Economic design of a circular consecutive-k-out-of-n:F system with (k-1)-step Markov dependence

A circular consecutive-k-out-of-n:F system consists of n components arranged along a circular path. The system fails if and only if at least k consecutive components in the system fail. The system reliability, the expected system life, and the expected number of failures are obtained under the assumption that the failure rate of a component depends on the number of consecutive failed components that follow it. A procedure to find the optimal k and a simulation procedure to search the near-optimal k are proposed with illustrative numerical examples. An expected cost per unit time is considered as the objective function to be minimized