ON THE RELIABILITY OF GAVER'S PARALLEL SYSTEM SUSTAINED BY A COLD STANDBY UNIT AND ATTENDED BY TWO REPAIRMEN

Abstract

We analyse the reliability of Gaver'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 but a general repair time distribution. Our reliability analysis is based on a time dependent version of the supplementary variable method. We transform the basic equation into an integro-differential equation of the (mixed) Fredholm type. The equation generalizes Takacs' integro-differential equation. In order to present computational results, we outline the solution procedure for a repair time distribution with an arbitrary rational Laplace-Stieltjes transform. A particular numerical example displays the survivor function with the security interval that ensures a reliability level of at least 95%.