A general model for consecutive- k-out-of- n: F repairable system with exponential distribution and ( k−1)-step Markov dependence

Abstract

In this paper, a general model for consecutive- k-out-of- n: F repairable system with exponential distribution and ( k−1)-step Markov dependence is introduced. The lifetime of a 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. Then the transition density matrix of the system is determined. Some reliability indices, including the system availability, rate of occurrence of failures and reliability are evaluated accordingly. For the demonstration of the model and methodology, a linear system example and a circular system example are investigated.