Multistate Systems Reliability Theory with Applications

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.

Most books in reliability theory are dealing with a description ofcomponent and system states as binary: functioning or failed.However, many systems are composed of multi-state components withdifferent performance levels and several failure modes. There is agreat need in a series of applications to have a more refineddescription of these states, for instance, the amount of powergenerated by an electrical power generation system or the amount ofgas that can be delivered through an offshore gas pipeline network.This book provides a descriptive account of various types ofmultistate system, bound-for multistate systems, probabilisticmodeling of monitoring and maintenance of multistate systems withcomponents along with examples of applications.Key Features:* Looks at modern multistate reliability theory with applicationscovering a refined description of components and systemstates.* Presents new research, such as Bayesian assessment of systemavailabilities and measures of component importance.* Complements the methodological description with two substantialcase studies.Reliability engineers and students involved in the field ofreliability, applied mathematics and probability theory willbenefit from this book.

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 coherentsystems.2.5 Stochastic performance of binary type multistate stronglycoherent systems.2.6 Exercises.3 Bounds for system availabilities andunavailabilities.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 modulardecompositions.3.4 Improved bounds at a fixed point of time using modulardecompositions.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 systemrevisited.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 andunavailabilities.5.3 Bounds for moments for system availabilities andunavailabilities.5.4 A simulation approach and an application to the simplenetwork system.6 Measures of importance of system components.6.1 Introduction.6.2 Measures of component importance in nonrepairablesystems.6.3 The Birnbaum and Barlow-Proschan measures of componentimportance in repairable systems and the latter's dualextension.6.4 The Natvig measure of component importance in repairablesystems and its dual extension.6.5 Concluding remarks.7 Measures of component importance - a numericalstudy.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 productionsystem.7.5 Concluding remarks.8 Probabilistic modeling of monitoring andmaintenance.8.1 Introduction and basic marked point process.8.2 Partial monitoring of components and the correspondinglikelihood formula.8.3 Incorporation of information from the observed systemhistory process.8.4 Cause control and transition rate control.8.5 Maintenance, repair and aggregation of operationalperiods.8.6 The offshore electrical power generation system.8.7 The data augmentation approach.Appendix A Remaining proofs of bounds given in Chapter3.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.