Intro; Preface; Contents; 1 Introduction; 1.1 Aim and Scope of the Book; 1.2 Brief Overview; References; 2 Preliminaries: Reliability and Point Processes; 2.1 Distribution Function and Failure Rate; 2.2 Mean Remaining Lifetime; 2.3 Monotonicity of the Failure Rate and the MRL Function; 2.4 Stochastic Ordering; 2.5 Point Processes and Their Characterization; 2.6 Perfect and Minimal Repair; 2.7 Shocks and Extreme Shock Model; References; 3 Renewal Processes and Applications; 3.1 Definition and Main Properties; 3.2 Limiting Properties; 3.3 Alternating Renewal and Renewal Reward Processes
3.4 Applications of Renewal Theory3.4.1 Renewal Reward Process with Continuous Output; 3.4.2 Alternating Renewal Process with Gradual Repair; 3.4.3 Classical Optimal Replacement Problem and Its Generalization; 3.4.4 Using Renewal Equations in Shocks Modeling; 3.4.5 Renewal in Populations of Technical Items and Organisms; References; 4 Poisson Process; 4.1 Homogeneous Poisson Process; 4.2 Nonhomogeneous Poisson Process; 4.3 Minimal Repair and Applications to Optimal Maintenance; 4.4 Simple Poisson Shock Models; 4.4.1 â#x80;#x98;Classicalâ#x80;#x99; Extreme Shock Model; 4.4.2 Direct Impact on the Failure Rate
4.5 General Compound Poisson Process and a Shot Noise Process4.6 Mixed Poisson Process; References; 5 Advanced Poisson Shock Models; 5.1 The Terminating Shock Process with Independent Wear Increments; 5.1.1 General Setting; 5.1.2 Exponentially Distributed Boundary; 5.1.3 Deterministic Boundary; 5.2 History-Dependent Termination Probability; 5.3 Shot Noise Process for the Failure Rate; 5.3.1 Shot Noise Process Without Critical Shocks; 5.3.2 Shot Noise Process with Critical Shocks and Deterioration; 5.4 Extreme Shock Model with Delayed Termination
5.5 Cumulative Shock Model with Initiated Wear Processes5.6 â#x80;#x98;Curableâ#x80;#x99; Shock Processes; 5.7 Stress-Strength Model with Delay and Cure; 5.8 Survival of Systems with Protection Subject to Two Types of External Attacks; 5.9 Information-Based Thinning of Shock Processes; 5.9.1 General Setting; 5.9.2 Formal Description of the Information-Dependent Thinning; 5.9.3 Stress-Strength Type Classification Model; References; 6 Poisson Shock Model with Applications to Preventive Maintenance; 6.1 Conditional Characteristics and Interpretation; 6.1.1 Conditional Characteristics; 6.1.2 A Specific Case
6.1.3 The Dynamics of Conditional Distributions6.2 Univariate Preventive Maintenance Policy; 6.2.1 The Failure Model and Supplementary Results; 6.2.2 The PM Models for Systems Under Shocks; 6.3 Bivariate Preventive Maintenance Policy; 6.4 Bivariate Preventive Maintenance Policy with Minimal Repair; References; 7 Generalizations of Renewal Process; 7.1 Virtual Age; 7.2 G-Renewal Process; 7.3 General Repair Process; 7.4 Equilibrium Virtual Age; 7.5 Aging and Limiting Properties; 7.6 Application: Optimal Degree of Repair; 7.7 Renewal Equations; 7.8 Failure Rate Reduction Models

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Context of Point processes for reliability analysis : shocks and repairable systems, Ji Hwan Cha, Maxim Finkelstein

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