Let the semi-Markov process Y = (Yt : t ∈ [0, ∞)) be the model of a repairable system, and let its finite state space 𝒮 be partitioned into the set of ‘up’ states 𝒰 and the set of ‘down’ states 𝒟; i.e. 𝒮 = 𝒰 ∪ 𝒟. For an interval [t1, t2] ⊂ [0, ∞), the interval availability A(t1, t2) is defined as the fraction of time spent by the system in 𝒰. In this paper, a system of integral equations is established for the interval availability. To demonstrate the practical utility of the integral equations, we compute the cumulative distribution function of the interval availability for the semi-Markov model of a two-unit system with sequential preventive maintenance. The specific method devised for the numerical solution of the resulting system of integral equations is based on the two-point trapezoidal rule. The system of implementation is the matrix-computation package MATLAB on the Apple Macintosh Quadra 610. The numerical results are compared with those from simulation.
