Application of decomposable semi-regenerative processes to the study of k-out-of-n systems

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. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Авторы
Rykov V. 1, 2, 3 , Ivanova N. 1, 4 , Kozyrev D. 1, 4
Журнал
Издательство
MDPI AG
Номер выпуска
16
Язык
Английский
Статус
Опубликовано
Номер
1933
Том
9
Год
2021
Организации
  • 1 Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., Moscow, 117197, Russian Federation
  • 2 Department of Applied Mathematics and Computer Modelling, Gubkin Oil & Gas Russian State University (Gubkin University), 65 Leninsky Prospect, Moscow, 119991, Russian Federation
  • 3 Institute for Transmission Information Problems (named after A.A. Kharkevich) RAS, Bolshoy Karetny, 19, GSP-4, Moscow, 127051, Russian Federation
  • 4 V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Str., Moscow, 117997, Russian Federation
Ключевые слова
Decomposable semi-regenerative processes; Generally distributed repair times; K-out-of-n system; Time-dependent and stationary probabilities
Дата создания
16.12.2021
Дата изменения
05.04.2022
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/76702/
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