the theory of decomposable semi-regenerative processes are used for the study of a k -out-of- n renewable system with exponentially distributed life and generally distributed repair times of its components. This system is very important for practice and its special cases have previously been considered (including by the authors); however, only special cases and using other methods are considered herein. In the current paper, two scenarios of system repair after its failure are considered for the first time: the partial and the full system repair scenarios. For both scenarios, the time-dependent system state probabilities are calculated in terms of their Laplace transforms. The closed form representation of the stationary probabilities for both scenarios are also presented. These latest results represent a new contribution to the study of this system.

Keywords: decomposable semi-regenerative processes; k-out-of-n system; generally distributed repair times; time-dependent and stationary probabilities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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