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1 Introduction 1.1 Basic Concepts of Reliability Theory 1.2 Main Indicators of Reliability 1.2.1 Failure-Free Indicators 1.2.2 Durability Indicators 1.2.3 Indicators of Maintainability and Preservation 1.2.4 Complex Indicators 1.3 Base Dependencies of the Reliability Theory 1.4 Reliability During Regular Operation 1.5 Reliability During Gradual Failures 1.5.1 The Normal Distribution 1.5.2 The Truncated Normal Distribution 1.5.3 In a Log-Normal Distribution 1.5.4 The Weibull Distribution 1.6 Combined Action of Sudden and Gradual Failures 1.7 Features of the Reliability of Recoverable Products 1.8 Questions References 2 Mathematical Basis of Reliability 2.1 Introduction 2.2 Random Events and Probabilities 2.3 Numerical Features and Distributions of Random Variables 2.3.1 Mathematical Expectation 2.3.2 Dispersion 2.3.3 Average Square-Law Deviation 2.3.4 Moments of Distribution 2.3.5 Asymmetry 2.3.6 Excess 2.3.7 Mode of Discrete Random Variable 2.3.8 Median of Random Variable 2.4 Distribution Functions of Random Variables 2.4.1 Distribution Functions for Discrete Random Variables 2.4.2 Distribution Functions for Continuous Random Variables 2.5 Questions References 3 System Reliability Models 3.1 Introduction 3.2 Non-repair System Reliability Analysis 3.2.1 Classification of System Reliability Function 3.2.2 Analysis of the Reliability Function 3.2.3 Redundancy System Reliability 3.2.4 Methods of the Reliability Function 3.3 Repair System Reliability Analysis 3.3.1 General Information 3.3.2 System Reliability Function 3.3.3 Non-parametric Analysis Methods 3.3.4 Parametric Analysis Methods 3.3.5 Markov Chain and Its Application 3.4 Questions References 4 Complex System Reliability Analysis Methods 4.1 Introduction 4.2 Failure Mode and Effect Critical Analysis 4.2.1 Basic Concepts 4.2.2 Types of FMECA 4.2.3 Steps for FMECA 4.2.4 Criticality Assessment 4.2.5 FMECA Application 4.3 Fault Tree Analysis 4.3.1 Basic Concepts 4.3.2 Basic Approach 4.3.3 Qualitative Analysis 4.3.4 Quantitative Analysis 4.3.5 Reliability Graph 4.3.6 FTA Application 4.4 Comparison FMECA and FTA 4.5 Questions References 5 Model-Based Reliability Analysis Methods 5.1 Introduction 5.2 Multi-Source Reliability Data Processing System for Mechanical Parts 5.2.1 Comprehensive Reliability Assessment Model Based on Multi-Source Data 5.2.2 Case Study 5.3 Multi-Phase Mission Reliability Analysis 5.3.1 PMS System Characteristics 5.3.2 PMS Reliability Modeling Process 5.3.3 Static Reliability Analysis Method Based on BDD 5.3.4 Dynamic Reliability Analysis Method Based on Semi-Markov 5.3.5 Modular Analysis Method 5.3.6 Case Study 5.4 Conclusions References 6 System Reliability Prediction and Allocation 6.1 Introduction 6.2 Reliability Prediction 6.2.1 Reliability Block Diagram 6.2.2 Series Systems 6.2.3 Parallel Systems 6.2.4 Combined Structure 6.2.5 k-Out-of-n Systems 6.2.6 Redundant System 6.2.7 Reliability Evaluation of Complex Systems 6.2.8 Confidence Ranges for System Reliability 6.2.9 Component Importance 6.3 Reliability Allocation 6.3.1 Criteria for Reliability Allocation 6.3.2 Equal Allocation Approach 6.3.3 ARINC Approach 6.3.4 AGREE Allocation Approach 6.3.5 Customer-Driven Allocation Approach 6.3.6 Optimal Allocation Approaches 6.4 Questions References 7 Mechanical Reliability Analysis 7.1 Introduction 7.2 Basic Concepts 7.2.1 Types of Operational Loads 7.2.2 Specifics of Static Load 7.2.3 Specifics of Cycling Loading 7.2.4 Specifics of Temperature Effect 7.2.5 Creep and Relaxation of Stresses 7.3 Factors Affect Mechanical Reliability 7.3.1 Corrosion 7.3.2 Chemical Medium 7.3.3 Fields Environment 7.3.4 Space Medium 7.3.5 Structural Materials' Selection 7.4 Short Observe of Structural Elements 7.5 Probabilistic Calculations of Machinery Parts 7.5.1 Some Aspects of Probability Theory for Machinery Parts 7.5.2 Specifics of Probabilistic Strength Computing of Shafts and Axles 7.5.3 Computing Examples for Various Machinery Components 7.6 Civil Aircraft Jettison Fuel Subsystem Reliability Analysis 7.6.1 Background for the Computation 7.6.2 Risks and Challenges of Aircraft Fuel Jettison Subsystem 7.6.3 Function Hazard Assessment 7.6.4 Primary System Safety Assessment Facing on Reliability Distribution 7.6.5 Reliability Analysis of Each Independent Fuel Tank for Dumping 7.6.6 Reliability Analysis of the Whole Fuel Jettison Subsystem 7.7 Conclusions 7.8 Questions References 8 Reliability Tests 8.1 Introduction 8.1.1 Targets of Reliability and Life Tests 8.1.2 Specifics of Life Tests and Reliability 8.1.3 Test Types 8.1.4 Test Planning and Documentation 8.2 Reliability Tests Plan 8.2.1 Types of Tests 8.2.2 Test Samples 8.2.3 Test Stresses 8.2.4 Test Time 8.3 Zero-Failure Test 8.3.1 Binomial Zero-Failure Testing 8.3.2 Weibull Zero-Failure Testing 8.4 Life Tests 8.4.1 Theoretical Concept 8.4.2 Binomial Series Life Testing 8.4.3 Exponential Series Life Testing 8.4.4 Weibull Series Life Testing 8.5 Accelerated Tests 8.5.1 Principles for Accelerating Tests 8.5.2 Operational Cycles Compressing 8.5.3 Extrapolation in Time 8.5.4 Revision of Loading Range 8.5.5 Increased Frequency of Operational Cycles 8.5.6 Loading Extrapolation 8.5.7 Break Completely 8.5.8 Progressive Load Forcing 8.5.9 Alternating Modes Loading 8.5.10 Some Specifics of the Accelerated Tests 8.6 Verification of Reliability Based on Prior Information 8.7 Verification of Reliability by Means of Degradation Tests 8.8 Questions References 9 Risk Analysis of Aircraft Structure and Systems 9.1 Introduction 9.2 Risk Assessment of Aeroengine Life-Limited Parts 9.2.1 ELLPS Airworthiness Regulations and AC Analysis 9.2.2 Determination Method of ELLPs Based on FMEA 9.2.3 Probabilistic Risk Assessment of ELLPs 9.2.4 Case Analysis 9.3 Risk Warning of Aircraft Bleed Air System 9.3.1 Risk Warning Method 9.3.2 Application of Risk Warning on the BAS 9.4 Conclusions References