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对实际工程系统进行可靠性分析时,常简化为串联可修系统,其平均修复时间是工程系统可靠性分析和风险分析的主要指标之一。串联可修系统的特点是串联元件中任一部分失效都可导致系统失效。为了对由N个元件在逻辑上组成的串联可修系统进行可靠性分析,设元件的工作和维修均服从马尔可夫过程,系统和元件只有工作和故障两种状态,元件状态转移可在任何时刻进行,但在很小的时间间隔内不会发生两个及两个以上元件的状态转移,因此得到由n+1个状态组成的系统状态方程。考虑到初始条件的特解,将状态方程展开后作拉氏变换,得到串联复杂系统的全部不可用状态概率和系统平均修复时间的便捷表达式。实例计算表明,用这些公式进行计算非常方便,计算精度高且易编制计算机程序。
When analyzing the reliability of an actual engineering system, it is often simplified as a series-repairable system. The average repair time is one of the main indicators of the reliability analysis and risk analysis of an engineering system. A feature of a series repairable system is that failure of any part of the series components can lead to system failure. In order to analyze the reliability of a series repairable system logically composed of N elements, the work and maintenance of the elements are subject to the Markov process. The system and the elements have only two states of operation and fault. The state transition of the elements can be performed in any But at a very small time interval, the state transition of two or more elements will not occur, thus the system state equation composed of n + 1 states is obtained. Considering the special solution of the initial conditions, the state equation is expanded and transformed into Laplace transform to obtain a convenient expression of the total unavailability probability and the average system repair time of the complex system. The example calculation shows that it is very convenient to calculate with these formulas, and the calculation accuracy is high and the computer program can be easily programmed.