Автор(ы): Рыков В. В. (РГУНиГ)Иванова Н. М. (ИПУ РАН, Лаборатория 69)Козырев Д. В. (ИПУ РАН, Лаборатория 69)Автор(ов): 3 Параметры публикацииТип публикации: Статья в журнале/сборникеНазвание: Application of Decomposable Semi-Regenerative Processes to the Study of k-out-of-n SystemsЭлектронная публикация: ДаISBN/ISSN: 2227-7390DOI: 10.3390/math9161933Наименование источника: MathematicsОбозначение и номер тома: Vol. 9, issue 16Город: BaselИздательство: Multidisciplinary Digital Publishing Institute (MDPI)Год издания: 2021Страницы: https://doi.org/10.3390/math9161933 АннотацияThis 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. Библиографическая ссылка: Рыков В.В., Иванова Н.М., Козырев Д.В. Application of Decomposable Semi-Regenerative Processes to the Study of k-out-of-n Systems // Mathematics. 2021. Vol. 9, issue 16. С. https://doi.org/10.3390/math9161933.