基于马尔科夫过程的储备系统稳态性能分析

Markov Process-based Performance Analysis of Standby Systems for the Steady State

由于储备系统组成部件在存储期间的失效概率各不相同,当部件状态趋于稳定时,各个状态对系统性能的影响也存在差异。为了识别关键部件及其状态对系统性能的影响程度,本文以重要度为主要指标,应用马尔科夫过程研究储备系统在稳态时的性能变化模式。首先基于综合重要度研究系统性能的变化规律,并结合冷储备系统和温储备系统的状态转移矩阵推导出马尔科夫过程中稳态值的计算方法;其次基于稳态综合重要度获得系统稳态时的性能变化模式;最后以双臂机器人为例,分析部件处于不同状态时对系统性能的影响模式,比较了不同部件综合重要度的变化,验证了提出方法的有效性。

The failure probability of each component in a standby system is different,and as a result,the deteriorate states have a distinguishing influence on the system as the component becomes stable.The importance measures can quantitatively describe the effects of failure or state transactions of components on the system reliability.In order to identify the degree of influence of key components and their status on system performance,this paper uses importance as the main index and applies Markov processes to study the performance change pattern of standby systems at steady state.First of all,based on the comprehensive importance,the variation of the system performance is studied,and the system state transition matrix is combined to derive the calculation method of the steady state value in Markov process for cold standby system and warm standby system.Then we obtain the change law of the system performance in steady state based on comprehensive importance.At last,a numerical example of the two-armed industrial robot is used to analyze the different effects on the system performance of different component states,and demonstrate the developed method.