Failures Ignored Or The Single Components Of The Lag Markov Repairable System

This thesis establishes three models for a single-unit Markov repairable system, and derives some reliability indexes by the method of stochastic process and probability. The thesis is based on the practice problems of maintenance and the idea of Ion-Channel. Some numerical examples done by the mathematical software Maple are given to illustrate the results at the end.This thesis introduces three new models 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. The main assumption in the three models is as follows, respectively. First we suppose that the critical repair time is a constant. Second the model is then generalized to allow the critical repair time to be a non-negative random variable. Third we suppose that the effect of the break-down is delayed.Usually, we can say that the process is Markov process if the durations of working and repair have negative-exponentials, so we take the Markov process as the original system, the system set up by modeling as the new system. New systems have not the Markov properties, which is worth to study. We derive and prove some system reliability indexes such as reliability, instantaneous availability, steady-state availability, MUT, MDT and so on for these three new models. Some numerical examples are given to illustrate the results in the thesis.