Multistate Systems Reliability Theory with Applications (Wiley Series in Probability and Statistics) - Hardcover

Natvig, Bent

Hardcover

ISBN 10: 0470697504 ISBN 13: 9780470697504

Verlag: Wiley, 2010

Inhaltsangabe

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.

Über diesen Titel

Über die Autorin bzw. den Autor

Bent Natvig is Professor in Mathematics Statistics, University of Oslo.
Member of Research Education Committee, Faculty of Mathematics and Natural Sciences, 2000-. Member of User Committee, G.H. Sverdrup's Building, 2000-. Guest/Invited speaker at numerous lectures around Europe and America for the past 30 years. Speaking on reliability theory and mathematics and statistics. Research interests include: Reliability theory and risk analysis, Bayesian statistics, Bayesian forecasting and dynamic models and queuing theory. Currently Associate Editor of Methodology and Computing in Applied Probability.

Von der hinteren Coverseite

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.

The 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.

Aus dem Klappentext

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.

The 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.

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Multistate Systems Reliability Theory with Applications

By Bent Natvig

John Wiley & Sons

Copyright © 2011 John Wiley & Sons, Ltd
All right reserved.
ISBN: 978-0-470-69750-4

Chapter One

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 bihnary 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 been developed, and published in Natvig (2011), with accompanying advanced discrete simulation methods and an application to a West African production site for oil and gas.

1.1 Basic notation and two simple examples

Let S = {0, 1, ..., M} be the set of states of the system; the M + 1 states representing successive levels of performance ranging from the perfect functioning level M down to the complete failure level 0. Furthermore, let ITLITL = {1, ..., n} be the set of components and S_{i, i} = 1, ..., n the set of states of the ith component. We claim {0, M} [??] S_i< [??] S. Hence, the states 0 and M are chosen to represent the endpoints of a performance scale that might be used for both the system and its components. Note that in most applications there is no need for the same detailed description of the components as for the system.

Let x_i, i = 1, ..., n denote the state or performance level of the ith component at a fixed point of time and x = (x₁, ..., x_n). It is assumed that the state, f, of the system at the fixed point of time is a deterministic function of x, i.e. f = f(x). Here x takes values in S₁ x S₂ x ... x S_n and f takes values in S. The function f is called the structure function of the system. We often denote a multistate system by (ITLITL, f). Consider, for instance, a system of n components in parallel where S_i = {0, M}, i = 1, ..., n. Hence, we have a binary description of component states. In binary theory, i.e. when M = 1, the system state is 1 iff at least one component is functioning. In multistate theory we may let the state of the system be the number of components functioning, which is far more informative. In this case, for M = n,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.1)

As another simple example consider the network depicted in Figure 1.1. Here component 1 is the parallel module of the branches a₁ and b₁ and component 2 the parallel module of the branches a₂ and b₂. For i = 1, 2 let x_i = 0 if neither of the branches work, 1 if one branch works and 3 if two branches work. The states of the system are given in Table 1.1.

Note, for instance, that the state 1 is critical both for each component and the system as a whole in the sense that the failing of a branch leads to the 0 state. In binary theory the functioning state comprises the states {1, 2, 3} and hence only a rough description of the system's performance is possible. It is not hard to see that the structure function is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.2)

where I (·) is the indicator function.

The following notation is needed throughout the book.

(i, x) = (x₁, ..., x_i-1, ..., x_i+1, ..., x_n). y < x means y_i = x_i for i = 1, ..., n, and y_i < x_i for some i.

Let A [??] C. Then

x^A = vector with elements x_i, i [element of] A,

A^c = subset of ITLITL complementary to A.

1.2 An offshore electrical power generation system

In Figure 1.2 an outline of an offshore electrical power generation system, considered in Natvig et al. (1986), is given. The purpose of this system is to supply two nearby oilrigs with electrical power. Both oilrigs have their own main generation, represented by equivalent generators...

Details zur Ausgabe

• Verlag: Wiley
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 0470697504
• ISBN 13: 9780470697504
• Einband: Gebundene Ausgabe
• Auflage: 1
• Anzahl der Seiten: 262
• Kontakt zum Hersteller: Wiley-VCH GmbH; product_safety@wiley.com; ; Boschstrasse 12; Weinheim; 69469; Deutschland