均匀分布下系统瞬时可用度理论分析

对单部件可修系统的瞬时可用度在其初期出现的波动现象进行了理论分析,介绍了现今2种可用度研究进展并分析了对瞬时可用度研究的重要性。分别讨论了系统部件的故障时间及修复时间都服从相同和不同均匀分布的情况,通过把可用度的更新方程转化为分段的时滞或常微分方程,运用初值与连续性给出了系统瞬时可用度的解析表达式。提出了判断瞬时可用度波动的方法,即判断是否存在小于稳态可用度的点,并验证了该方法的有效性。得到了无论均匀分布为何种参数组合,瞬时可用度均存在波动性的结论。最终的仿真结果和理论结果相一致。 

Theory analysis of system instantaneous availability under uniform distribution

The early volatility of instantaneous availability which belonged to one-unit repairable system was analyzed in theory. Recent research progress on two kinds of availabilities was reported and the importance of research on the instantaneous availability was highlighted. It was respectively discussed that the failure time and repair time of system components obeyed the same as well as different uniform distribution, and then the renewal equation was transformed into piecewise ordinary differential equations or delay differential equations. The analytical expressions of instantaneous availability were obtained from the differential equations by the use of the continuity and initial value. A method was put forward to judge the volatility of instantaneous availability, that is, to judge whether there existed the value of instantaneous availability less than that of the steady-state availability. The method has been proved to be effective, and the conclusion demonstrates that the volatility exists regardless of any parameter combination under uniform distribution. The final simulation results are in good agreement with the theoretical results.