一类多级适应性休假的串联可修系统分析

Analysis of a series repairable system with multiple adaptive vacations

在经典串联可修系统中引入了多级适应性休假策略,并考虑了修理设备更换对系统可靠性的影响.假定部件和修理设备的寿命均服从指数分布,部件的修理时间、修理设备的更换时间和修理工的休假时间均服从任意分布.借助更新过程理论和概率分解法,得到了系统的可用度、(0,t]时间内系统的平均故障次数和系统的更新时间分布.此外,也首次得到了修理工的闲期、假期和实际休假次数等指标.数值分析了系统参数对主要可靠性指标的影响.最后,作为实际应用,获得了一个串联工作站系统的最大利润.

The multiple adaptive vacation policy is introduced into a classical series repairable system and the impacts of a replaceable facility on the system reliability are also considered. It is assumed that the lifetimes of each unit and the facility are exponentially distributed, and the repair time of the unit, the replace time of the facility and the vacation time of the repairman are all arbitrarily distributed. By means of renewal process theory and probability decomposition method, the system availability, the mean failure numbers during （0, t], and the renewal time distribution of the system, are obtained. Moreover, the idle period, vacation period and the actual vacation number of the repairman are derived respectively. The impact of the system parameters on the main reliability indices is numerically analyzed. Finally, as a practical application, the maximum profit for a series workstation system is obtained.