Maintenance of systems by means of replacements and repairs: the case of phase-type distributions

We present two models for studying a system maintained by means of imperfect repairs before a replacement or a perfect repair is allowed. The operational and repair times follow phase-type distributions. Imperfect repair means that successive operational times decrease and successive repair times increase. Under these assumptions, models that govern the systems are Markov processes, whose structures are determined, and several performance measures are calculated in transient and stationary regime. These models extend other previously studied in the literature. The incorporation of phase-type distributions allows to apply the model to many other distributions. A numerical example illustrates the calculations and allows a comparison of the results.