Markov Skeleton Processes In Cold Standby System

In this thesis, we analyze the two identical units cold standby repairable system with vacations of a repairman applying Markov skeleton process theory and the density evolution approach, and the two identical units cold standby repairable system with a replaceable facility and delay repair by using the Markov renewal process theory. Markov skeleton process is a kind of comprehensive stochastic process, which is firstly put forward by Prof. Hou Zhenting and his colleagues in 1997. The process contains many exist classical stochastic process models, such as Markov process, semi-Markov process etc .They have important value in theory and application. Recently, the theory has got complemented and perfected.Compared with the former research, in this system, we assume that the distributions of the life of each unit, the repair time, the vacation time of the repairman and the delay repair time are more general. But the previous studies were all supposed that at least one of them has exponential distribution.We drew the following conclusions:Firstly, applying the Markov skeleton process approach and the density evolution approach, we present the equations which satisfy the state transition probability of the two identical units cold standby repairable system with vacations, and obtain the Laplace transform of the reliability of the system.Secondly, we discuss the more complex model considering a replaceable facility and delay repair with the Markov renewal process theory, and get a series of reliability results of the system and the repair facility, respectively.