Reliability Engineering

Description

Get a firm handle on the engineering reliability process with this insightful and complete resource The newly and thoroughly revised 3rd Edition of Reliability Engineering delivers a comprehensive and insightful analysis of this crucial field. Accomplished author, professor, and engineer, Elsayed. A. Elsayed includes new examples and end-of-chapter problems to illustrate concepts, new chapters on resilience and the physics of failure, revised chapters on reliability and hazard functions, and more case studies illustrating the approaches and methodologies described within. The book combines analyses of system reliability estimation for time independent and time dependent models with the construction of the likelihood function and its use in estimating the parameters of failure time distribution. It concludes by addressing the physics of failures, mechanical reliability, and system resilience, along with an explanation of how to ensure reliability objectives by providing preventive and scheduled maintenance and warranty policies. This new edition of Reliability Engineering covers a wide range of topics, including: Reliability and hazard functions, like the Weibull Model, the Exponential Model, the Gamma Model, and the Log-Logistic Model, among others System reliability evaluations, including parallel-series, series-parallel, and mixed parallel systems The concepts of time- and failure-dependent reliability within both repairable and non-repairable systems Parametric reliability models, including types of censoring, and the Exponential, Weibull, Lognormal, Gamma, Extreme Value, Half-Logistic, and Rayleigh Distributions Perfect for first-year graduate students in industrial and systems engineering, Reliability Engineering, 3rd Edition also belongs on the bookshelves of practicing professionals in research laboratories and defense industries. The book offers a practical and approachable treatment of a complex area, combining the most crucial foundational knowledge with necessary and advanced topics. Cover Title Page Copyright Page Contents Preface Prelude Chapter 1 Reliability And Hazard Functions 1.1 INTRODUCTION 1.2 RELIABILITY DEFINITION AND ESTIMATION 1.3 HAZARD FUNCTIONS 1.3.1 Constant Hazard 1.3.2 Linearly Increasing Hazard 1.3.3 Linearly Decreasing Hazard 1.3.4 Weibull Model 1.3.5 Mixed Weibull Model 1.3.6 Exponential Model (The Extreme Value Distribution) 1.3.7 Normal Model 1.3.8 Lognormal Model 1.3.9 Gamma Model 1.3.10 Log-Logistic Model 1.3.11 Beta Model 1.3.12 The Inverse Gaussian Model 1.3.13 The Frechet Model 1.3.14 Birnbaum–Saunders Distribution 1.3.15 Other Forms 1.4 MULTIVARIATE HAZARD RATE 1.5 COMPETING RISK MODEL AND MIXTURE OF FAILURE RATES 1.5.1 Competing Risk Model 1.5.2 Mixture of Failure Rates Model 1.6 DISCRETE PROBABILITY DISTRIBUTIONS 1.6.1 Basic Reliability Definition 1.6.2 Geometric Distribution 1.6.3 Binomial Distribution 1.6.4 Poisson Distribution 1.6.5 Hypergeometric Distribution 1.7 MEAN TIME TO FAILURE 1.8 MEAN RESIDUAL LIFE 1.9 TIME OF FIRST FAILURE PROBLEMS REFERENCES Chapter 2 System Reliability Evaluation 2.1 INTRODUCTION 2.2 RELIABILITY BLOCK DIAGRAMS 2.3 SERIES SYSTEMS 2.4 PARALLEL SYSTEMS 2.5 PARALLEL–SERIES, SERIES–PARALLEL, AND MIXED-PARALLEL SYSTEMS 2.5.1 Parallel–Series 2.5.2 Series–Parallel 2.5.3 Mixed-Parallel 2.5.4 Variance of System Reliability Estimate 2.5.5 Optimal Assignments of Units 2.6 CONSECUTIVE-k-OUT-OF-n:F SYSTEM 2.6.1 Consecutive-2-Out-of-n:F System 2.6.2 Generalization of the Consecutive-k-out-of-n:F Systems 2.6.3 Reliability Estimation of the Consecutive-k-Out-of-n:F Systems 2.6.4 Optimal Arrangement of Components in Consecutive-2-Out-of-n:F Systems 2.7 RELIABILITY OF k-OUT-OF-n SYSTEMS 2.8 RELIABILITY OF k-OUT-OF-n BALANCED SYSTEMS 2.9 COMPLEX RELIABILITY SYSTEMS 2.9.1 Decomposition Method 2.9.2 Tie-Set and Cut-Set Methods 2.9.3 Event-Space Method 2.9.4 Boolean Truth Table Method 2.9.5 Reduction Method 2.9.6 Path-Tracing Method 2.9.7 Factoring Algorithm 2.10 SPECIAL NETWORKS 2.11 MULTISTATE MODELS 2.11.1 Series Systems 2.11.2 Parallel Systems 2.11.3 Parallel–Series and Series–Parallel 2.12 REDUNDANCY 2.12.1 Redundancy Allocation for a Series System 2.13 IMPORTANCE MEASURES OF COMPONENTS 2.13.1 Birnbaum's Importance Measure 2.13.2 Criticality Importance 2.13.3 Fussell–Vesely Importance 2.13.4 Barlow–Proschan Importance 2.13.5 Upgrading Function 2.14 WEIGHTED IMPORTANCE MEASURES OF COMPONENTS PROBLEMS REFERENCES Chapter 3 Time- And Failure-Dependent Reliability 3.1 INTRODUCTION 3.2 NONREPAIRABLE SYSTEMS 3.2.1 Series Systems 3.2.2 Parallel Systems 3.2.3 k-out-of-n Systems 3.3 MEAN TIME TO FAILURE 3.3.1 MTTF for Series Systems 3.3.2 MTTF for Parallel Systems 3.3.3 k-out-of-n Systems 3.4 REPAIRABLE SYSTEMS 3.4.1 Alternating Renewal Process 3.4.2 Markov Models 3.5 AVAILABILITY 3.5.1 Instantaneous Point Availability, A(t) 3.5.2 Average Uptime Availability, A(T) 3.5.3 Steady-State Availability, A(∞) 3.5.4 Inherent Availability, Ai 3.5.5 Achieved Availability, Aa 3.5.6 Operational Availability, Ao 3.5.7 Other Availabilities 3.6 DEPENDENT FAILURES 3.6.1 Markov Model for Dependent Failures 3.6.2 Joint Density Function Approach 3.6.3 Compound-Events Approach 3.7 REDUNDANCY AND STANDBY 3.7.1 Nonrepairable Simple Standby Systems 3.7.2 Nonrepairable Multiunit Standby Systems 3.7.3 Repairable Standby Systems PROBLEMS REFERENCES Chapter 4 Estimation Methods Of The Parameters 4.1 INTRODUCTION 4.2 METHOD OF MOMENTS 4.2.1 Confidence Intervals 4.3 THE LIKELIHOOD FUNCTION 4.3.1 The Method of Maximum Likelihood 4.3.2 Exponential Distribution 4.3.3 The Rayleigh Distribution 4.3.4 The Normal Distribution 4.3.5 The Gamma Distribution 4.3.6 Information Matrix and the Variance–Covariance Matrix 4.4 METHOD OF LEAST SQUARES 4.4.1 MLE of the Parameters of the Linear Regression Model 4.5 BAYESIAN APPROACH 4.6 BOOTSTRAP METHOD 4.7 GENERATION OF FAILURE TIME DATA 4.7.1 Exponential Distribution 4.7.2 Weibull Distribution 4.7.3 Rayleigh Distribution 4.7.4 Birnbaum–Saunders Distribution PROBLEMS REFERENCES Chapter 5 Parametric Reliability Models 5.1 INTRODUCTION 5.2 APPROACH 1: HISTORICAL DATA 5.3 APPROACH 2: OPERATIONAL LIFE TESTING 5.4 APPROACH 3: BURN-IN TESTING 5.5 APPROACH 4: ACCELERATED LIFE TESTING 5.6 TYPES OF CENSORING 5.6.1 Type 1 Censoring 5.6.2 Type 2 Censoring 5.6.3 Random Censoring 5.6.4 Hazard-Rate Calculations Under Censoring 5.7 THE EXPONENTIAL DISTRIBUTION 5.7.1 Testing for Abnormally Short Failure Times 5.7.2 Testing for Abnormally Long Failure Times 5.7.3 Data with Type 1 Censoring 5.7.4 Data with Type 2 Censoring 5.7.4.1 Testing the Lives of Units from Different Processes or Manufacturers 5.8 THE RAYLEIGH DISTRIBUTION 5.8.1 Estimation of the Rayleigh Parameter for Data without Censored Observations 5.8.2 Estimation of the Rayleigh Parameter for Data with Censored Observations 5.8.3 Best Linear Unbiased Estimate for the Rayleigh Parameter for Data with and without Censored Observations 5.8.3.1 BLUE for the Rayleigh Parameter 5.8.3.2 Confidence Interval Estimate for θ22 for Noncensored Observations 5.8.3.3 Confidence Interval Estimate for θ22 for Censored Observations 5.9 THE WEIBULL DISTRIBUTION 5.9.1 Failure Data without Censoring 5.9.2 Failure Data with Censoring 5.9.3 Variance of the MLE Estimates 5.9.4 Unbiased Estimate of Ŷ 5.9.5 Confidence Interval for Ŷ 5.9.6 Inferences on θ 5.10 THE LOGNORMAL DISTRIBUTION 5.10.1 Failure Data without Censoring 5.10.2 Failure Data with Censoring 5.11 THE GAMMA DISTRIBUTION 5.11.1 Failure Data without Censoring 5.11.2 Failure Data with Censoring 5.11.3 Variance of γ and θ 5.11.4 Confidence Intervals for γ 5.12 THE EXTREME VALUE DISTRIBUTION 5.13 THE HALF-LOGISTIC DISTRIBUTION 5.14 THE FRECHET DISTRIBUTION 5.14.1 Failure Data without Censoring 5.14.2 Failure Data with Censoring 5.15 THE BIRNBAUM–SAUNDERS DISTRIBUTION 5.15.1 Failure Data without Censoring 5.15.2 Failure Data with Censoring 5.16 LINEAR MODELS 5.17 MULTICENSORED DATA 5.17.1 Product-Limit Estimator or Kaplan–Meier (K–M) Estimator 5.17.2 Cumulative-Hazard Estimator PROBLEMS REFERENCES Chapter 6 Accelerated Life Testing 6.1 INTRODUCTION 6.2 TYPES OF RELIABILITY TESTING 6.2.1 Highly Accelerated Life Testing 6.2.2 Reliability Growth Test 6.2.3 Highly Accelerated Stress Screening 6.2.4 Reliability Demonstration Test 6.2.5 Reliability Acceptance Test 6.2.6 Burn-in Test 6.2.7 Accelerated Life Testing and Accelerated Degradation Testing 6.3 ACCELERATED LIFE TESTING 6.3.1 Stress Loading 6.3.2 Stress Type 6.4 ALT MODELS 6.4.1 Accelerated-Failure-Time Models 6.4.2 Statistic-Based Models: Parametric 6.5 STATISTICS-BASED MODELS: NONPARAMETRIC 6.5.1 The Linear Model 6.5.2 Proportional-Hazards Model 6.5.3 Proportional-Odds Model 6.5.4 Other ALT Models 6.6 PHYSICS-STATISTICS-BASED MODELS 6.6.1 The Arrhenius Model 6.6.2 The Eyring Model 6.6.3 The Inverse Power Rule Model 6.6.4 Combination Model 6.7 PHYSICS-EXPERIMENTAL-BASED MODELS 6.7.1 Electromigration Model 6.7.2 Humidity Dependence Failures 6.7.3 Fatigue Failures 6.8 DEGRADATION MODELS 6.8.1 Resistor Degradation Model 6.8.2 Laser Degradation 6.8.3 Hot Carrier Degradation 6.9 STATISTICAL DEGRADATION MODELS 6.9.1 Degradation Path: Brownian Motion Model 6.9.2 Degradation Path: Gamma Process Model 6.9.3 Degradation Path: Inverse Gaussian Model 6.10 ACCELERATED LIFE TESTING PLANS 6.10.1 Design of ALT Plans 6.10.2 Formulation of the Test Plan 6.10.3 Stress Sequence Loading and Life Prediction PROBLEMS REFERENCES Chapter 7 Physics Of Failures 7.1 INTRODUCTION 7.2 FAULT TREE ANALYSIS 7.2.1 Quantification of Fault Tree Analysis 7.3 FAILURE MODES AND EFFECTS ANALYSIS 7.4 STRESS–STRENGTH RELATIONSHIP 7.5 PoF: FAILURE TIME MODELS 7.5.1 PoF of Electronic Component 7.5.2 PoF of Mechanical Components 7.6 PoF: DEGRADATION MODELS 7.6.1 Corrosion Degradation 7.6.2 Degradation of Nanodiodes PROBLEMS REFERENCES Chapter 8 System Resilience 8.1 INTRODUCTION 8.2 RESILIENCE OVERVIEW 8.3 MULTI-HAZARD 8.3.1 Natural Hazard 8.3.2 Man-Made Hazard 8.3.3 Multi-hazard Modeling 8.4 RESILIENCE MODELING 8.5 RESILIENCE DEFINITIONS AND ATTRIBUTES 8.6 RESILIENCE QUANTIFICATION 8.6.1 Resilience Quantification for Non-repairable Systems 8.6.2 Resilience Quantification for Repairable Systems 8.7 IMPORTANCE MEASURES 8.7.1 IMs for Non-repairable Systems 8.7.2 IMs for Repairable Systems 8.8 CASCADING FAILURES 8.9 CYBER NETWORKS 8.9.1 Cyber Resilience 8.9.2 Resilience and IM Applications in Cyber Network 8.9.3 IM of Nodes in Subnetwork (a) PROBLEMS REFERENCES Chapter 9 Renewal Processes And Expected Number Of Failures 9.1 INTRODUCTION 9.2 PARAMETRIC RENEWAL FUNCTION ESTIMATION 9.2.1 Continuous Time 9.2.2 Discrete Time 9.3 NONPARAMETRIC RENEWAL FUNCTION ESTIMATION 9.3.1 Continuous Time 9.3.2 Discrete Time 9.4 ALTERNATING RENEWAL PROCESS 9.4.1 Expected Number of Failures in an Alternating Renewal Process 9.4.2 Probability That Type j Component Is in Use at Time t 9.5 APPROXIMATIONS OF M(t) 9.6 OTHER TYPES OF RENEWAL PROCESSES 9.7 THE VARIANCE OF THE NUMBER OF RENEWALS 9.8 CONFIDENCE INTERVALS FOR THE RENEWAL FUNCTION 9.9 REMAINING LIFE AT TIME t 9.10 POISSON PROCESSES 9.10.1 Homogeneous Poisson Process 9.10.2 Nonhomogeneous Poisson Process 9.11 LAPLACE TRANSFORM AND RANDOM VARIABLES 9.11.1 Laplace Transform and Expectations 9.11.2 Laplace Transform and Renewals PROBLEMS REFERENCES Chapter 10 Maintenance And Inspection 10.1 INTRODUCTION 10.2 PREVENTIVE MAINTENANCE AND REPLACEMENT MODELS: COST MINIMIZATION 10.2.1 The Constant Interval Replacement Policy 10.2.2 Replacement at Predetermined Age 10.3 PREVENTIVE MAINTENANCE AND REPLACEMENT MODELS: DOWNTIME MINIMIZATION 10.3.1 The Constant Interval Replacement Policy 10.3.2 Preventive Replacement at Predetermined Age 10.4 MINIMAL REPAIR MODELS 10.4.1 Optimal Replacement under Minimal Repair 10.5 OPTIMUM REPLACEMENT INTERVALS FOR SYSTEMS SUBJECT TO SHOCKS 10.5.1 Periodic Replacement Policy: Time-Independent Cost 10.5.2 Periodic Replacement Policy: Time-Dependent Cost 10.6 PREVENTIVE MAINTENANCE AND NUMBER OF SPARES 10.6.1 Number of Spares and Availability 10.7 GROUP MAINTENANCE 10.8 PERIODIC INSPECTION 10.8.1 An Optimum Inspection Policy 10.8.2 Periodic Inspection and Maintenance 10.9 CONDITION-BASED MAINTENANCE 10.10 ON-LINE SURVEILLANCE AND MONITORING PROBLEMS REFERENCES Chapter 11 Warranty Models 11.1 INTRODUCTION 11.2 WARRANTY MODELS FOR NONREPAIRABLE PRODUCTS 11.2.1 Warranty Cost for Nonrepairable Products 11.2.2 Warranty Reserve Fund: Lump Sum Rebate 11.2.3 Mixed Warranty Policies 11.2.4 Optimal Replacements for Items Under Warranty 11.3 WARRANTY MODELS FOR REPAIRABLE PRODUCTS 11.3.1 Warranty Cost for Repairable Products 11.3.2 Warranty Models for a Fixed Lot Size Arbitrary Failure-Time Distribution 11.3.3 Warranty Models for a Fixed Lot Size: Minimal Repair Policy 11.3.4 Warranty Models for a Fixed Lot Size: Good-as-New Repair Policy 11.3.5 Warranty Models for a Fixed Lot Size: Mixed Repair Policy 11.4 TWO-DIMENSIONAL WARRANTY 11.5 WARRANTY CLAIMS 11.5.1 Warranty Claims with Lag Times 11.5.2 Warranty Claims for Grouped Data PROBLEMS REFERENCES Chapter 12 Case Studies 12.1 CASE 1: A CRANE SPREADER SUBSYSTEMBased on actual operation of a major shipping company. 12.1.1 Introduction 12.1.2 Statement of the Problem 12.1.3 Solution 12.2 CASE 2: DESIGN OF A PRODUCTION LINEBased on an actual production line initiated by the Defense Logistics Agency and th... 12.2.1 Introduction 12.2.2 Statement of the Problem 12.2.3 Solution 12.3 CASE 3: AN EXPLOSIVE DETECTION SYSTEMThis system was developed by SCAN-TECH Security L.P., Northvale, New Jersey. 12.3.1 Introduction 12.3.2 Statement of the Problem 12.3.3 Solution 12.4 CASE 4: RELIABILITY OF FURNACE TUBESA partial description of this case was reprinted with permission. 1995. Syncrude,... 12.4.1 Introduction 12.4.2 Statement of the Problem 12.4.3 Solution 12.5 CASE 5: RELIABILITY OF SMART CARDSThis case is contributed by Loon Ching Tang of The National University of Singapore. 12.5.1 Introduction 12.5.2 Statement of the Problem 12.5.3 Solution 12.6 CASE 6: LIFE DISTRIBUTION OF SURVIVORS OF QUALIFICATION AND CERTIFICATION* 12.6.1 Introduction 12.6.2 Background 12.6.3 Qualification as a Decision Process 12.6.4 Certification as a Decision Process 12.7 CASE 7: RELIABILITY MODELING OF TELECOMMUNICATION NETWORKS FOR THE AIR TRAFFIC CONTROL SYSTEM 12.7.1 Introduction 12.7.2 Statement of the Problem 12.7.3 Solution 12.8 CASE 8: SYSTEM DESIGN USING RELIABILITY OBJECTIVES* 12.8.1 Introduction 12.8.2 Availability Design Objectives 12.8.3 Availability Service Performance 12.8.4 Evaluation of Availability Design Objectives 12.9 CASE 9: RELIABILITY MODELING OF HYDRAULIC FRACTURE PUMPS* 12.9.1 Introduction 12.9.2 Pump Engine 12.9.3 Statement of the Problem 12.9.4 Solution 12.10 CASE 10: AVAILABILITY OF MEDICAL INFORMATION TECHNOLOGY SYSTEM 12.10.1 Introduction 12.10.2 Statement of the Problem 12.10.3 Approach 12.11 CASE 11: PRODUCER AND CONSUMER RISK IN SYSTEM OF SYSTEMS 12.11.1 Introduction REFERENCES APPENDIX A Gamma Table APPENDIX B Computer Program To Calculate The Reliability Of A Consecutive-k-Out-Of-n:f System APPENDIX C Optimum Arrangement Of Components In Consecutive-2-Out-Of-N:f Systems APPENDIX D Computer Program For Solving The Time-Dependent Equations APPENDIX E The Newton–Raphson Method APPENDIX F Coefficients Of bi's For i=1, ..., n* APPENDIX G Variance Of θ*2's In Terms Of θ22/nANDK3/K*2* APPENDIX H Computer Listing Of The Newton–Raphson Method APPENDIX I Coefficients (ai And bi) Of The Best Estimates Of The Mean (μ) And Standard Deviation (σ) In Censored Samples Up To n=20 From a Normal Population* APPENDIX J Baker's Algorithm* APPENDIX K Standard Normal Distribution* Normal Distribution and Related Functions APPENDIX L Critical Values Of χ2* APPENDIX M Solutions Of Selected Problems CHAPTER 1 CHAPTER 2 CHAPTER 3 CHAPTER 4 CHAPTER 5 CHAPTER 6 CHAPTER 9 CHAPTER 10 CHAPTER 11 Author Index Subject Index EULA