Systems Engineering

Reliability Analysis Using k-out-of-n Structures

Mangey Ram, Tadashi Dohi

• Publisher: CRC Press
• Year: 2019
• Print ISBN: 9780367780005
• eBook ISBN: 9781351056441
• Edition: 1
• Topic: Biological Sciences
• Subtopic: Biology
• Index: Biological Sciences

A substantial amount of research has been conducted on consecutive k -out-of- n and related reliability systems over the past four decades. These systems have been used to model various engineering systems such as the microwave stations of telecoms network, oil pipeline systems, and vacuum systems in an electron accelerator. As such, studies of reliability properties of consecutive k -out-of- n structures have attracted significant attention from both theoretical and practical approaches. In the modern era of technology, the redundancies are employed in the various industrial systems to prevent them from failure/sudden failure or to recover from failures. This book is meant to provide knowledge and help engineers and academicians in understanding reliability engineering by using k -out-of- n structures. The material is also targeted at postgraduate or senior undergraduate students pursuing reliability engineering.

CHAPTER

1

Evaluation Methods for Reliability of Consecutive-k Systems

Tomoaki Akiba^1*, Taishin Nakamura², Xiao Xiao² and Hisashi Yamamoto²

¹ Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba, 275-0016, Japan

² Tokyo Metropolitan University, 6-6 Asahigaoka, Hino, Tokyo, 191-0065, Japan

1. Introduction

Consecutive-k system is a general term for the systems, where a concentration of failed components causes the system failure. One of the consecutive-k systems is a consecutive-k-out-of-n system. It has been extensively studied since the early 1980s and was first studied by Kontoleon (1980). The consecutive-k-out-of-n:F (G) systems consist of n components and fail (work) if and only if at least k “consecutive” components fail (work). Based on this definition, we can see that a consecutive-1-out-of-n:F (G) system is equivalent to a series (parallel) system, while a consecutive-n-out-of-n:F (G) system is equivalent to a parallel (series) system.

Consecutive-k-out-of-n systems have also been extended to two-dimensional systems by Salvia and Lasher (1990). Boehme et al. (1992) defined the more general two-dimensional system, which later are called linear or circular connected-X-out-of-(m, n):F lattice systems. The linear connected-X-out-of-(m, n):F lattice system contains the components which are arranged into a rectangular pattern with m rows and n columns. X denotes the figure consisting of the failed components which leads to the system failure and is called “failure pattern” throughout this chapter. The system fails if and only if all the components which constitute failure pattern X fail. Salvia and Lasher (1990) also described d-dimensional consecutive-k-out-of-n systems (d ≥ 2). We call these systems multi-dimensional consecutive-k-out-of-n systems in this chapter.

One of the most important problems in reliability theory is the reliability evaluation under the assumption that all the component reliabilities are given. In this chapter, we review the evaluation methods for the reliability of consecutive-k systems. In particular, we focus on our previous studies. The reliability of the consecutive-k-out-of-n system can be computed relatively easily via the existing evaluation methods. However, when a multi-dimensional consecutive-k-out-of-n system consists of many components, it takes much computing time to obtain the exact system reliability. To overcome this problem, we also show bounds and approximate values for the reliability of multi-dimensional consecutive-k-out-of-n systems in this chapter. And, we assume the case of independent component failure in the system, through the chapter. Please note that some researchers provided assumption of dependent component f...

Table of contents

• Cover
• Title Page
• Copyright Page
• Table of Contents
• Preface
• List of Contributors
• 1. Evaluation Methods for Reliability of Consecutive-k Systems
• 2. Reliability Properties of K-out-of-N:G Systems
• 3. A Summary of Maintenance Policies for K-out-of-N Models and Their Applications to Consecutive Systems
• 4. Reliability Modeling and Estimation of (k1, k2)-out-of-(n, m) Pairs: G Balanced Systems
• 5. Sequencing Optimization for k-out-of-n:G Cold-standby Systems Considering Reliability and Energy Consumption
• 6. Impact of Correlated Failure on the Maintenance of Multi-state Consecutive 2-out-of-n: Failed Systems
• 7. Structural and Probabilistic Examinations of k-out-of-n:G System and Their Application to an Optimal Construction of a Safety Monitoring System
• 8. An Analysis of (k+1)-out-of-n:F Fault Tolerant System with Fixed Warranty Period
• 9. Reliability Analysis of Three-stage Weighted 4-out-of n:F System Subject to Possibility of Degradation after Repair with Inspection
• 10. Signature of Linear Consecutive k-out-of-n System
• Index