Exact Reliability and Signature Formulas for Linear m-Consecutive-k-out-of-n: F Systems

Abstract

An m-consecutive-k-out-of-n: F (m/C/k/n: F) system consists of n linearly ordered components such that the system fails if and only if there are at least m nonoverlapping runs of k consecutive failed components. Our motivation in this work is to obtain efficient formulas for the signature and reliability of the m/C/k/n: F system with independent and identical (i.i.d) components that are easy to implement and have a low computational time. We demonstrate that the reliability formula derived for this system requires less computational time than the m/C/k/n: F system formula currently in use. For the minimal and maximal signatures of the m/C/k/n: F system, we provide precise equations. In addition, the average number of faulty components at the time of an m/C/k/n: F system failure and mean time to failure (MTTF) of an m/C/k/n: F system are analyzed through the system signature.