泊松冲击下带有一个贮备部件和修理工的两部件并联可修系统的可靠性分析（英文）

RELIABILITY ANALYSIS OF A TWO-UNIT-PARALLEL SYSTEM SUSTAINED BY A COLD STANDBY UNIT AND REPAIRMAN UNDER POISSON SHOCKS

研究了由三个同型部件,两个部件并联,一个作冷贮备的可修系统在随机冲击下的可靠性问题.假设冲击流以泊松过程到达,且不同次的冲击量是独立同分布的,都服从某一固定分布.当冲击到达时,它会对系统中工作的部件独立地产生影响,但不对贮备部件产生影响,且与其历史无关.当冲击量大于工作部件的阈值时,工作部件发生故障,工作部件的阈值为具有某一确定分布的非负随机变量.修理工可进行多重休假.当工作部件发生故障,贮备部件立即开始工作,当所有部件都故障时,系统故障.此外,还假设部件的修理时间和修理工的休假时间为一般的连续分布.利用补充变量方法和向量Markov过程理论,显式地给出了系统可靠度函数、系统平均工作时间和系统稳态可用度等可靠性指标,最后,我们给出了一个数值模拟例子来验证所给出的结果.

This paper analyses the reliability of a two-unit-parallel system consisting of two units in parallel, one standby unit, one switch and a repairman who might take multiple vacations. Additionally, there is one kind of shocks that arrive according to a Poisson process. The magnitude of shocks is assumed to be i.i.d, random variables. Whenever the magnitude of the shock is greater than the threshold of the operating unit, the operating unit fails. When an operating unit fails, the cold standby unit will start to operate immediately. It is assumed that the repair time of the unit and the vacation time of the repairman are non-negative random variables following general continuous distributions. Using the supplementary variable method and the vector Markov process theory, some reliability indices such as the steady-state availability of the system, the steady-state failure frequency of the system and the mean time to the first failure of the system etc. are explicitly obtained. Finally, a numerical example is given to validate the derived indices.