### 考虑维修力量影响及载荷动态分配的k/n系统模糊可靠性分析

1. 海军工程大学 管理工程系, 武汉 430033
• 收稿日期:2017-09-06 修回日期:2017-10-22 出版日期:2018-04-15 发布日期:2017-10-21
• 通讯作者: 何有宸,E-mail:771585315@qq.com E-mail:771585315@qq.com
• 基金资助:
国家自然科学基金（71501183）

### Reliability analysis of fuzzy k-out-of-n system considering maintenance influence and dynamic load distribution mechanism

LI Fang, HE Youchen, DI Peng, CHEN Tong, YIN Dongliang

1. Department of Management Science, Naval University of Engineering, Wuhan 430033, China
• Received:2017-09-06 Revised:2017-10-22 Online:2018-04-15 Published:2017-10-21
• Supported by:
National Natural Science Foundation of China (71501183)

Abstract: In engineering practice, the preparation period usually exists before maintenance activities. Because of external environment and deterioration of the system after a long period of operation, the state performance level of the components is uncertain, making the system reliability modeling more difficult. Therefore, the failure transfer rate, repair transfer rate and state performance level of components are regarded as fuzzy numbers. By using Power Law rule, the failure-correlation between components is characterized, and the failure-correlation phenomena is found to occur when the load on the component exceeds a threshold. The influence of the quantitative relationship between repairmen and fault components on system reliability is considered. A model for the k-out-of-n system with dynamic load distribution and maintenance preparation period is analyzed, and the state transfer differential equations are established. The inverse hierarchical analysis method is put forward to present the recursive relation of the steady-state probability coefficient of the system. By using the α-cut level set and the Zadeh-expansion principle, the level set internal of the fuzzy state probability is determined. The steady measures of the system are obtained and the influence of the fuzzy degree of the repairman number and component parameters on steady measures is presented by a numerical simulation, proving the applicability of the model.