A study on a single-unit repairable system with state aggregations

This article analyzes a single-unit repairable system consisting of an operating subsystem and a maintenance subsystem that is solely used to repair the operating subsystem in the event of it breaking down. Formulae for reliability indexes such as availability and distributions concerned with visits to certain subsets of states are presented in terms of state aggregations in which two partitions are used. The situation with exponentially distributed operational times is discussed not only as a special case of the approach used in this article but also using a Markov model. A numerical example is given to illustrate the results obtained in this article.