Reliability Analysis For Several Repairable Systems

Reliability of repairable system is very important in the research of reliability. On the base of the existing research harvest of repairable system, the paper has extended some system reliability of repairable models, and gives some system reliability indexes.Firstly, we gives two new repairable models with repair time omission, namely, a single-unit non Markov repairable system and a series Markov repairable system with repair time omission. For the single-unit non Markov repairable system, using Probability Theory and the method of Laplace transformation theory, the reliability indexes of this system are obtained under the condition that the lifetime distributions and repair time distributions of the unit are all general. For the series Markov repairable system, by using Probability Theory and the Markov process theory, some reliability indexes of this system are obtained under the condition that the lifetime distributions and repair time distributions of the unit are all exponential.Secondly, this paper discusses standby repairable system. We shall deal with cold standby repairable system and warm standby repairable system with k (k≤n)repair facilities. Under the assumptions that the failure time of unit and the repair time of failed unit are assumed to follow exponential distribution, by using the Markov process theory, some reliability indexes of this system are obtained. Especially for the warm standby repairable system, we consider a n-unit warm standby repairable system with two repair facilities, the steady-state and instantaneous (when n = 2) reliability quantities of the system are obtained.Finally, this paper discusses warm standby repairable system. Under the condition of unreliable switch, we study the warm standby repairable system which consists of two components with priority. A repairable model of this system is set up where both the lifetime and repaired time of the components and the switch obey the general time-distribution and the system fails immediately when the switch fails. By using the Markov Renewal Process theory the method of Laplace transformation theory and the method of Laplace-Stieltjes transformation theory, several reliability indices of this model was obtained.