On Gaver’s parallel system sustained by a cold standby unit and attended by two repairmen

The authors consider Graver’s parallel system sustained by a cold standby unit and attended by two identical repairmen. The System satisfies the usual conditions (i.i.d. random variables, perfect repair, instantaneous and perfect switch, queueing). Each operative unit has a constant failure rate and a deterministic repair time. They analyse the total joint idle time of both repairmen during the survival time of the system. The analysis requires the solution of a so-called delay-differential equation. A numerical example illustrates the structure of the solution for some particular values of the underlying parameters.