A New Iterative Approach to Evaluate the Reliability of a Combined Consecutive k and v-Out-Of-n System

摘要

Consecutive k-out-of-n: F systems have applications in the fields of telecommunications and oil pumping. A consecutive k-out-of-n: F system fails if at least consecutive k components fail. However, practical systems may fail due to either the failure of a number of consecutive components or the failure of a total number of components. In this paper, we consider a system with linearly arranged components, where the system fails if at least a pre-specified number of consecutive components fail or a pre-specified total number of components fail. The system is termed as a combined consecutive k and v-out-of-n system. The iterative relationship between the failure probability of a consecutive k-out-of-n: F system has been proposed. This paper focuses on the iterative relationship between the success probabilities and proposes the detailed calculation process for illustrative purposes.