Reliability and Risk Analysis (What Every Engineer Should Know)

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Table of Contents
Preface to the Second Edition
Authors
Chapter 1 Reliability Engineering Perspective and Fundamentals
	1.1 Why Study Reliability?
	1.2 History and Evolution of the Field
	1.3 Reliability Modeling Approaches
		1.3.1 Physics of Failure Approach
			1.3.1.1 Performance-Requirement Model
			1.3.1.2 Stress-Strength Model
			1.3.1.3 Damage-Endurance Model
		1.3.2 Failure Agents
	1.4 Definitions
		1.4.1 Reliability
		1.4.2 Risk
		1.4.3 Availability and Maintainability
		1.4.4 Failure Modes and Failure Mechanisms
	1.5 Systems, Functions, and Failure
		1.5.1 Failure Modes and Mechanisms for Mechanical Equipment
		1.5.2 Failure Modes and Mechanisms for Electrical Equipment
		1.5.3 Human Functions, Failure, and Reliability
	1.6 Putting It All Together: Risk Assessment Modeling
	1.7 Exercises
	References
Chapter 2 Basic Reliability Mathematics: Probability
	2.1 Introduction
	2.2 Events and Random Variables Used in Reliability
	2.3 Sets and Boolean Algebra
	2.4 Probability Terminology and Interpretations
		2.4.1 Classical Interpretation of Probability (Equally Likely Concept, or Sample Space Partitioning)
		2.4.2 Frequency Interpretation of Probability
		2.4.3 Subjective Interpretation of Probability (Bayesian Probability; Evidential Probability)
	2.5 Laws and Mathematics of Probability
		2.5.1 Definitions
		2.5.2 Axioms of Probability and Their Implications
		2.5.3 Mathematics of Probability
	2.6 Probability Distribution Basics
		2.6.1 Probability Distributions Defined
		2.6.2 Distribution Properties
			2.6.2.1 Central Tendency
			2.6.2.2 Dispersion, Shape, and Spread
			2.6.2.3 Covariance and Correlation
			2.6.2.4 Algebra of Expectations
	2.7 Probability Distributions Used in Reliability
		2.7.1 Discrete Distributions
			2.7.1.1 Binomial Distribution
			2.7.1.2 Poisson Distribution
			2.7.1.3 Geometric Distribution
		2.7.2 Continuous Distributions
			2.7.2.1 Exponential Distribution
			2.7.2.2 Continuous Uniform Distribution
			2.7.2.3 Normal Distribution
			2.7.2.4 Lognormal Distribution
			2.7.2.5 Weibull Distribution
			2.7.2.6 Gamma Distribution (and Chi-Squared)
			2.7.2.7 Beta Distribution
		2.7.3 Truncated Distributions
		2.7.4 Multivariate Distributions
	2.8 Exercises
	References
Chapter 3 Elements of Component Reliability
	3.1 Definitions for Reliability
		3.1.1 Reliability Function
		3.1.2 MTTF, MRL, MTBF, and Quantiles
		3.1.3 Hazard Rate and Failure Rate
	3.2 Common Distributions in Component Reliability
		3.2.1 Exponential Distribution and Poisson Distribution
		3.2.2 Weibull Distribution
		3.2.3 Gamma Distribution
		3.2.4 Normal Distribution
		3.2.5 Lognormal Distribution
		3.2.6 Beta Distribution
	3.3 Exercises
	References
Chapter 4 Basic Reliability Mathematics: Statistics
	4.1 Introduction
	4.2 Descriptive Statistics
	4.3 Empirical Distributions and Histograms
	4.4 Parameter Estimation: Point Estimation
		4.4.1 Method of Moments
		4.4.2 Linear Regression
		4.4.3 Maximum Likelihood Estimation
		4.4.4 Bayesian Parameter Estimation
	4.5 Parameter Estimation: Interval Estimation
		4.5.1 Confidence Intervals
		4.5.2 Credible Intervals
	4.6 Hypothesis Testing and Goodness of Fit
		4.6.1 Hypothesis Testing Basics
		4.6.2 Chi-Squared Test
		4.6.3 Kolmogorov-Smirnov (K-S) Test
	4.7 Linear Regression
	4.8 Exercises
	References
Chapter 5 Reliability Data Analysis and Model Selection
	5.1 Context and Types of Data
		5.1.1 Types of Field and Test Data
		5.1.2 Complete Data
		5.1.3 Censored Data
			5.1.3.1 Left, Right, and Interval Censoring
			5.1.3.2 Type I Censoring
			5.1.3.3 Type II Censoring
	5.2 Reliability Data Sources
	5.3 Nonparametric and Plotting Methods for Reliability Functions
		5.3.1 Nonparametric Procedures for Reliability Functions
			5.3.1.1 Nonparametric Component Reliability Estimation Using Small Samples
			5.3.1.2 Nonparametric Component Reliability Estimation Using Large Samples
		5.3.2 Probability Distribution Plotting Using Life Data
			5.3.2.1 Exponential Distribution Probability Plotting
			5.3.2.2 Weibull Distribution Probability Plotting
			5.3.2.3 Normal and Lognormal Distribution Probability Plotting
	5.4 Maximum Likelihood Estimation of Reliability Distribution Parameters
		5.4.1 Elements of MLE Using Reliability Data
		5.4.2 Exponential Distribution MLE Point Estimation
			5.4.2.1 Type I Life Test with Replacement
			5.4.2.2 Type I Life Test without Replacement
			5.4.2.3 Type II Life Test with Replacement
			5.4.2.4 Type II Life Test without Replacement
		5.4.3 Exponential Distribution Interval Estimation
		5.4.4 Normal Distribution
		5.4.5 Lognormal Distribution
		5.4.6 Weibull Distribution
		5.4.7 Binomial Distribution
	5.5 Classical Nonparametric Distribution Estimation
		5.5.1 Confidence Intervals for cdf and Reliability
Function for Complete and Censored Data
		5.5.2 Confidence Intervals of Reliability Function for
Censored Data
	5.6 Bayesian Estimation Procedures
		5.6.1 Estimation of the Parameter of Exponential Distribution
			5.6.1.1 Selecting Hyperparameters for the Gamma Prior Distribution
			5.6.1.2 Uniform Prior Distribution
			5.6.1.3 Jeffrey’s Prior Distribution
		5.6.2 Bayesian Estimation of the Parameter of Binomial Distribution
			5.6.2.1 Standard Uniform Prior Distribution
			5.6.2.2 Beta Prior Distribution
			5.6.2.3 Jeffrey’s Prior Distribution
			5.6.2.4 Lognormal Prior Distribution
		5.6.3 Bayesian Estimation of Other Distributions
	5.7 Exercises
	References
Chapter 6 System Reliability Analysis
	6.1 Important Notes and Assumptions
	6.2 Reliability Block Diagram Method
		6.2.1 Series System
		6.2.2 Parallel Systems
		6.2.3 k-Out-of-n Redundant Systems
		6.2.4 Standby Systems
		6.2.5 Load-Sharing Systems
	6.3 Complex System Evaluation Methods
		6.3.1 Decomposition Method
		6.3.2 Path Tracing Methods (Path Sets, Cut Sets)
	6.4 Fault Tree and Success Tree Methods
		6.4.1 Fault Tree Method
		6.4.2 Evaluation of Fault Trees
			6.4.2.1 Analysis of Logic Trees Using Boolean Algebra
			6.4.2.2 Combinatorial (Truth Table) Technique for Evaluation of Logic Trees
			6.4.2.3 Binary Decision Diagrams
		6.4.3 Success Tree Method
	6.5 Event Tree Method
		6.5.1 Construction of Event Trees
		6.5.2 Evaluation of Event Trees
	6.6 Event Sequence Diagram Method
	6.7 Failure Modes and Effects Analysis
		6.7.1 Objectives of FMEA
		6.7.2 FMEA/FMECA Procedure
		6.7.3 FMEA Implementation
			6.7.3.1 FMEA Using MIL-STD-1629A
			6.7.3.2 FMEA Using SAE J1739
		6.7.4 FMECA Procedure: Criticality Analysis
			6.7.4.1 Failure Probability Failure Rate Data Source
			6.7.4.2 Failure Effect Probability β
			6.7.4.3 Failure Rate λ[sub(p)]
			6.7.4.4 Failure Mode Ratio α
			6.7.4.5 Operating Time T
			6.7.4.6 Failure Mode Criticality Number C[sub(m)]
			6.7.4.7 Item Criticality Number C[sub(r)]
	6.8 Exercises
	References
Chapter 7 Reliability and Availability of Repairable Components and Systems
	7.1 Definition of Repairable System and Types of Repairs
	7.2 Variables of Interest: Availability, ROCOF, MTBF
	7.3 Repairable System Data
	7.4 Stochastic Point Processes (Counting Processes)
		7.4.1 Homogeneous Poisson Process
		7.4.2 Renewal Process
		7.4.3 Nonhomogeneous Poisson Process
		7.4.4 Generalized Renewal Process
	7.5 Data Analysis for Point Processes
		7.5.1 Parameter Estimation for the HPP
		7.5.2 Data Analysis for the NHPP
			7.5.2.1 Maximum Likelihood Procedures
			7.5.2.2 Laplace Test
	7.6 Availability of Repairable Systems
		7.6.1 Instantaneous (Point) Availability of Revealed-Fault Items
		7.6.2 Instantaneous (Point) Availability of Periodically-Tested Items
		7.6.3 Limiting Point Availability
		7.6.4 Average Availability
		7.6.5 Other Average Measures of Availability
			7.6.5.1 Inherent Availability
			7.6.5.2 Achieved Availability
			7.6.5.3 Operational Availability
	7.7 Markov Processes for System Availability
	7.8 Availability of Complex Systems
	7.9 Exercises
	References
Chapter 8 Selected Advanced Topics in Reliability and Risk Analysis
	8.1 Uncertainty Analysis
		8.1.1 Steps in Uncertainty Analysis for Risk and Reliability Models
		8.1.2 Uncertainty Propagation Methods
			8.1.2.1 Method of Moments for Propagation of Uncertainties
			8.1.2.2 Monte Carlo Methods for Propagation of Uncertainties
	8.2 Analysis of Dependent Failures
		8.2.1 Single-Parameter Models
		8.2.2 Multiple-Parameter Models
		8.2.3 Data Analysis for CCFs
	8.3 Importance Measures
		8.3.1 Birnbaum Importance
		8.3.2 Criticality Importance
		8.3.3 Fussell-Vesely Importance
		8.3.4 Risk Reduction Worth Importance
		8.3.5 Risk Achievement Worth Importance
	8.4 Human Reliability Analysis
		8.4.1 The HRA Process
		8.4.2 Identifying Human Failure Events
			8.4.2.1 THERP
			8.4.2.2 SPAR-H
			8.4.2.3 IDAC and Phoenix
			8.4.2.4 IDHEAS
		8.4.3 Representing and Quantifying HFEs
			8.4.3.1 THERP
			8.4.3.2 SPAR-H
			8.4.3.3 IDAC and Phoenix
			8.4.3.4 IDHEAS
	8.5 Exercises
	References
Chapter 9 Risk Analysis
	9.1 QRA Defined
	9.2 QRA Process
		9.2.1 Initiating Event
		9.2.2 Hazard Exposure Scenarios
		9.2.3 Identification of Hazards
		9.2.4 Identification of Barriers
		9.2.5 Identification of Challenges to Barriers
	9.3 PRA Process
		9.3.1 Objectives and Methodology
		9.3.2 Familiarization and Information Assembly
		9.3.3 Identification of Initiating Events
		9.3.4 Scenario Development
		9.3.5 Causal Logic Modeling
		9.3.6 Failure Data Collection, Analysis, and Assessment
		9.3.7 Consequence Analysis
		9.3.8 Quantification and Integration
		9.3.9 Uncertainty Analysis
		9.3.10 Sensitivity Analysis
		9.3.11 Risk Ranking and Importance Analysis
		9.3.12 Interpretation of Results
	9.4 Strengths of PRA
	9.5 Example: Simple Fire Protection PRA
		9.5.1 Objectives and Methodology
		9.5.2 System Familiarization and Information Assembly
		9.5.3 Identification of Initiating Events
		9.5.4 Scenario Development
		9.5.5 Causal Logic Model Development
		9.5.6 Failure Data Analysis
		9.5.7 Quantification and Interpretation
		9.5.8 Consequences Evaluation
		9.5.9 Risk Calculation and Interpretation of Results
	9.6 Exercises
	References
Appendix A: Statistical Tables
Appendix B: Generic Failure Data
Index