Reliability analysis of a cold standby system with imperfect repair and under Poisson shocks
type: Item
instance of: scholarly article
title: Reliability analysis of a cold standby system with imperfect repair and under Poisson shocks
zbMATH Open document ID: 1407.90126
DOI: 10.1155/2014/507846
author: Yutian Chen
author: Shengqiang Chen
author: Xian-Yun Meng
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: This paper considers the reliability analysis of a two-component cold standby system with a repairman who may have vacation. The system may fail due to intrinsic factors like aging or deteriorating, or external factors such as Poisson shocks. The arrival time of the shocks follows a Poisson process with the intensity \(\lambda > 0\). Whenever the magnitude of a shock is larger than the prespecified threshold of the operating component, the operating component will fail. The paper assumes that the intrinsic lifetime and the repair time on the component are an extended Poisson process, the magnitude of the shock and the threshold of the operating component are nonnegative random variables, and the vacation time of the repairman obeys the general continuous probability distribution. By using the vector Markov process theory, the supplementary variable method, Laplace transform, and Tauberian theory, the paper derives a number of reliability indices: system availability, system reliability, the rate of occurrence of the system failure, and the mean time to the first failure of the system. Finally, a numerical example is given to validate the derived indices.
Mathematics Subject Classification ID: 90B25
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 62N05
zbMATH DE Number: 7016612
Wikidata QID: Q59068001
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/507846
OpenAlex ID: W2002882430
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description: scientific article; zbMATH DE number 7016612