Stochastic Models in Reliability Engineering (Advanced Research in Reliability and System Assurance Engineering)

Cover
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Preface
Editors
Contributors
Chapter 1 Reliability Analysis of a Pseudo Working Markov Repairable System
	1.1 Introduction
	1.2 Basic Assumptions
	1.3 Reliability Indexes
		1.3.1 Case of Constant τ
			1.3.1.1 Time to First Failure
			1.3.1.2 Point-Wise and Interval Availabilities
		1.3.2 Case of Random τ
	1.4 Numerical Examples and Special Cases
	1.5 Conclusions
	References
Chapter 2 System Reliability Assessment with Multivariate Dependence Models
	2.1 Background
		2.1.1 A Motivating Example
		2.1.2 Literature Review
		2.1.3 Overview
	2.2 Copula Theory
	2.3 Copula-Based Multivariate Dependence Models
		2.3.1 Elliptical Copula (EC)
		2.3.2 Exchangeable Archimedean Copula (EAC)
		2.3.3 Hierarchical Archimedean Copula (HAC)
		2.3.4 Mixed Copula (MC)
		2.3.5 Vine Copula (VC)
	2.4 System Reliability Assessment from Copula Perspective
	2.5 Revisiting the Motivating Example
		2.5.1 Illustration Using EC
		2.5.2 Illustration Using EAC
		2.5.3 Illustration Using HAC
		2.5.4 Illustration Using MC
		2.5.5 Illustration Using VC
	2.6 Discussion and Future Study
	References
Chapter 3 Reliability Modelling of Multi-Phased Linear Consecutively Connected Systems
	3.1 Introduction
	3.2 The Model
		3.2.1 System Structure
		3.2.2 Signal Transmission of CE
		3.2.3 Signal Transmission of Node
		3.2.4 Reliability of LMCCSs
	3.3 Illustrative Example
	3.4 Summary
	References
Chapter 4 A Method for Complex Multi-State Systems Reliability Analysis Based on Compression Inference Algorithm and Bayesian Network
	4.1 Introduction
	4.2 Format of NPT
	4.3 Proposed Multi-State Compression Algorithm
		4.3.1 Run and Phrase
		4.3.2 Multi-State Compression Algorithm
	4.4 Proposed Multi-State Inference Algorithm
		4.4.1 Rules for Calculating Intermediate Variables
		4.4.2 Proposed Multi-State Inference Algorithm
	4.5 Case Study
		4.5.1 Case Background
		4.5.2 Calculation and Analysis
	4.6 Summary
	Appendix A
	Appendix B
	References
Chapter 5 Reliability Analysis of Demand-Based Warm Standby System with Multi-State Common Bus
	5.1 Introduction
	5.2 Model Description for a DBWSS with Multi-State Common Bus Performance Sharing
	5.3 Time-Varying Reliability Evaluation Based on MDD
		5.3.1 The Construction of System MDD
		5.3.2 System Reliability Evaluation Based on MDD
	5.4 Numerical Studies
		5.4.1 Illustrative Example
		5.4.2 System MDD for the Illustrative Example
		5.4.3 System Reliability Assessment for the Illustrative Example
	5.5 Conclusions
	References
Chapter 6 An Upside-Down Bathtub-Shaped Failure Rate Model Using a DUS Transformation of Lomax Distribution
	6.1 Introduction
	6.2 DUS-Lomax Distribution
	6.3 Shapes
		6.3.1 Shape of Probability Density Function
		6.3.2 Shape of Failure Rate Function
	6.4 Statistical Properties
		6.4.1 Moments
		6.4.2 Moment Generating Function
		6.4.3 Characteristic Function
		6.4.4 Quantile Function
		6.4.5 Entropy
	6.5 Distributions of Maximum and Minimum
	6.6 Estimation of Parameters
	6.7 Asymptotic Distribution and Confidence Bounds
	6.8 Stress-Strength Reliability Estimation
		6.8.1 The Maximum Likelihood Estimation of R
	6.9 Simulation Study
	6.10 Data Analysis
	6.11 Conclusion
	References
Chapter 7 Reliability Analysis of Multi-State Systems with Dependent Failures Based on Copula
	7.1 Introduction
	7.2 Copula
		7.2.1 Definition of Copula
		7.2.2 Copula Selection and Parameter Estimation
	7.3 Modelling and Reliability Analysis of Dependent Multi-State Systems
		7.3.1 Series Dependent Multi-State System
		7.3.2 Parallel Dependent Multi-State System
	7.4 Application
		7.4.1 Series Process of a Hydrocyclone System
		7.4.2 Parallel Process of a Hydrocyclone System
	7.5 Conclusions
	Acknowledgement
	References
Chapter 8 Modelling and Inference for Special Types of Semi-Markov Processes
	8.1 Introduction
	8.2 Semi-Markov Processes and Multi-State Systems
		8.2.1 INID Random Variables – The Maximum Case
		8.2.2 INID Random Variables – The Minimum Case
	8.3 Parameter Estimation and Consistency
	8.4 Markov Renewal Function and Semi-Markov Transition Matrix
	8.5 Reliability Indicators
	8.6 Simulation Study
	Acknowledgements
	References
Chapter 9 Weighted Multi-Attribute Acceptance Sampling Plans
	9.1 Introduction: Background and Driving Forces
	9.2 Two Acceptance Sampling Plans
	9.3 OC Function of Acceptance Sampling Plans
		9.3.1 OC Function of Acceptance Sampling Plan I
		9.3.2 OC Function of Acceptance Sampling Plan II
	9.4 Design of Acceptance Sampling Plans
	9.5 Results and Discussions
	9.6 Conclusions
	List of Abbreviations
	References
Chapter 10 Reliability Assessment for Systems Suffering Common Cause Failure Based on Bayesian Networks and Proportional Hazards Model
	10.1 Introduction
	10.2 Multi-Component Systems with Dynamic Environment and Common Cause Failure
		10.2.1 System Description
		10.2.2 Assumptions
	10.3 Modelling Multi-Component Systems with Dynamic Environment and Common Cause Failure
		10.3.1 Modelling Component with Dynamic Environment by Proportional Hazards Model
		10.3.2 Dynamic Bayesian Networks Framework for System with CCF
			10.3.2.1 Bayesian Networks and Dynamic Bayesian Networks
			10.3.2.2 BN Representation of System with CCF
	10.4	Numerical Examples
	10.5	Conclusions
	Acknowledgements
	References
Chapter 11 Early Warning Strategy of Sparse Failures for Highly Reliable Products Based on the Bayesian Method
	11.1 Introduction
	11.2 Modelling
		11.2.1 Dirichlet-Multinomial Model
		11.2.2 Beta-Binomial Model
	11.3 Early Warning Framework
	11.4 Case Study
	11.5 Conclusion
	Acknowledgement
	References
Chapter 12 Fault Detection and Prognostics of Aero Engine by Sensor Data Analytics
	12.1 Introduction
	12.2 Principles of Aero Engine PHM
	12.3 Degradation Diagnostics
		12.3.1 Single-Channel Signal and Single Working Condition and Failure Modes
		12.3.2 Multiple-Channel Signal and Single Working Condition and Failure Modes
		12.3.3 Multiple-Channel Signal and Multiple Working Conditions and Failure Modes
	12.4 Degradation Trend and RUL Prediction
		12.4.1 Degradation Trend Prediction
		12.4.2 RUL Prediction
	12.5 Case Study
		12.5.1 Evaluation of Aero Engine Degradation
		12.5.2 Prediction Method of Aero Engine Degradation Trend
	12.6 Conclusions
	References
Chapter 13 Stochastic Modelling of Opportunistic Maintenance for Series Systems with Degrading Components
	13.1 Introduction
	13.2 Description of the System
	13.3 Dependability and Performance Measures
		13.3.1 Asymptotic Availability
		13.3.2 Total Expected Operational Cost
	13.4 Numerical Examples
	13.5 Conclusions and Future Work
	Appendix
	References
Chapter 14 On Censored and Truncated Data in Survival Analysis and Reliability Models
	14.1 Introduction
	14.2 Formulation – Marginal Non-parametric Likelihood
	14.3 Formulation – Complete Non-Parametric Likelihood
		14.3.1 The Law of Censoring and Truncation
			14.3.1.1 Random Covering
			14.3.1.2 The Mechanism of Censoring and Truncation
			14.3.1.3 The Distribution Associated with the Random Covering
			14.3.1.4 The Distribution of the Random Vector (L(x), R(x), L(z), R(z))
			14.3.1.5 The Distribution of the Random Vector (L(X), R(X), L(Z), R(Z))
		14.3.2 Estimation of the Density of Survival or Reliability
	14.4 Example
	References
Chapter 15 Analysis of Node Resilience Measures for Network Systems
	15.1 Introduction: Background and the Main Purpose
	15.2 The Generation of an Example Network
		15.2.1 Network Topology
		15.2.2 Cascading Failure
		15.2.3 New Level Values of Nodes after Failure
	15.3 The Matrix of Node Resilience (MNR)
	15.4 The Relationship between the QRN and the Node Importance
	15.5 The Iteration of MNRs and Trend Analysis in the Process of Iteration
	15.6 Conclusions
	References
Chapter 16 Reliability Analysis of General Purpose Parts for Special Vehicles Based on Durability Testing Technology
	16.1 Introduction
	16.2 Reliability Test
		16.2.1 Reliability Test Method for Vehicle
		16.2.2 Theory of Linear Fatigue Damage
		16.2.3 Selection of Working Condition for Durability Test
		16.2.4 Calculation of Acceleration Coefficient
		16.2.5 Equivalent Stress-Strength Interference Model
	16.3 Durability Test Analysis of Vehicle General Parts
		16.3.1 Calculation of Cumulative Damage of Water Pump Bearing
		16.3.2 Calculation of the Damage Amount Based on Bearing Durability Tests
	16.4 Reliability Analysis of Bearing
		16.4.1 Calculation of Equivalent Stress Distribution
		16.4.2 Fatigue Strength Distribution
		16.4.3 Reliability Calculation
	16.5 Discussion
	16.6 Conclusion
	Acknowledgements
	References
Chapter 17 State of Health Prognostics of Lithium-Ion Batteries
	17.1 Introduction
	17.2 Prognostics of State of Health for Lithium-Ion Batteries
		17.2.1 Battery Dataset
		17.2.2 Charging Process
		17.2.3 Discharge Process
		17.2.4 Capacity Degradation
		17.2.5 Prognostics of Battery Capacity Degradation
	17.3 Gaussian Process Regression-Based Prognostics of State of Health for Lithium-Ion Batteries
	17.4 Conclusion
	List of Abbreviations
	References
Chapter 18 Life Prediction of Device Based on Material’s Micro-Structure Evolution by Means of Computational Materials Science
	18.1 Introduction
	18.2 Technology Roadmap
	18.3 Cases Studies
		18.3.1 The Grain Growth
			18.3.1.1 Background
			18.3.1.2 Phase Field Method
			18.3.1.3 Simulation Results
			18.3.1.4 Discussions
			18.3.1.5 Conclusions
		18.3.2 Dendrite Growth Simulation
			18.3.2.1 Background
			18.3.2.2 Monte Carlo Methods
			18.3.2.3 Simulation Results
			18.3.2.4 Discussion
			18.3.2.5 Conclusions
	18.4 Summary
	Acknowledgements
	References
Chapter 19 Low-Cycle Fatigue Damage Assessment of Turbine Blades Using a Substructure-Based Reliability Approach
	19.1 Introduction
	19.2 Substructure-Based Distributed Collaborative MLS for Probabilistic Analysis
		19.2.1 Moving Least Squares (MLS)
		19.2.2 Distributed Collaborative Response Surface Method (DCRSM)
		19.2.3 MLS-Based DCRSM, DCMLS
		19.2.4 Substructure-Based DCMLS, SDCMLS
			19.2.4.1 Basic Idea of SDCMLS
			19.2.4.2 Substructure Method
			19.2.4.3 Mathematical Model of SDCMLS
			19.2.4.4 Advantages of SDCMLS
	19.3 Probabilistic Strain-Life Relationships
	19.4 Basics of Probabilistic LCF Damage Prediction
		19.4.1 Preparation
		19.4.2 Basic Principle
	19.5 Probabilistic Low-Cycle Fatigue Life Prediction
		19.5.1 Construction of SDMLSFs-I
		19.5.2 Low-Cycle Fatigue Life Prediction
		19.5.3 Model Comparison and Method Validation
			19.5.3.1 Model Comparison
			19.5.3.2 Method Validation
	19.6 Probabilistic Analysis of LCF Damage
		19.6.1 Reliability Analysis of LCF Damage
		19.6.2 Sensitivity Analysis
	19.7 Conclusions
	Acknowledgements
	Acronyms
	Notation
	References
Chapter 20 Phased-Mission Modelling of Physical Layer Reliability for Smart Homes
	20.1 Introduction
	20.2 Dynamic Behaviour and Phased-Mission Modelling
		20.2.1 Dynamic Behaviour
		20.2.2 Dynamic Fault Tree Modelling
	20.3 Phase-Modular Reliability Analysis
		20.3.1 MDD-Based PMS Analysis
		20.3.2 CTMC-Based PMS Reliability Analysis
	20.4 Example Analysis and Results
		20.4.1 Modularization
		20.4.2 MDD-Based Analysis of the Static Part
		20.4.3 CTMC-Based Analysis of Dynamic Part
		20.4.4 Integration for Mission Reliability
	20.5 Conclusion and Future Directions
	References
Chapter 21 Comparative Reliability Analysis of Different Traction Drive Topologies for a Search-and-Rescue Helicopter
	21.1 Introduction
	21.2 Topologies of the Different Traction Drives
		21.2.1 Topology of Conventional Traction Drive
		21.2.2 Topologies of Hybrid-Electric Traction Drives
			21.2.2.1 Serial Hybrid 1
			21.2.2.2 Serial Hybrid 2
			21.2.2.3 Parallel Hybrid
			21.2.2.4 Combined Hybrid
		21.2.3 Topologies of Full-Electric Traction Drives
			21.2.3.1 Single-Line Electric
			21.2.3.2 Dual-Electric 1
			21.2.3.3 Dual-Electric 2
	21.3 Markov Models and Comparisons of Reliability and Availability
		21.3.1 Elements Description
			21.3.1.1 Elements with Two States
			21.3.1.2 Three-State Gas Turbine Engine Element
			21.3.1.3 Elements in the Repairable Systems
		21.3.2 Reliability Models for Different Propulsion Systems
			21.3.2.1 Conventional System
			21.3.2.2 Hybrid-Electric
			21.3.2.3 Full-Electric
		21.3.3 Failure Probability Comparison between Different Traction Drive Topologies
		21.3.4 Availability Comparison for Different Propulsion System
		21.3.5 Comparison between the Representative Propulsion Systems
	21.4 Method for Element Sensitivity Analysis
	21.5 Conclusion
	Acknowledgements
	References
Chapter 22 Reliability and Fault Tolerance Assessment of Different Operation Modes of Air Conditioning Systems for Chemical Laboratories
	22.1 Introduction
	22.2 Multi-State Models of Chemical Laboratory Air Conditioning Systems
		22.2.1 Description of the System
		22.2.2 Description of the System’s Elements
		22.2.3 Multi-State Models for an Air Conditioning System for a Chemical Laboratory
			22.2.3.1 Working in the Regular Regime
			22.2.3.2 Working in the Emergency Regime
		22.2.4 Calculation of the Reliability Indices of an Air Conditioning System for a Chemical Laboratory
	22.3 Conclusion
	References
Chapter 23 Dependability Analysis of Ship Propulsion Systems
	23.1 Introduction
	23.2 Data and Methodology
	23.3 Results
	23.4 Conclusions and Discussion
	References
Chapter 24 Application of Markov Reward Processes to Reliability, Safety, Performance Analysis of Multi-State Systems with Internal and External Testing
	24.1 Introduction: Background and Driving Forces
	24.2 Basic Relations of the Markov Reward Model
	24.3 A Unified Approach to Calculation of RSP indices in MRM
	24.4 Case Study I: Reliability and Safety Analysis of a Master-Slave Redundant System with an Internal Built-in Test
		24.4.1 The Functioning of the Schema in the Case of Violations of Performability of One Module
		24.4.2 The Functioning of the Schema in the Case of Violations of Performability of Two Modules
	24.5 Case Study II: Performance Analysis of a System with an External Test
	24.6 Conclusion
	Appendix
	References
Chapter 25 Multi-Objective Maintenance Optimization of Complex Systems Based on Redundancy-Cost Importance
	25.1 Introduction
	25.2 Multi-Objective Maintenance Optimization Model for Complex Systems
	25.3 The Theory of Redundancy-Maintenance Cost Importance
		25.3.1 Birnbaum Importance
		25.3.2 Redundant Importance
		25.3.3 The Relation between System Reliability and Direct Maintenance Cost
		25.3.4 The Relation between Reliability and Redundancy-Maintenance Cost
		25.3.5 Redundancy-Maintenance Cost Importance
	25.4 Multi-Objective Maintenance Optimization Algorithm Based on NSGA-II
		25.4.1 NSGA-II in Maintenance Optimization
		25.4.2 BI-NSGA-II and RMCI-NSGA-II in Maintenance Optimization
	25.5 Numerical Experiments
		25.5.1 Design of Experiments
		25.5.2 Simulation Results
	25.6 Conclusion
	Acknowledgements
	References
Chapter 26 Which Replacement Maintenance Policy Is Better for Multi-State Systems?: Policy T or Policy N?
	26.1 Introduction
	26.2 Problem Statement and Some Basic Assumptions
	26.3 Reliability Evaluation
	26.4 Optimal Replacement Maintenance Policy
	26.5 An Illustrative Example
	26.6 Concluding Remarks
	References
Chapter 27 Design of Multi-Stress Accelerated Life Testing Plans Based on D-Optimal Experimental Design
	27.1 Introduction
	27.2 Assumptions and Fisher Information Matrix
		27.2.1 The Assumptions
		27.2.2 The Fisher Information Matrix
	27.3 Optimal Design of MALT
		27.3.1 Find Test Points Based on D-Optimal Design
		27.3.2 Unit Allocation
			27.3.2.1 Optimal Designs under V-Optimality
			27.3.2.2 Optimal Designs under D-Optimality
	27.4 Case Study
		27.4.1 Design Matrix Based on D-Optimal Design
		27.4.2 Unit Allocation
			27.4.2.1 Unit Allocation under V-Optimality
			27.4.2.2 Unit Allocation under D-Optimality
	27.5 Conclusions
	Acknowledgement
	References
Chapter 28 An Extended Optimal Replacement Policy for a Simple Repairable Modelling
	28.1 Introduction
	28.2 System Description and Model Assumptions
	28.3 Model Analysis
		28.3.1 Policy (T,N)
		28.3.2 New Policy (T,N)
	28.4 Numerical Cases
		28.4.1 Long-Run ACR Function
		28.4.2 Sensitive Analysis
	28.5 Conclusion
	List of Abbreviations
	References
	Appendix
Index