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Numerical solution of the steady-state probability and reliability of a repairable system with three unites
Zheng, Fu1,2; Xu, Shuangshuang1; Li, Xin1
2015-07-15
Source PublicationAPPLIED MATHEMATICS AND COMPUTATION
ISSN0096-3003
Volume263Pages:251-267
AbstractIn the present paper, a series-parallel repairable system with three unites was developed under some assumptions. By using the supplementary variables method, probability arguments and limiting transitions, the integro-differential equations governing the behavior of the system were obtained. Since some of the system equations have two hazard functions involved, the numerical simulation methods were used to analyze the reliability of the system. Firstly, combining the boundary conditions and characteristic curve method, the state equations were transformed into a set of integral equations. Secondly, the sequences of approximating functions were constructed for the integral equations which are analogous to the Gauss-Seidel or SOR iterative scheme for solving a system of linear equations. It was showed that the sequences of approximating functions converge pointwise to the solution of integral equations and they have continuously differential solutions. Finally, the numerical solutions of the integral equations, system equations and some reliability indices were presented by building a discretization of approximating sequence. (C) 2015 Elsevier Inc. All rights reserved.
KeywordRepairable system Numerical solution Availability Mean up-time
DOI10.1016/j.amc.2015.04.015
Language英语
Funding ProjectNational Natural Science Foundation of China[11201037] ; National Natural Science Foundation of China[11371070]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000355144500022
PublisherELSEVIER SCIENCE INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/19832
Collection中国科学院数学与系统科学研究院
Affiliation1.Bohai Univ, Dept Math, Jinzhou 121013, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Zheng, Fu,Xu, Shuangshuang,Li, Xin. Numerical solution of the steady-state probability and reliability of a repairable system with three unites[J]. APPLIED MATHEMATICS AND COMPUTATION,2015,263:251-267.
APA Zheng, Fu,Xu, Shuangshuang,&Li, Xin.(2015).Numerical solution of the steady-state probability and reliability of a repairable system with three unites.APPLIED MATHEMATICS AND COMPUTATION,263,251-267.
MLA Zheng, Fu,et al."Numerical solution of the steady-state probability and reliability of a repairable system with three unites".APPLIED MATHEMATICS AND COMPUTATION 263(2015):251-267.
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