Reliability of linear and circular consecutive-k-out-of-n systems with shock model

A consecutive k-out-of-n system consists of an ordered sequence of n components, such that the system functions if and only if at least k (k ≤ n) consecutive components function. The system is called linear (L) or circular (C) depending on whether the components are arranged on a straight line or form a circle. In the rst part, we use a shock model to obtain the reliability function of consecutve-k-out-of-n systems with dependent and nonidentical components. In the second part, we treat some numerical examples to show the derive results and deduce the failure rate of each component and the system.Keywords: Linear and circular consecutive-k-out-of-n system; Feliability function; Failure rate; Shock mode