Reliability analysis of a repairable system with geometric reneging and threshold-based recovery policy

This article attempts to investigate the reliability measures of a repairable system with M identical operating units, S standby units, and a repairman. The repairman is subject to breakdowns and operates threshold-based recovery policy. As soon as the repairman breaks down, the repair does not start immediately until the number of failed units in the system reaches a specified threshold value Q(0 <= Q <= S). When the repairman is working or broken down, failed units arriving for maintenance may renege and decide sequentially whether to leave the queue or not. The failed times of operating and standby units, maintenance times and reneging time of failed units, and breakdown and repair times of the repairman are all assumed to be exponential distributions. We develop the system reliability and mean time to system failure. Through numerical results, sensitivity analysis is carried out to assess the impact of various system parameters on the system reliability and mean time to system failure. Finally, an application example is given to evaluate the reliability measures of an electric power system.