Semi-Markovian reliability models for systems with testable components and general test/outage times

Semi-Markov models for systems undergoing periodic test and maintenance are developed. In particular, systems undergoing specific changes of state at predetermined instances of time and transiting to states with generally distributed sojourn times are considered. Problems addressed by the models are those concerned with optimum assessment of test intervals, and allowable outage times. Equivalent Markovian models allowing for the decomposition of a system of dimensionality N+M into two smaller problems of dimensionality N and M, respectively are developed. The general model is also specialized to systems with instantaneously testable components, unmonitored components undergoing tests (repair, maintenance) of fixed duration, and systems containing components characterized by limited allowable outage time (under test, or repair). Approximate equivalent Markov models are derived in these cases. Simple numerical examples are also presented.