Reliability and Some Characteristics of Circular Consecutive-k-Within-m-Out-of-n:F System

Abstract

A system can be classified with respect to the physical arrangement of its components and the functioning principle. A circular consecutive k-within-m-out-of-n:F system consists of n circularly ordered components and fails if and only if there are m consecutive components that include among them at least k failed components. A circular consecutive k-within-m-out-of-n:F system turns into circular consecutive k-out-of-n:F for m = k and k-out-of-n:F system for m = n. In this study, signature-based analysis of circular consecutive k-within-m-out-of-n:F system is performed. A new approximation to this system is provided based on maximum number of failed components and an illustrative example is given for different values of n, m, k to compare the approximate results with simulated and exact results.

Keywords:

• Circular consecutive k-within-m-out-of-n:F system
• Exchangeability
• Stochastic ordering
• System signature

Mathematics Subject Classification:

• Primary 62N05
• Secondary 60E15

Acknowledgments

The authors are grateful to two referees for their careful reading of a previous version of this manuscript and for their helpful comments and suggestions that improved the article.