基于Phase-type分布的多状态系统可靠性模型研究

针对现有多状态系统可靠性模型存在假设条件严格、重用性较差、计算复杂，不利于装备可靠性分析、评估与设计优化等工作的情况，计划从模型的假设条件入手，建立适用性和计算性更好的解析模型。采用Phase-type（PH）分布作为一般分布的表示形式，描述系统部件的工作时间、维修时间等随机变量，开展多状态系统典型结构和多状态复杂系统可靠性建模研究，分别建立：多状态单部件可修系统可靠性模型、单一工作部件温储备系统多状态可靠性模型、考虑随机冲击的多状态系统可靠性模型、考虑预防维修次数的多状态系统可靠性模型、考虑多种维修效果的多状态系统可靠性模型以及n中取k系统多状态可靠性模型；然后，针对解析建模过程中遇到的状态空间庞大的情况，从多状态可靠性模型PH分布阶数控制和系统状态空间缩减两方面开展模型状态空间控制方法研究，达到有效降低解析模型计算复杂度的目的。研究成果能为复杂装备系统研发提供有效的可靠性分析与建模工具

This research investigates the reliability models of multi-state system(MSS) with strict assumptions, poor reuse ability and complex computation, which is hard to be used in equipment reliability analysis, estimation and design optimization. In order to provide the analytic reliability models that are more suitable to characterize the real situations and have the better applicability and analytical performance, the project plans to change the assumptions of models firstly. It is assumed that the random variables, such as system operation time and repair time, are subject to general distribution, which is described by the Phase-type (PH) distribution. Then analytic models are constructed for the multi-state basic structures and complex system as follows: the single-component repairable system, the warm standby repairable system with a single working unit, the repairable system subject to random shocks, the repairable system with replacement policy N, the system with multiple repair effects and the k-out-of-n multi-state repairable system. Then, for avoiding the potential appearance of models with enormous state space and simplifying the computation, two kinds of control techniques: the method for controlling the order of PH distribution, the method for reducing the number of system states are to be studied. Therefore, the research results will offer the effective tools of reliability analysis and modeling for complex equipment system development.