Dynamic Reliability Evaluation of Consecutive-k-Within-m-Out-of-n:F System

Abstract

A consecutive k-within-m-out-of-n:F system consists of n linearly ordered components and fails if and only if there are m consecutive components which include among them at least k failed components. This system model generalizes both consecutive k-out-of-n:F and k-out-of-n:F systems. In this article, we study the dynamic reliability properties of consecutive k-within-m-out-of-n:F system consisting of exchangeable dependent components. We also obtain some stochastic ordering results and use them to get simple approximation formulae for the survival function and mean time to failure of this system.

Keywords:

• Consecutive k-out-of-n:F system
• Consecutive k-within-m-out-of-n:F system
• Exchangeable lifetimes
• Failure rate
• Mean residual life
• Mixtures
• Signature
• Stochastic ordering

Mathematics Subject Classification:

• 62N05
• 62E15

Acknowledgment

The authors are grateful to the referees for their helpful comments and suggestions, which improved the article.