Cost benefit analysis of availability systems with warm standby units and imperfect coverage

We study the cost benefit analysis of availability systems with warm standby units and imperfect coverage. The time-to-failure and the time-to-repair of the active and standby units are assumed to be exponentially and generally distributed, respectively. We assume that the coverage factor is the same for an active-unit failure as that for a standby-unit failure. We present a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining repair time, to develop the steady-state availability, (or Av), for three availability models. For each availability model, the explicit expressions for the Av for three various repair time distributions, such as exponential, k-stage Erlang, and deterministic are provided. Under the cost/benefit criterion, comparisons are performed based on assumed numerical values given to the distribution parameters, and to the cost of the active and standby units.