Reliability Analysis Of The Voting Repairable System With Markov Dependence

The k-out-of-n:F(G) system and conseutive-k-out-of -n.F (G) system are widely applied in engineering. These systems have been investigated by many researchers so far, but they supposed that components are independent and the failure components can be repaired "as good as new". In this paper we will study these two systems in the following respects:First, a circular conseutive-2-out-of-n:F repairable system isstudied. Both the working time and the repair time of each component are assumed to be exponentially distributed and the n components in the system have homogeneous Markov dependence. By using the definition of generalized transition probability and a rule with priority to repair the key components, we derive the state transition probability matrix of the system. When n is given, some important reliability indices of the system can be obtained.Second, a general model for consecutive-k-out-of -n.F repairable system with r repairmen is studied, and introduce the definition of the k -1 step Markov dependence. The lifetime of component is an exponential random variable, its parameter depends on the number of consecutive failed components that precede the component. The repair time is also an exponential random variable. A priority repair rule on the basis of the system failure risk is adopted. We can obtain the result of the Kolmogorov forward equation by using the Runge-Kutta method. Then, some reliability indices of system can be evaluated accordingly. By comparing the reliability indices of liner and circular con/k/n:F system, we can see that a liner con/k/n: F system is always 'better' than the corresponding circular system.Finally, a 2 - out -of -n:F system is studied. It is assumed that the lifedistribution of each component is exponential distribution and the repair distribution of each component is general distribution. Under this assumption, the failure components can not be repaired "as good as new" and are to be repaired by "first in first out" rule. By using the theory of geometric process and introducting supplementary variable I_i(t) which is the period of the component i at time t and the repair time Y_i(t) that has been spent on the being repaired component i in the I_i(t) th period, we construct a generalized Markov process and derive Laplace transforms of some reliability indices.