多状态多阶段任务系统的可靠度理论计算方法

多状态多阶段任务系统常见于关键性系统,其可靠性要求较高而其可靠度计算又相对困难.为实现该类系统可靠度的精准预测,研究了部件劣化符合马尔科夫过程的多状态多阶段任务系统的可靠度理论计算方法.首先,基于工作效率与需求的关系对该类系统可靠度进行了界定.其次,依据条件概率理论,建立了多阶段任务系统任务成功完成的概率公式.基于此,根据部件劣化的马尔科夫性及部件状态的跨阶段依赖性,推导了多状态多阶段任务系统的可靠度理论计算方法,并提出一种快速穷举部件状态组合的方法用于提高该计算方法的计算效率.最后,通过与蒙特卡罗模拟方法对比,验证了推导的可靠度理论计算方法的准确性与计算的有效性.

Theoretical Calculation Method of Reliability for Multi-state Phased-Mission Systems

Multi-state phased-mission systems(MS-PMSs)are often used in critical systems and require high reliability. However, their reliability calculation is relatively difficult. In order to make an accurate prediction of reliability for such systems, the theoretical calculation method of reliability for MS-PMSs with component degradation conforming to Markov process is studied. First, the reliability for such systems is defined based on the relationship between working efficiency and demand. Then, according to the conditional probabilistic theory, the probability of mission success is formulated. On the basis, according to the Markov property of component degradation and the dependence on component states among phases, the theoretical calculation method of reliability for MS-PMSs is derived, and a fast exhaustion method of component state combination is proposed to improve the computational efficiency of the calculation method. Finally, by comparing with the Monte-Carlo simulation method, the accuracy and computational effectiveness of the derived theoretical calculation method are verified.