The optimal system for series systems with warm standby components and a repairable service station

This paper deals with the reliability and availability characteristics of three different series system configurations with warm standby components and a repairable service station. The failure time of the primary and warm standby are assumed to be exponentially distributed with parameters λ and α respectively. The repair time distribution of each server is also exponentially distributed with parameter μ . The breakdown time and the repair time of the service station are also assumed exponentially distributed with parametersγ and β respectively. We derive the reliability dependent on time, availability dependent on time, the mean time to failure, MTTF i , and the steady-state availability A i (∞) for three configurations and perform comparisons. Comparisons are made for specific values of distribution parameters and of the cost of the components. The three configurations are ranked based on: MTTFi , Ai (∞), and C i / B i where B i is either MTTF i or A i (∞).