On the reliability of a cold standby system attended by a single repairman

We present a reliability analysis of a multiple cold standby system satisfying the usual conditions (i.i.d. random variables, single repair facility, perfect repair, queueing). Each unit has a constant failure rate but an arbitrary repair time distribution. We introduce a basic set of measures related to a stochastic process defined on some filtered probability space. The set of measures constitutes a system of renewal integral equations. The solution is constructed by means of a Cauchy integral. A particular case (deterministic repair) provides some explicit results illustrated by a computer-plotted graph.