Multistate Systems Reliability Theory with Applications

Bent Natvig

• Publisher: Wiley
• Year: 2010
• Print ISBN: 9780470697504
• eBook ISBN: 9780470977132
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Most books in reliability theory are dealing with a description of component and system states as binary: functioning or failed. However, many systems are composed of multi-state components with different performance levels and several failure modes. There is a great need in a series of applications to have a more refined description of these states, for instance, the amount of power generated by an electrical power generation system or the amount of gas that can be delivered through an offshore gas pipeline network.

This book provides a descriptive account of various types of multistate system, bound-for multistate systems, probabilistic modeling of monitoring and maintenance of multistate systems with components along with examples of applications.

Key Features:

• Looks at modern multistate reliability theory with applications covering a refined description of components and system states.
• Presents new research, such as Bayesian assessment of system availabilities and measures of component importance.
• Complements the methodological description with two substantial case studies. 

Reliability engineers and students involved in the field of reliability, applied mathematics and probability theory will benefit from this book.

1

Introduction

In reliability theory a key problem is to find out how the reliability of a complex system can be determined from knowledge of the reliabilities of its components. One inherent weakness of traditional binary reliability theory is that the system and the components are always described just as functioning or failed. This approach represents an oversimplification in many real-life situations where the system and their components are capable of assuming a whole range of levels of performance, varying from perfect functioning to complete failure. The first attempts to replace this by a theory for multistate systems of multistate components were done in the late 1970s in Barlow and Wu (1978), El-Neweihi et al. (1978) and Ross (1979). This was followed up by independent work in Griffith (1980), Natvig (1982a), Block and Savits (1982) and Butler (1982) leading to proper definitions of a multistate monotone system and of multistate coherent systems and also of minimal path and cut vectors. Furthermore, in Funnemark and Natvig (1985) upper and lower bounds for the availabilities and unavailabilities, to any level, in a fixed time interval were arrived at for multistate monotone systems based on corresponding information on the multistate components. These were assumed to be maintained and interdependent. Such bounds are of great interest when trying to predict the performance process of the system, noting that exactly correct expressions are obtainable just for trivial systems. Hence, by the mid 1980s the basic multistate reliability theory was established. A review of the early development in this area is given in Natvig (1985a). Rather recently, probabilistic modeling of partial monitoring of components with applications to preventive system maintenance has been extended by Gåsemyr and Natvig (2005) to multistate monotone systems of multistate components. A newer review of the area is given in Natvig (2007).

The theory was applied in Natvig et al. (1986) to an offshore electrical power generation system for two nearby oilrigs, where the amounts of power that may possibly be supplied to the two oilrigs are considered as system states. This application is also used to illustrate the theory in Gåsemyr and Natvig (2005). In Natvig and Mørch (2003) the theory was applied to the Norwegian offshore gas pipeline network in the North Sea, as of the end of the 1980s, transporting gas to Emden in Germany. The system state depends on the amount of gas actually delivered, but also to some extent on the amount of gas compressed, mainly by the compressor component closest to Emden. Rather recently the first book (Lisnianski and Levitin, 2003) on multistate system reliability analysis and optimization appeared. The book also contains many examples of the application of reliability assessment and optimization methods to real engineering problems. This has been followed up by Lisnianski et al. (2010).

Working on the present book a series of new results have been developed. Some generalizations of bounds for the availabilities and unavailabilities, to any level, in a fixed time interval given in Funnemark and Natvig (1985) have been established. Furthermore, the theory for Bayesian assessment of system reliability, as presented in Natvig and Eide (1987) for binary systems, has been extended to multistate systems. Finally, a theory for measures of component importance in nonrepairable and repairable multistate strongly coherent systems has ...

Table of contents

• Cover
• Wiley Series in Probability and Statistics
• Title Page
• Copyright
• Dedication
• Preface
• Acknowledgements
• List of Abbreviations
• Chapter 1: Introduction
• Chapter 2: Basics
• Chapter 3: Bounds for System Availabilities and Unavailabilities
• Chapter 4: An Offshore Gas Pipeline Network
• Chapter 5: Bayesian Assessment of System Availabilities
• Chapter 6: Measures of Importance of System Components
• Chapter 7: Measures of Component Importance—A Numerical Study
• Chapter 8: Probabilistic Modeling of Monitoring and Maintenance
• Appendix A: Remaining Proofs of Bounds given in Chapter 3
• Appendix B: Remaining Intensity Matrices in Chapter 4
• References
• Index
• Wiley Series in Probability and Statistics