A repairable system with imperfect coverage and reboot

In this paper, we examine a repairable system with imperfect coverage, reboot delay and one repair facility. The failure times and repair times of failed units are assumed to be exponential and general distributions, respectively. As a unit fails, it can be immediately detected, located and replaced with a coverage probability c by a standby, if one is available. We use a recursive method and the supplementary variable technique to develop the steady-state probabilities of down units at an arbitrary epoch. Then, an efficient algorithm is constructed to compute the steady-state availability. We adopt two repair time distributions, namely, exponential and gamma, to illustrate the method. Finally, we also perform a sensitivity analysis of the steady-state availability with respect to the system parameters for various repair time distributions.