Interval-availability distribution of 2-state systems with exponential failures and phase-type repairs

Interval availability is a dependability measure defined as the fraction of time during which a system is in operation over a finite observation period. Usually, for computing systems, the models used to evaluate interval availability distribution are Markov models. Numerous papers using these models have been published, and only complex numerical methods have been proposed as solutions to this problem even in simple cases such as the 2-state Markov model. This paper proposes a new way to compute this distribution when the model is a 2-state semi-Markov process in which the holding times have an exponential distribution for the operational state and a phase-type distribution for the nonoperational one. The main contribution of this paper is to define a new algorithm to compute the interval availability distribution for systems having only one operational state. The computational complexity depends weakly on the number of states of the system, and sometimes it can deal also with infinite state spaces. Moreover, simple closed expressions of this distribution are shown when repair periods are of the Erlang type with eventually absorbing states