Numerical solution of the steady-state probability and reliability of a repairable system with three unites

doi:10.1016/j.amc.2015.04.015

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	Numerical solution of the steady-state probability and reliability of a repairable system with three unites
	Zheng, Fu 1,2; Xu, Shuangshuang 1; Li, Xin 1
	2015-07-15
发表期刊	APPLIED MATHEMATICS AND COMPUTATION
ISSN	0096-3003
卷号	263 页码:251-267
摘要	In 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.
关键词	Repairable system Numerical solution Availability Mean up-time
DOI	10.1016/j.amc.2015.04.015
语种	英语
资助项目	National Natural Science Foundation of China[11201037] ; National Natural Science Foundation of China[11371070]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000355144500022
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19832
专题	中国科学院数学与系统科学研究院
通讯作者	Zheng, Fu
作者单位	1.Bohai Univ, Dept Math, Jinzhou 121013, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 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.