A study on a single-unit Markov repairable system with repair time omission

This paper introduces a new model for a single-unit Markov repairable system in which repair times that are sufficiently short (less than some critical value) do not result in system failure. We can say that such a repair interval is omitted from the downtime record. First we suppose that the critical repair time is a constant. The model is then generalized to allow the critical repair time to be a non-negative random variable. We calculate system availability for these new models as a measure of reliability. Some numerical examples are given to illustrate the results in the paper.