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

A circular consecutive-kk-out-of-nn:F system consists of nn components arranged along a circular path. The system fails if and only if at least kk 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 kk and a simulation procedure to search the near-optimal kk are proposed with illustrative numerical examples. An expected cost per unit time is considered as the objective function to be minimized.