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

工程实际中，维修活动开展前往往存在一定时长的准备期，且由于环境时变性、系统长期运行后的劣化累积等因素导致部件状态性能水平存在不确定性，使得系统可靠性建模较为困难。对此，运用模糊数表征系统部件的失效转移率、修复转移率及修理工维修准备率的同时，以Power Law规则刻画部件间的故障相关关系，认为部件承担载荷超过某阈值时才会引发故障相关现象，并考虑了修理工数量与故障件数量之间关系对系统可靠性的影响，研究了载荷动态分配条件下带维修准备期的多修理工n中取k模糊多状态系统模型，建立了状态转移微分方程组，提出用逆向逐层分析的思路建立系统稳态概率系数的递推关系，应用α水平截集及Zadeh扩张原理确定了模糊状态概率的截集区间，得到了系统模糊稳态指标，最后通过算例给出了修理工数量及部件参数模糊程度对系统稳态指标的影响，验证了模型的适用性。

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

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.