Systems With Repairman Vacation And Multistate

Obtaining reliability indices of different repairable system is an important part in the reliability analysis theory. The repairman with multiple delay vacations and component with more than one state are gradually introduced into these models, reliability indices are obtained, including system reliability, availability, the rate of occurrence of failures and so on.At first, a repairable system with multiple delay vacations and each component with multistate is analyzed. The system consists of different components and a repairman, and each component of the system has two types of failure. Assuming that the delay vacation time of the repairman and the working time of component are subject to exponential distribution, but the vacation time of the repairman and the repair time of component are subject to general continuous distribution. By using the method of generalized Markov progress, Laplace transform and other theory, reliability indices of the system are derived, including steady-state results of system availability and so on.At second, a parallel repairable system with multiple delay vacations and each component with multistate is analyzed. The system consists of two different components and a repairman, and each component of the system has two types of failure. Assuming that the delay vacation time of the repairman and the working time of component are subject to exponential distribution, but the vacation time of the repairman and the repair time of component are subject to general continuous distribution. By generalized Markov progress, supplementary variables and other method, steady-state results of the probability of the repairman on vacations and so on are obtained.At third, a degenerative repairable system with multiple delay vacations and component with multistate is analyzed. The system consists of two different components and a repairman, the repair of component 1 is not as good as new, component 2 has two types of failure. Assuming that the working time and repair time of component 1 are subject to geometric distribution, but the vacation time of the repairman are subject to general continuous distribution, and others are subject to exponential distribution. By using the geometric process theory and the method of generalized Markov progress, system reliability and other important reliability indices are derived.At last, a multistate degenerative cold standby repairable system is analyzed. The system consists of two different components and a repairman, the repair of component 1 is not as good as new and has more than one type of failure. Based on model assumptions, by using the geometric process and the Laplace transform, the Laplace transform of the rate of occurrence of failures and so on are derived.