Profit analysis of a system with two-units having guarantee periods and delayed operation of standby

Abstract

A single-server two-unit (one priority, p and the other ordinary, o) cold standby system model is investigated. The p-unit has four different modes—excellent (E), good (G), satisfactory (S) and total failure (F)—of which the first three are operative modes while the o-unit has only two modes—normal (N) and total failure (F). When the p-unit enters F-mode the repairman starts the operation of the o-unit. The time taken to start the operation of the o-unit is not negligible and is assumed to be a finite quantity T r. The failure time distributions of the o-unit and the p-unit in the E-mode are taken to be truncated exponential while all the other time distributions are negative exponential over the range 0 to ∞. By identifying the system at suitable regenerative epochs, the profit functions under two different policies are obtained.