Open AccessAnalysis of two components parallel repairable degenerate system with vacation
Author(s) -
Yanling Li,
Genqi Xu,
Hao Chen
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2021616
Subject(s) - component (thermodynamics) , computer science , degenerate energy levels , reliability engineering , engineering , physics , thermodynamics , quantum mechanics
This article studies a parallel repairable degradation system with two similar components and a repairman who can take a single vacation. Suppose that the system consists of two components that cannot be repaired "as good as new" after failures; when the repairman has a single vacation, the fault component of system may not be repaired immediately, namely, if a component fails and the repairman is on vacation, the repair of the component will be delayed, if a component fails and the repairman is on duty, the fault component can be repaired immediately. Under these assumptions, a replacement policy $ N $ based on the failed times of component 1 is studied. The explicit expression of the system average cost rate $ C(N) $ and the optimal replacement policy $ N^{\ast} $ by minimizing the $ C(N) $ are obtained, which means the two components of the system will be replaced at the same time if the failures of component 1 reach $ N^{\ast} $. To show the advantage of a parallel system, a replacement policy $ N $ of the cold standby system consisting of the two similar components is also considered. The numerical results of both systems are given by the numerical analysis. The optimal replacement policy $ N^* $ for both systems are obtained. Finally, the comparison of numerical results shows the advantages of the parallel system.