Application Of Markov Skeleton Processes To Reliability Theory

Reliability theory is a greatly important kind of application stochastic processes. The series system and parallel system are the most typical and the important reliability modes among all the reliability systems. In this dissertation, we mainly study state transition probability of two-unit series system and paralleled system and stable availability of system. We first introduce the basic knowledge of Markov skeleton processes and vector Markov processes, the present condition of reliability theory, the mainly models and index. Then we systematically study state transition probability of two-unit series system and paralleled system and stable availability of system, and drew the following conclusions:Firstly, we present the partial differential equation which satisfies state transition probability of the two-unit series system, and proves that state transition probability satisfy the equation, and are their minimal nonnegative solutions. At the same time, we give out another solution of stable availability of system.Secondly, we state the partial differential equation which satisfies state transition probability of the two-unit paralleled system, and proves that state transition probability satisfy the equation, and are their minimal nonnegative solutions.Lastly, for a basic model, we give out a new solution of stable availability of system.