book

Reliability and Risk Analysis, 2nd Edition

by Mohammad Modarres, Katrina Groth

April 2023

Intermediate to advanced

480 pages

13h 15m

English

CRC Press

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1.1 Why Study Reliability?1.2 History and Evolution of the Field1.3 Reliability Modeling Approaches1.3.1 Physics of Failure Approach1.3.1.1 Performance-Requirement Model1.3.1.2 Stress-Strength Model1.3.1.3 Damage-Endurance Model1.3.2 Failure Agents1.4 Definitions1.4.1 Reliability1.4.2 Risk1.4.3 Availability and Maintainability1.4.4 Failure Modes and Failure Mechanisms1.5 Systems, Functions, and Failure1.5.1 Failure Modes and Mechanisms for Mechanical Equipment1.5.2 Failure Modes and Mechanisms for Electrical Equipment1.5.3 Human Functions, Failure, and Reliability1.6 Putting It All Together: Risk Assessment Modeling1.7 ExercisesReferences

2.1 Introduction2.2 Events and Random Variables Used in Reliability2.3 Sets and Boolean Algebra2.4 Probability Terminology and Interpretations2.4.1 Classical Interpretation of Probability (Equally Likely Concept, or Sample Space Partitioning)2.4.2 Frequency Interpretation of Probability2.4.3 Subjective Interpretation of Probability (Bayesian Probability; Evidential Probability)2.5 Laws and Mathematics of Probability2.5.1 Definitions2.5.2 Axioms of Probability and Their Implications2.5.3 Mathematics of Probability2.6 Probability Distribution Basics2.6.1 Probability Distributions Defined2.6.2 Distribution Properties2.6.2.1 Central Tendency2.6.2.2 Dispersion, Shape, and Spread2.6.2.3 Covariance and Correlation2.6.2.4 Algebra of Expectations2.7 Probability Distributions Used in Reliability2.7.1 Discrete Distributions2.7.1.1 Binomial Distribution2.7.1.2 Poisson Distribution2.7.1.3 Geometric Distribution2.7.2 Continuous Distributions2.7.2.1 Exponential Distribution2.7.2.2 Continuous Uniform Distribution2.7.2.3 Normal Distribution2.7.2.4 Lognormal Distribution2.7.2.5 Weibull Distribution2.7.2.6 Gamma Distribution (and Chi-Squared)2.7.2.7 Beta Distribution2.7.3 Truncated Distributions2.7.4 Multivariate Distributions2.8 ExercisesReferences
3.1 Definitions for Reliability3.1.1 Reliability Function3.1.2 MTTF, MRL, MTBF, and Quantiles3.1.3 Hazard Rate and Failure Rate3.2 Common Distributions in Component Reliability3.2.1 Exponential Distribution and Poisson Distribution3.2.2 Weibull Distribution3.2.3 Gamma Distribution3.2.4 Normal Distribution3.2.5 Lognormal Distribution3.2.6 Beta Distribution3.3 ExercisesReferences
4.1 Introduction4.2 Descriptive Statistics4.3 Empirical Distributions and Histograms4.4 Parameter Estimation: Point Estimation4.4.1 Method of Moments4.4.2 Linear Regression4.4.3 Maximum Likelihood Estimation4.4.4 Bayesian Parameter Estimation4.5 Parameter Estimation: Interval Estimation4.5.1 Confidence Intervals4.5.2 Credible Intervals4.6 Hypothesis Testing and Goodness of Fit4.6.1 Hypothesis Testing Basics4.6.2 Chi-Squared Test4.6.3 Kolmogorov-Smirnov (K-S) Test4.7 Linear Regression4.8 ExercisesReferences
5.1 Context and Types of Data5.1.1 Types of Field and Test Data5.1.2 Complete Data5.1.3 Censored Data5.1.3.1 Left, Right, and Interval Censoring5.1.3.2 Type I Censoring5.1.3.3 Type II Censoring5.2 Reliability Data Sources5.3 Nonparametric and Plotting Methods for Reliability Functions5.3.1 Nonparametric Procedures for Reliability Functions5.3.1.1 Nonparametric Component Reliability Estimation Using Small Samples5.3.1.2 Nonparametric Component Reliability Estimation Using Large Samples5.3.2 Probability Distribution Plotting Using Life Data5.3.2.1 Exponential Distribution Probability Plotting5.3.2.2 Weibull Distribution Probability Plotting5.3.2.3 Normal and Lognormal Distribution Probability Plotting5.4 Maximum Likelihood Estimation of Reliability Distribution Parameters5.4.1 Elements of MLE Using Reliability Data5.4.2 Exponential Distribution MLE Point Estimation5.4.2.1 Type I Life Test with Replacement5.4.2.2 Type I Life Test without Replacement5.4.2.3 Type II Life Test with Replacement5.4.2.4 Type II Life Test without Replacement5.4.3 Exponential Distribution Interval Estimation5.4.4 Normal Distribution5.4.5 Lognormal Distribution5.4.6 Weibull Distribution5.4.7 Binomial Distribution5.5 Classical Nonparametric Distribution Estimation5.5.1 Confidence Intervals for cdf and Reliability Function for Complete and Censored Data5.5.2 Confidence Intervals of Reliability Function for Censored Data5.6 Bayesian Estimation Procedures5.6.1 Estimation of the Parameter of Exponential Distribution5.6.1.1 Selecting Hyperparameters for the Gamma Prior Distribution5.6.1.2 Uniform Prior Distribution5.6.1.3 Jeffrey’s Prior Distribution5.6.2 Bayesian Estimation of the Parameter of Binomial Distribution5.6.2.1 Standard Uniform Prior Distribution5.6.2.2 Beta Prior Distribution5.6.2.3 Jeffrey’s Prior Distribution5.6.2.4 Lognormal Prior Distribution5.6.3 Bayesian Estimation of Other Distributions5.7 ExercisesReferences
6.1 Important Notes and Assumptions6.2 Reliability Block Diagram Method6.2.1 Series System6.2.2 Parallel Systems6.2.3 k-Out-of-n Redundant Systems6.2.4 Standby Systems6.2.5 Load-Sharing Systems6.3 Complex System Evaluation Methods6.3.1 Decomposition Method6.3.2 Path Tracing Methods (Path Sets, Cut Sets)6.4 Fault Tree and Success Tree Methods6.4.1 Fault Tree Method6.4.2 Evaluation of Fault Trees6.4.2.1 Analysis of Logic Trees Using Boolean Algebra6.4.2.2 Combinatorial (Truth Table) Technique for Evaluation of Logic Trees6.4.2.3 Binary Decision Diagrams6.4.3 Success Tree Method6.5 Event Tree Method6.5.1 Construction of Event Trees6.5.2 Evaluation of Event Trees6.6 Event Sequence Diagram Method6.7 Failure Modes and Effects Analysis6.7.1 Objectives of FMEA6.7.2 FMEA/FMECA Procedure6.7.3 FMEA Implementation6.7.3.1 FMEA Using MIL-STD-1629A6.7.3.2 FMEA Using SAE J17396.7.4 FMECA Procedure: Criticality Analysis6.7.4.1 Failure Probability Failure Rate Data Source6.7.4.2 Failure Effect Probability β6.7.4.3 Failure Rate λp6.7.4.4 Failure Mode Ratio α6.7.4.5 Operating Time T6.7.4.6 Failure Mode Criticality Number Cm 6.7.4.7 Item Criticality Number Cr 6.8 ExercisesReferences
7.1 Definition of Repairable System and Types of Repairs7.2 Variables of Interest: Availability, ROCOF, MTBF7.3 Repairable System Data7.4 Stochastic Point Processes (Counting Processes)7.4.1 Homogeneous Poisson Process7.4.2 Renewal Process7.4.3 Nonhomogeneous Poisson Process7.4.4 Generalized Renewal Process7.5 Data Analysis for Point Processes7.5.1 Parameter Estimation for the HPP7.5.2 Data Analysis for the NHPP7.5.2.1 Maximum Likelihood Procedures7.5.2.2 Laplace Test7.6 Availability of Repairable Systems7.6.1 Instantaneous (Point) Availability of Revealed-Fault Items7.6.2 Instantaneous (Point) Availability of Periodically-Tested Items7.6.3 Limiting Point Availability7.6.4 Average Availability7.6.5 Other Average Measures of Availability7.6.5.1 Inherent Availability7.6.5.2 Achieved Availability7.6.5.3 Operational Availability7.7 Markov Processes for System Availability7.8 Availability of Complex Systems7.9 ExercisesReferences
8.1 Uncertainty Analysis8.1.1 Steps in Uncertainty Analysis for Risk and Reliability Models8.1.2 Uncertainty Propagation Methods8.1.2.1 Method of Moments for Propagation of Uncertainties8.1.2.2 Monte Carlo Methods for Propagation of Uncertainties8.2 Analysis of Dependent Failures8.2.1 Single-Parameter Models8.2.2 Multiple-Parameter Models8.2.3 Data Analysis for CCFs8.3 Importance Measures8.3.1 Birnbaum Importance8.3.2 Criticality Importance8.3.3 Fussell-Vesely Importance8.3.4 Risk Reduction Worth Importance8.3.5 Risk Achievement Worth Importance8.4 Human Reliability Analysis8.4.1 The HRA Process8.4.2 Identifying Human Failure Events8.4.2.1 THERP8.4.2.2 SPAR-H8.4.2.3 IDAC and Phoenix8.4.2.4 IDHEAS8.4.3 Representing and Quantifying HFEs8.4.3.1 THERP8.4.3.2 SPAR-H8.4.3.3 IDAC and Phoenix8.4.3.4 IDHEAS8.5 ExercisesReferences
9.1 QRA Defined9.2 QRA Process9.2.1 Initiating Event9.2.2 Hazard Exposure Scenarios9.2.3 Identification of Hazards9.2.4 Identification of Barriers9.2.5 Identification of Challenges to Barriers9.3 PRA Process9.3.1 Objectives and Methodology9.3.2 Familiarization and Information Assembly9.3.3 Identification of Initiating Events9.3.4 Scenario Development9.3.5 Causal Logic Modeling9.3.6 Failure Data Collection, Analysis, and Assessment9.3.7 Consequence Analysis9.3.8 Quantification and Integration9.3.9 Uncertainty Analysis9.3.10 Sensitivity Analysis9.3.11 Risk Ranking and Importance Analysis9.3.12 Interpretation of Results9.4 Strengths of PRA9.5 Example: Simple Fire Protection PRA9.5.1 Objectives and Methodology9.5.2 System Familiarization and Information Assembly9.5.3 Identification of Initiating Events9.5.4 Scenario Development9.5.5 Causal Logic Model Development9.5.6 Failure Data Analysis9.5.7 Quantification and Interpretation9.5.8 Consequences Evaluation9.5.9 Risk Calculation and Interpretation of Results9.6 ExercisesReferences

Content preview from Reliability and Risk Analysis, 2nd Edition

5 Reliability Data Analysis and Model Selection

DOI: 10.1201/9781003307495-5

In Chapter 3, we discussed several common distribution models useful for reliability analysis of items. It is necessary at this point to discuss how field and reliability test data can support the selection and estimation of the parameters of a probability distribution model for reliability analysis. In this chapter, we first describe the types of data used in reliability model development, then we discuss the common procedures for selecting and estimating the model parameters using data and information. These procedures can be divided into two groups: nonparametric methods (that do not need a particular distribution function) and parametric methods (that are based ...

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ISBN: 9781000864137

Reliability and Risk Analysis, 2nd Edition

by Mohammad Modarres, Katrina Groth

5 Reliability Data Analysis and Model Selection

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and much more.