Can Ignore The Series Of Failures Multi-state Markov Repairable System

The model is the basis of the maintenance problems,but in most of time the practice problems are different with the mathematical models.The thesis is based on the practice problems of maintenance and establishes two models for a series-unit, multi-state,Markov repairable system by the method of reliability theory, probability and stochastic process.The two kinds of models are first established and derived some reliability indexes by the writer. Some numerical examples done by the mathematical software Maple are given to illustrate and explain the results at the end.One part of the original system has three states, the normal working, the first kind failure and the second kind failure.The model is based on the assumption that, for the higher failure and complex repairable system, when a system is done the mission and one certain component is broken, the component immediately is repaired.If the failure can carry out repairs in a very short time, the fault that can be ignored and the system still work on. If the repair time is longer than the acceptable time, this failure omission can not be ignored.Based on the assumption, this thesis establishes the original and new maintenance models for a series-unit, multi-state Markov repairable system.In the original system,the maintenance and working time of a certain component is subject to exponential distribution.So the original system can be used to describe by the Markov process.The new maintenance models for a series-unit, multi-state Markov repairable system has not the Markov properties,which is worth to study. We derive and prove some system reliability indexes for these two repairable models.