马尔可夫过程的k/N系统使用任务完成能力分析

摘要

In k out of N system the mission completion capability was researched considering spare replacement maintenance and supply during mission. Firstly, the system state transition process was analyzed through Markov process, and the working process was researched under given maintenance supply strategy. Secondly, mission completion probability was understood as distributing function of k out of N system sojourn time at working state within fixed time. And its numerical value was got by total probability decomposition and renewal process. At last, curves of mission completion probability vs. Mission time, mission numbers,spare number and spare average supply time were plotted in Matlab by the mission ompletion probability model,and their influences on mission completion probability were analyzed.%研究了任务期间允许换件维修和备件供应时k/N系统的任务完成能力.首先,利用马尔可夫过程分析了k/N系统的状态转移过程,研究了k/N系统在特定维修保障策略下的运行过程.然后,以k/N系统固定任务时间内在正常状态停留时间的分布函数作为其任务完成概率模型,并通过全概率分解和更新过程的分析方法对任务完成概率进行求解.最后,利用任务完成概率模型在Matlab中绘制了任务完成概率随任务时间、任务量、备件携行数量以及备件平均供应时间的变化曲线,讨论并分析了对任务完成概率的影响.