Analysis of two components parallel repairable system with vacation

Yan Ling Li and Gen Qi Xu

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 10, 2429-2450

Abstract: In this paper, a parallel repairable system is investigated. The system consisting of two similar components and a repairman with single vacation, in which suppose that the life of component satisfies the exponentially distribution and the repair time of the component and the vacation time of the repairman both follow the general distribution while the repairman take a vacation at the beginning. Firstly, a mathematical model via partial differential equations is driven, and then the system is formulated into a suitable Banach space. Next the existence of positive solution, the non-negative steady-state solution and the exponential stability of the system is proved by the functional analysis method and C0-semigroup theory of bounded linear operators. Based on above results, some reliability indices of the system are deduced, while the reliability indexes of the repairman on duty is obtained at the initial time. Finally, the reliability indexes of the two situations of the repairman are analyzed and compared.

Date: 2021
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DOI: 10.1080/03610926.2019.1670847

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