Cost benefit analysis of series systems with warm standby components and general repair time

Abstract

We study the availability analysis of three different series system configurations with warm standby components and general repair times. The time-to-failure for each of the primary and warm standby components is assumed to be exponentially distributed with respective parameter λ and α. This paper presents a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining repair time, to develop the steady-state probability distribution of the number of working components in the system. We develop the explicit expressions for the steady-state availability, Aν, for three configurations and perform comparisons. For all three configurations, comparisons are made for specific values of distribution parameters and of the cost of the components. The configurations are ranked based on Aν and cost/benefit, for three various repair time distributions: exponential, 3-stage Erlang, and deterministic, where benefit is Aν.