Multistate Systems Reliability Theory with Applications (eBook)

Bent Natvig (Autor)

eBook Download: PDF

2010
John Wiley & Sons (Verlag)
978-0-470-97707-1 (ISBN)

Infos

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.

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.

Inhalt

Preface.

Acknowledgements.

List of abbreviations.

1 Introduction.

1.1 Basic notation and two simple examples.

1.2 An offshore electrical power generation system.

1.3 Basic definitions from binary theory.

1.4 Early attempts to define multistate coherent systems.

1.5 Exercises.

2 Basics.

2.1 Multistate monotone and coherent systems.

2.2 Binary type multistate systems.

2.3 Multistate minimal path and cut vectors.

2.4 Stochastic performance of multistate monotone and coherent
systems.

2.5 Stochastic performance of binary type multistate strongly
coherent systems.

2.6 Exercises.

3 Bounds for system availabilities and
unavailabilities.

3.1 Performance processes of the components and the system.

3.2 Basic bounds in a time interval.

3.3 Improved bounds in a time interval using modular
decompositions.

3.4 Improved bounds at a fixed point of time using modular
decompositions.

3.5 Strict and exactly correct bounds.

3.6 Availabilities and unavailabilities of the components.

3.7 The simple network system revisited.

3.8 The offshore electrical power generation system
revisited.

4 An offshore gas pipeline network.

4.1 Description of the system.

4.2 Bounds for system availabilities and unavailabilities.

5 Bayesian assessment of system availabilities.

5.1 Basic ideas.

5.2 Moments for posterior component availabilities and
unavailabilities.

5.3 Bounds for moments for system availabilities and
unavailabilities.

5.4 A simulation approach and an application to the simple
network system.

6 Measures of importance of system components.

6.1 Introduction.

6.2 Measures of component importance in nonrepairable
systems.

6.3 The Birnbaum and Barlow-Proschan measures of component
importance in repairable systems and the latter's dual
extension.

6.4 The Natvig measure of component importance in repairable
systems and its dual extension.

6.5 Concluding remarks.

7 Measures of component importance - a numerical
study.

7.1 Introduction.

7.2 Component importance in two three-component systems.

7.3 Component importance in the bridge system.

7.4 Application to an offshore oil and gas production
system.

7.5 Concluding remarks.

8 Probabilistic modeling of monitoring and
maintenance.

8.1 Introduction and basic marked point process.

8.2 Partial monitoring of components and the corresponding
likelihood formula.

8.3 Incorporation of information from the observed system
history process.

8.4 Cause control and transition rate control.

8.5 Maintenance, repair and aggregation of operational
periods.

8.6 The offshore electrical power generation system.

8.7 The data augmentation approach.

Appendix A Remaining proofs of bounds given in Chapter
3.

A.1 Proof of the inequalities 14, 7 and 8 of Theorem 3.12.

A.2 Proof of inequality 14 of Theorem 3.13.

A.3 Proof of inequality 10 of Theorem 3.17.

Appendix B Remaining intensity matrices in Chapter 4.

References.

Index.

Rezensionen

"This work is both text and research monograph, offering the
fundamentals as well as new research as he says, "on its way to
being published in international journals." (Booknews, 1 April
2011)

Produkt-Details

• Erscheint lt. Verlag: 9.11.2010
• Reihe/Serie: Wiley Series in Probability and Statistics
• Reihe/Serie: Wiley Series in Probability and Statistics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Angewandte Wahrscheinlichkeitsrechnung u. Statistik • Applied Probability & Statistics • Electrical & Electronics Engineering • Elektrotechnik u. Elektronik • Engineering statistics • Multistate Systems Reliability Theory with Applications, binary type multistate systems, multistate minimal path, cut vectors, Basic bounds in a time interval, Strict and exactly correct bounds, offshore electrical power generation system, offshore gas pipeline network, Bayesian assessment of system availabilities, • Qualität u. Zuverlässigkeit • Qualität u. Zuverlässigkeit • Quality & Reliability • Statistics • Statistik • Statistik in den Ingenieurwissenschaften
• ISBN-10: 0-470-97707-8 / 0470977078
• ISBN-13: 978-0-470-97707-1 / 9780470977071