The Downtime Distribution After a Failure of a System with Multistate Independent Components

Aven and Jensen (1999) proposed an approximation to the downtime distribution for arbitrary coherent systems with binary and independent repairable components, where each component follows an alternating renewal process. The approximation is based on a mixture of the duration distributions of the cut sets in the system. We extend this approach to coherent systems composed by multistate independent components, where every component follows a semi-Markov process and where we introduce the concept of a minimal cut set in the multistate setting. We test our proposal on a simple power demand-generation system, by comparing the analytic approximation with simulation results, and we find it is accurate when the system is highly available.