Title Lévy processes and their applications in reliability and storage / Mohamed Abdel-Hameed

Published Heidelberg : Springer, 2014

Table of Contents
1.	Levy Processes and Their Characteristics					1
1.1.	Levy Processes					1
1.2.	The Levy-Ito Decomposition					2
1.3.	The Strong Markov Property for Levy Processes					3
1.4.	Subordinators					5
1.5.	Spectrally Positive Processes					7
1.6.	Examples of Spectrally Positive Processes					12
1.7.	The Compensation Formula					15
1.8.	Non-homogeneous Levy Processes					16
1.9.	Potentials					17
	References					22
2.	Degradation Processes					23
2.1.	Introduction					23
2.2.	Basic Definitions and Results					25
2.3.	Life Distributions of Devices Subject to Degradation					30
2.4.	Control-Limit Maintenance Policies for Continuously Monitored Degradable Systems					34
2.5.	One-Level Control-Limit Maintenance Policies for Non-Continuously Monitored Degradable Systems					41
2.6.	Multi-Level Control-Limit Maintenance Policies for Non-Continuously Monitored Degradable Systems					59
2.7.	Examples					62
2.8.	Inference for the Parameters of the Degradation Process					65
	References					73
3.	Storage Models: Control of Dams Using PMγ,π Policies					77
3.1.	Introduction and Summary					77
3.2.	Basic Definitions and Results					78
3.3.	The PMγ,π Control Policies and Their Associated Cost Functionals					80
3.4.	Subordinator Input					83
3.5.	Spectrally Positive and Spectrally Positive Reflected at its Infimum Inputs					92
3.6.	Examples					100
	References					108
	Appendix: Preliminaries					109
	Index					115

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Description 1 online resource (xiv, 116 pages) Series SpringerBriefs in Statistics, 2191-544X SpringerBriefs in statistics, 2191-544X Contents Preface -- Notation and Terminology -- Lévy Processes and Their Characteristics -- Degradation Processes -- Storage Models: Control of Dams Using P M{lambda, tau} Policies -- Appendix -- Index Summary This book covers Lévy processes and their applications in the contexts of reliability and storage. Special attention is paid to life distributions and the maintenance of devices subject to degradation; estimating the parameters of the degradation process is also discussed, as is the maintenance of dams subject to Lévy input Bibliography Includes bibliographical references and index Notes English Subject Lévy processes. Mathematics. Distribution (Probability theory) Industrial engineering. Mathematics distribution (statistics-related concept) industrial engineering. MATHEMATICS -- Applied. MATHEMATICS -- Probability & Statistics -- General. Distribution (Probability theory) Industrial engineering Lévy processes Mathematics Form Electronic book ISBN 9783642400759 3642400752 130654338X 9781306543385

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