ABSTRACT
In the literature on reliability, the involved distribution functions are frequently continuous. This is natural when the systems can be continuously monitored, and is useful as an approach to the systems being observed. When the model is constructed from the observations, sometimes it is difficult to select one particular distribution, because none of the known ones is well fitted to the dataset. The continuous case solves this problem by approaching the distribution or the dataset by a continuous phase-type distribution; this is possible by the density of the continuous class in the family of continuous distribution functions defined in the positive real line. The family of phase type distributions (PH) was introduced by Neuts (1975, 1981) as a tool for unifying a variety of stochasticmodels and for constructing new models that would lead to algorithmic analysis. Thus, Pérez-Ocón and Ruiz-Castro (2004) created two models for a repairable two-system and a multi-component G-out-of-M was analysed by PerezOcón et al., (2006) using aMarkov process with vector states incorporating geometric processes.
