A New Analytical Approach for Interval Availability Analysis of Markov Repairable Systems

Interval availability, defined as the fraction of time that a system is operational during a period of time $[ {0,T} ]$, is an important indicator of system performance, especially for industries with a Service Level Agreement, e.g., telecommunication industry, computer industry, etc. Most existing methods to compute interval availability are based on numerical simulations. In this paper, we present a new analytical solution for interval availability of Markov repairable systems. Three interval availability indexes, i.e., interval availability, interval availability in a general interval, and interval availability in multiple intervals, are considered. The interval availability indexes are derived based on aggregated stochastic processes and the results are obtained in closed form using Laplace transforms. A numerical example is presented and the results are compared with those of Monte Carlo simulation. The developed methods are applied to calculate the interval availability of a fault-tolerant database system from the literature.

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