Reliability analysis of a distribution system considering imperfect maintenance to failure

Kijima's model is one of the most important in reliability theory, it focuses on the idea of the virtual age of repairable systems, which is reduced in each maintenance action to a certain degree. However, due to the complexity of the integral equation resulting from this model, exact solutions have been found for a reduced number of distribution functions. This paper deals with the special case of Weibull distribution that adequately models the lifetime of power equipment. Finding a solution for short times complementing the asymptotic solutions found in recent works. Based on this solution, certain outage indexes oriented to a simple distribution system are calculated.