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论文:2014,Vol:32,Issue(6):923-928 |
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引用本文： |
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王丽英, 司书宾. 空间相依圆形马尔可夫可修系统可靠性分析[J]. 西北工业大学学报 |
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Wang Liying, Si Shubin. Reliability Analysis of Circular Markov Repairable Systems with Spatial Dependence[J]. Northwestern polytechnical university |
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| 空间相依圆形马尔可夫可修系统可靠性分析 |
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| 王丽英1, 司书宾2 |
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1. 石家庄铁道大学 数理系, 河北 石家庄 050043;
2．西北工业大学 机电学院, 陕西 西安 710072 |
| 摘要: |
| 针对具有一定拓扑结构的元件相依复杂系统的可靠性分析问题,提出了一类新的元件相依系统——空间相依圆形可修系统。该系统由若干个排列成圆形的元件组成,并且每个元件的运行依赖于空间上与之相邻的元件("邻居")。采用马尔可夫过程描述系统的运行过程,定义了四元件和五元件空间相依圆形可修系统的状态,得到了系统的状态转移率矩阵。运用Laplace变换方法,给出了系统的可用度。通过数值示例说明了结论的应用,并把上述2个系统的可用度与元件独立马尔可夫可修系统的可用度进行了对比。 |
| 关键词:
空间相依
圆形系统
马尔可夫可修系统
可用度
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| Reliability Analysis of Circular Markov Repairable Systems with Spatial Dependence |
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| Wang Liying1, Si Shubin2 |
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1. Department of Mathematics & Physics, Shijiazhuang Tiedao Institute, Shijiazhuang, 050045, China;
2. Ichool of Mechatronics, Northwestern Polytechnaical University, Xi'an 710072, Chian |
| Abstract: |
| Aim. The introduction of the full paper reviews a number of papers on reliability models with dependentunits in the open literature and proposes what we believe to be a new model mentioned in the title. The core of Sec-tion 1 consists of: (1) we present the assumptions of the circular Markov repairable systems with spatial depend-ence; (2) we put forward the Markov processes associated with the 4-unit and 5-unit circular Markov repairablesystems with spatial dependence and define their states as indicated in Fig.1 and Fig. 2. Section 2 analyzes the statetransitions of the 4-unit and 5-unit systems and obtains the state transition rate matrices corresponding to them. Sec-tion 3 discusses the instantaneous and asymptotic availabilities of the 4-unit and 5-unit systems,which are given byequations (3)-(5). Section 4 presents the numerical examples of the 4-unit and 5-unit systems. The curves of in-stantaneous availabilities are shown in Fig. 5 and Fig. 6. We obtain the conclusions that: (1) the system with inde-pendent units is more reliable than the circular Markov repairable system with spatial dependence; (2) the 5-unitcircular Markov repairable system is more reliable than the 4-unit system. |
| Key words:
availability
differential equations
inverse problems
Laplace transforms
Markov processes
mathe-matical models
MATLAB
matrix algebra
probability
reliability analysis
circular system
Markovrepairable system
spatial dependence
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| 收稿日期: 2014-04-12
修回日期:
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| DOI: |
| 基金项目: 国家自然科学基金(71201111);河北省高等学校科学技术研究项目(ZD20131017)资助 |
| 通讯作者:
Email： |
| 作者简介: 王丽英(1974-)，女，石家庄铁道大学副教授、硕士生导师，主要从事复杂系统可靠性分析研究。
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