KAILASH C. KAPUR, PHD, is a Professor of Industrial & Systems Engineering at the University of Washington, where he was also the Director from 1993 to 1999. Dr. Kapur has worked with General Motors Research Laboratories as a senior research engineer, Ford Motor Company as a visiting scholar, and the U.S. Army, Tank-Automotive Command as a reliability engineer. He is a Fellow of ASQ and IIE, and a registered professional engineer.MICHAEL G. PECHT, PHD, is the founder of CALCE (Center for Advanced Life Cycle Engineering) at the University of Maryland, which is funded by over 150 of the world’s leading electronics companies. He is also a Chair Professor in Mechanical Engineering and a Professor in Applied Mathematics at the University of Maryland. He consults for twenty-two major international electronics companies.

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• Preface xv1 Reliability Engineering in the Twenty-First Century 11.1 What Is Quality? 11.2 What Is Reliability? 21.2.1 The Ability to Perform as Intended 41.2.2 For a Specified Time 41.2.3 Life-Cycle Conditions 51.2.4 Reliability as a Relative Measure 51.3 Quality, Customer Satisfaction, and System Effectiveness 61.4 Performance, Quality, and Reliability 71.5 Reliability and the System Life Cycle 81.6 Consequences of Failure 121.6.1 Financial Loss 121.6.2 Breach of Public Trust 131.6.3 Legal Liability 151.6.4 Intangible Losses 151.7 Suppliers and Customers 161.8 Summary 16Problems 172 Reliability Concepts 192.1 Basic Reliability Concepts 192.1.1 Concept of Probability Density Function 232.2 Hazard Rate 262.2.1 Motivation and Development of Hazard Rate 272.2.2 Some Properties of the Hazard Function 282.2.3 Conditional Reliability 312.3 Percentiles Product Life 332.4 Moments of Time to Failure 352.4.1 Moments about Origin and about the Mean 352.4.2 Expected Life or Mean Time to Failure 362.4.3 Variance or the Second Moment about the Mean 362.4.4 Coefficient of Skewness 372.4.5 Coefficient of Kurtosis 372.5 Summary 39Problems 403 Probability and Life Distributions for Reliability Analysis 453.1 Discrete Distributions 453.1.1 Binomial Distribution 463.1.2 Poisson Distribution 503.1.3 Other Discrete Distributions 503.2 Continuous Distributions 513.2.1 Weibull Distribution 553.2.2 Exponential Distribution 613.2.3 Estimation of Reliability for Exponential Distribution 643.2.4 The Normal (Gaussian) Distribution 673.2.5 The Lognormal Distribution 733.2.6 Gamma Distribution753.3 Probability Plots 773.4 Summary 83Problems 844 Design for Six Sigma 894.1 What Is Six Sigma? 894.2 Why Six Sigma? 904.3 How Is Six Sigma Implemented? 914.3.1 Steps in the Six Sigma Process 924.3.2 Summary of the Six Sigma Steps 974.4 Optimization Problems in the Six Sigma Process 984.4.1 System Transfer Function 994.4.2 Variance Transmission Equation 1004.4.3 Economic Optimization and Quality Improvement 1014.4.4 Tolerance Design Problem 1024.5 Design for Six Sigma 1034.5.1 Identify (I) 1054.5.2 Characterize (C) 1064.5.3 Optimize (O) 1064.5.4 Verify (V) 1064.6 Summary 108Problems 1085 Product Development 1115.1 Product Requirements and Constraints 1125.2 Product Life Cycle Conditions 1135.3 Reliability Capability 1145.4 Parts and Materials Selection 1145.5 Human Factors and Reliability 1155.6 Deductive versus Inductive Methods 1175.7 Failure Modes, Effects, and Criticality Analysis 1175.8 Fault Tree Analysis 1195.8.1 Role of FTA in Decision-Making 1215.8.2 Steps of Fault Tree Analysis 1225.8.3 Basic Paradigms for the Construction of Fault Trees 1225.8.4 Definition of the Top Event 1225.8.5 Faults versus Failures 1225.8.6 Minimal Cut Sets 1275.9 Physics of Failure 1285.9.1 Stress Margins 1285.9.2 Model Analysis of Failure Mechanisms 1295.9.3 Derating 1295.9.4 Protective Architectures 1305.9.5 Redundancy 1315.9.6 Prognostics 1315.10 Design Review 1315.11 Qualification 1325.12 Manufacture and Assembly 1345.12.1 Manufacturability 1345.12.2 Process Verification Testing 1365.13 Analysis, Product Failure, and Root Causes 1375.14 Summary 138Problems 1386 Product Requirements and Constraints 1416.1 Defining Requirements 1416.2 Responsibilities of the Supply Chain 1426.2.1 Multiple-Customer Products 1426.2.2 Single-Customer Products 1436.2.3 Custom Products 1446.3 The Requirements Document 1446.4 Specifications 1446.5 Requirements Tracking 1466.6 Summary 147Problems 1477 Life-Cycle Conditions 1497.1 Defining the Life-Cycle Profile 1497.2 Life-Cycle Events 1507.2.1 Manufacturing and Assembly 1517.2.2 Testing and Screening 1517.2.3 Storage 1517.2.4 Transportation 1517.2.5 Installation 1517.2.6 Operation 1527.2.7 Maintenance 1527.3 Loads and Their Effects 1527.3.1 Temperature 1527.3.2 Humidity 1557.3.3 Vibration and Shock 1567.3.4 Solar Radiation 1567.3.5 Electromagnetic Radiation 1577.3.6 Pressure 1577.3.7 Chemicals 1587.3.8 Sand and Dust 1597.3.9 Voltage 1597.3.10 Current 1597.3.11 Human Factors 1607.4 Considerations and Recommendations for LCP Development 1607.4.1 Extreme Specifications-Based Design (Global and Local Environments) 1607.4.2 Standards-Based Profiles 1617.4.3 Combined Load Conditions 1617.4.4 Change in Magnitude and Rate of Change of Magnitude 1657.5 Methods for Estimating Life-Cycle Loads 1657.5.1 Market Studies and Standards Based Profiles as Sources of Data 1657.5.2 In Situ Monitoring of Load Conditions 1667.5.3 Field Trial Records, Service Records, and Failure Records 1667.5.4 Data on Load Histories of Similar Parts, Assemblies, or Products 1667.6 Summary 166Problems 1678 Reliability Capability 1698.1 Capability Maturity Models 1698.2 Key Reliability Practices 1708.2.1 Reliability Requirements and Planning 1708.2.2 Training and Development 1718.2.3 Reliability Analysis 1728.2.4 Reliability Testing 1728.2.5 Supply-Chain Management 1738.2.6 Failure Data Tracking and Analysis 1738.2.7 Verification and Validation 1748.2.8 Reliability Improvement 1748.3 Summary 175Problems 1759 Parts Selection and Management 1779.1 Part Assessment Process 1779.1.1 Performance Assessment 1789.1.2 Quality Assessment 1799.1.3 Process Capability Index 1799.1.4 Average Outgoing Quality 1829.1.5 Reliability Assessment 1829.1.6 Assembly Assessment 1859.2 Parts Management 1859.2.1 Supply Chain Management 1859.2.2 Part Change Management 1869.2.3 Industry Change Control Policies 1879.3 Risk Management 1889.4 Summary 190Problems 19110 Failure Modes, Mechanisms, and Effects Analysis 19310.1 Development of FMMEA 19310.2 Failure Modes, Mechanisms, and Effects Analysis 19510.2.1 System Definition, Elements, and Functions 19510.2.2 Potential Failure Modes 19610.2.3 Potential Failure Causes 19710.2.4 Potential Failure Mechanisms 19710.2.5 Failure Models 19710.2.6 Life-Cycle Profile 19810.2.7 Failure Mechanism Prioritization 19810.2.8 Documentation 20010.3 Case Study 20110.4 Summary 205Problems 20611 Probabilistic Design for Reliability and the Factor of Safety 20711.1 Design for Reliability 20711.2 Design of a Tension Element 20811.3 Reliability Models for Probabilistic Design 20911.4 Example of Probabilistic Design and Design for a Reliability Target 21111.5 Relationship between Reliability, Factor of Safety, and Variability 21211.6 Functions of Random Variables 21511.7 Steps for Probabilistic Design 21911.8 Summary 219Problems 22012 Derating and Uprating 22312.1 Part Ratings 22312.1.1 Absolute Maximum Ratings 22412.1.2 Recommended Operating Conditions 22412.1.3 Factors Used to Determine Ratings 22512.2 Derating 22512.2.1 How Is Derating Practiced? 22512.2.2 Limitations of the Derating Methodology 23112.2.3 How to Determine These Limits 23812.3 Uprating 23912.3.1 Parts Selection and Management Process 24112.3.2 Assessment for Uprateability 24112.3.3 Methods of Uprating 24212.3.4 Continued Assurance 24512.4 Summary 245Problems 24613 Reliability Estimation Techniques 24713.1 Tests during the Product Life Cycle 24713.1.1 Concept Design and Prototype 24713.1.2 Performance Validation to Design Specification 24813.1.3 Design Maturity Validation 24813.1.4 Design and Manufacturing Process Validation 24813.1.5 Preproduction Low Volume Manufacturing 24813.1.6 High Volume Production 24913.1.7 Feedback from Field Data 24913.2 Reliability Estimation 24913.3 Product Qualification and Testing 25013.3.1 Input to PoF Qualification Methodology 25013.3.2 Accelerated Stress Test Planning and Development 25513.3.3 Specimen Characterization 25713.3.4 Accelerated Life Tests 25913.3.5 Virtual Testing 26013.3.6 Virtual Qualification 26113.3.7 Output 26213.4 Case Study: System-in-Package Drop Test Qualification 26313.4.1 Step 1: Accelerated Test Planning and Development 26313.4.2 Step 2: Specimen Characterization 26513.4.3 Step 3: Accelerated Life Testing 26613.4.4 Step 4: Virtual Testing 27013.4.5 Global FEA 27113.4.6 Strain Distributions Due to Modal Contributions 27213.4.7 Acceleration Curves 27313.4.8 Local FEA 27313.4.9 Step 5: Virtual Qualification 27413.4.10 PoF Acceleration Curves 27513.4.11 Summary of the Methodology for Qualification 27613.5 Basic Statistical Concepts 27613.5.1 Confidence Interval 27713.5.2 Interpretation of the Confidence Level 27713.5.3 Relationship between Confidence Interval and Sample Size 27913.6 Confidence Interval for Normal Distribution 27913.6.1 Unknown Mean with a Known Variance for Normal Distribution 27913.6.2 Unknown Mean with an Unknown Variance for Normal Distribution 28013.6.3 Differences in Two Population Means with Variances Known 28113.7 Confidence Intervals for Proportions 28213.8 Reliability Estimation and Confidence Limits for Success–Failure Testing 28313.8.1 Success Testing 28613.9 Reliability Estimation and Confidence Limits for Exponential Distribution 28713.10 Summary 292Problems 29214 Process Control and Process Capability 29514.1 Process Control System 29514.1.1 Control Charts: Recognizing Sources of Variation 29714.1.2 Sources of Variation 29714.1.3 Use of Control Charts for Problem Identification 29714.2 Control Charts 29914.2.1 Control Charts for Variables 30614.2.2 X-Bar and R Charts 30614.2.3 Moving Range Chart Example 30814.2.4 X-Bar and S Charts 31114.2.5 Control Charts for Attributes 31214.2.6 p Chart and np Chart 31214.2.7 np Chart Example 31314.2.8 c Chart and u Chart 31414.2.9 c Chart Example 31514.3 Benefits of Control Charts 31614.4 Average Outgoing Quality 31714.4.1 Process Capability Studies 31814.5 Advanced Control Charts 32314.5.1 Cumulative Sum Control Charts 32314.5.2 Exponentially Weighted Moving Average Control Charts 32414.5.3 Other Advanced Control Charts 32514.6 Summary 325Problems 32615 Product Screening and Burn-In Strategies 33115.1 Burn-In Data Observations 33215.2 Discussion of Burn-In Data 33315.3 Higher Field Reliability without Screening 33415.4 Best Practices 33515.5 Summary 336Problems 33716 Analyzing Product Failures and Root Causes 33916.1 Root-Cause Analysis Processes 34116.1.1 Preplanning 34116.1.2 Collecting Data for Analysis and Assessing Immediate Causes 34316.1.3 Root-Cause Hypothesization 34416.1.4 Analysis and Interpretation of Evidence 34816.1.5 Root-Cause Identification and Corrective Actions 34816.1.6 Assessment of Corrective Actions 35016.2 No-Fault-Found 35116.2.1 An Approach to Assess NFF 35316.2.2 Common Mode Failure 35516.2.3 Concept of Common Mode Failure 35616.2.4 Modeling and Analysis for Dependencies for Reliability Analysis 36016.2.5 Common Mode Failure Root Causes 36216.2.6 Common Mode Failure Analysis 36416.2.7 Common Mode Failure Occurrence and Impact Reduction 36616.3 Summary 373Problems 37417 System Reliability Modeling 37517.1 Reliability Block Diagram 37517.2 Series System 37617.3 Products with Redundancy 38117.3.1 Active Redundancy 38117.3.2 Standby Systems 38517.3.3 Standby Systems with Imperfect Switching 38717.3.4 Shared Load Parallel Models 39017.3.5 (k, n) Systems 39117.3.6 Limits of Redundancy 39317.4 Complex System Reliability 39317.4.1 Complete Enumeration Method 39317.4.2 Conditional Probability Method 39517.4.3 Concept of Coherent Structures 39617.5 Summary 401Problems 40218 Health Monitoring and Prognostics 40918.1 Conceptual Model for Prognostics 41018.2 Reliability and Prognostics 41218.3 PHM for Electronics 41418.4 PHM Concepts and Methods 41718.4.1 Fuses and Canaries 41818.5 Monitoring and Reasoning of Failure Precursors 42018.5.1 Monitoring Environmental and Usage Profiles for Damage Modeling 42418.6 Implementation of PHM in a System of Systems 42918.7 Summary 431Problems 43119 Warranty Analysis 43319.1 Product Warranties 43419.2 Warranty Return Information 43519.3 Warranty Policies 43619.4 Warranty and Reliability 43719.5 Warranty Cost Analysis 43919.5.1 Elements of Warranty Cost Models 44019.5.2 Failure Distributions 44019.5.3 Cost Modeling Calculation 44019.5.4 Modeling Assumptions and Notation 44119.5.5 Cost Models Examples 44219.5.6 Information Needs 44419.5.7 Other Cost Models 44619.6 Warranty and Reliability Management 44819.7 Summary 449Problems 449Appendix A: Some Useful Integrals 451Appendix B: Table for Gamma Function 453Appendix C: Table for Cumulative Standard Normal Distribution 455Appendix D: Values for the Percentage Points tα,ν of the t-Distribution 457Appendix E: Percentage Points χ2α,ν of the Chi-Square Distribution 461Appendix F: Percentage Points for the F-Distribution 467Bibliography 473Index 487

KAILASH C. KAPUR, PHD, is a Professor of Industrial & Systems Engineering at the University of Washington, where he was also the Director from 1993 to 1999. Dr. Kapur has worked with General Motors Research Laboratories as a senior research engineer, Ford Motor Company as a visiting scholar, and the U.S. Army, Tank-Automotive Command as a reliability engineer. He is a Fellow of ASQ and IIE, and a registered professional engineer.MICHAEL G. PECHT, PHD, is the founder of CALCE (Center for Advanced Life Cycle Engineering) at the University of Maryland, which is funded by over 150 of the world’s leading electronics companies. He is also a Chair Professor in Mechanical Engineering and a Professor in Applied Mathematics at the University of Maryland. He consults for twenty-two major international electronics companies.

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• Preface xv1 Reliability Engineering in the Twenty-First Century 11.1 What Is Quality? 11.2 What Is Reliability? 21.2.1 The Ability to Perform as Intended 41.2.2 For a Specified Time 41.2.3 Life-Cycle Conditions 51.2.4 Reliability as a Relative Measure 51.3 Quality, Customer Satisfaction, and System Effectiveness 61.4 Performance, Quality, and Reliability 71.5 Reliability and the System Life Cycle 81.6 Consequences of Failure 121.6.1 Financial Loss 121.6.2 Breach of Public Trust 131.6.3 Legal Liability 151.6.4 Intangible Losses 151.7 Suppliers and Customers 161.8 Summary 16Problems 172 Reliability Concepts 192.1 Basic Reliability Concepts 192.1.1 Concept of Probability Density Function 232.2 Hazard Rate 262.2.1 Motivation and Development of Hazard Rate 272.2.2 Some Properties of the Hazard Function 282.2.3 Conditional Reliability 312.3 Percentiles Product Life 332.4 Moments of Time to Failure 352.4.1 Moments about Origin and about the Mean 352.4.2 Expected Life or Mean Time to Failure 362.4.3 Variance or the Second Moment about the Mean 362.4.4 Coefficient of Skewness 372.4.5 Coefficient of Kurtosis 372.5 Summary 39Problems 403 Probability and Life Distributions for Reliability Analysis 453.1 Discrete Distributions 453.1.1 Binomial Distribution 463.1.2 Poisson Distribution 503.1.3 Other Discrete Distributions 503.2 Continuous Distributions 513.2.1 Weibull Distribution 553.2.2 Exponential Distribution 613.2.3 Estimation of Reliability for Exponential Distribution 643.2.4 The Normal (Gaussian) Distribution 673.2.5 The Lognormal Distribution 733.2.6 Gamma Distribution753.3 Probability Plots 773.4 Summary 83Problems 844 Design for Six Sigma 894.1 What Is Six Sigma? 894.2 Why Six Sigma? 904.3 How Is Six Sigma Implemented? 914.3.1 Steps in the Six Sigma Process 924.3.2 Summary of the Six Sigma Steps 974.4 Optimization Problems in the Six Sigma Process 984.4.1 System Transfer Function 994.4.2 Variance Transmission Equation 1004.4.3 Economic Optimization and Quality Improvement 1014.4.4 Tolerance Design Problem 1024.5 Design for Six Sigma 1034.5.1 Identify (I) 1054.5.2 Characterize (C) 1064.5.3 Optimize (O) 1064.5.4 Verify (V) 1064.6 Summary 108Problems 1085 Product Development 1115.1 Product Requirements and Constraints 1125.2 Product Life Cycle Conditions 1135.3 Reliability Capability 1145.4 Parts and Materials Selection 1145.5 Human Factors and Reliability 1155.6 Deductive versus Inductive Methods 1175.7 Failure Modes, Effects, and Criticality Analysis 1175.8 Fault Tree Analysis 1195.8.1 Role of FTA in Decision-Making 1215.8.2 Steps of Fault Tree Analysis 1225.8.3 Basic Paradigms for the Construction of Fault Trees 1225.8.4 Definition of the Top Event 1225.8.5 Faults versus Failures 1225.8.6 Minimal Cut Sets 1275.9 Physics of Failure 1285.9.1 Stress Margins 1285.9.2 Model Analysis of Failure Mechanisms 1295.9.3 Derating 1295.9.4 Protective Architectures 1305.9.5 Redundancy 1315.9.6 Prognostics 1315.10 Design Review 1315.11 Qualification 1325.12 Manufacture and Assembly 1345.12.1 Manufacturability 1345.12.2 Process Verification Testing 1365.13 Analysis, Product Failure, and Root Causes 1375.14 Summary 138Problems 1386 Product Requirements and Constraints 1416.1 Defining Requirements 1416.2 Responsibilities of the Supply Chain 1426.2.1 Multiple-Customer Products 1426.2.2 Single-Customer Products 1436.2.3 Custom Products 1446.3 The Requirements Document 1446.4 Specifications 1446.5 Requirements Tracking 1466.6 Summary 147Problems 1477 Life-Cycle Conditions 1497.1 Defining the Life-Cycle Profile 1497.2 Life-Cycle Events 1507.2.1 Manufacturing and Assembly 1517.2.2 Testing and Screening 1517.2.3 Storage 1517.2.4 Transportation 1517.2.5 Installation 1517.2.6 Operation 1527.2.7 Maintenance 1527.3 Loads and Their Effects 1527.3.1 Temperature 1527.3.2 Humidity 1557.3.3 Vibration and Shock 1567.3.4 Solar Radiation 1567.3.5 Electromagnetic Radiation 1577.3.6 Pressure 1577.3.7 Chemicals 1587.3.8 Sand and Dust 1597.3.9 Voltage 1597.3.10 Current 1597.3.11 Human Factors 1607.4 Considerations and Recommendations for LCP Development 1607.4.1 Extreme Specifications-Based Design (Global and Local Environments) 1607.4.2 Standards-Based Profiles 1617.4.3 Combined Load Conditions 1617.4.4 Change in Magnitude and Rate of Change of Magnitude 1657.5 Methods for Estimating Life-Cycle Loads 1657.5.1 Market Studies and Standards Based Profiles as Sources of Data 1657.5.2 In Situ Monitoring of Load Conditions 1667.5.3 Field Trial Records, Service Records, and Failure Records 1667.5.4 Data on Load Histories of Similar Parts, Assemblies, or Products 1667.6 Summary 166Problems 1678 Reliability Capability 1698.1 Capability Maturity Models 1698.2 Key Reliability Practices 1708.2.1 Reliability Requirements and Planning 1708.2.2 Training and Development 1718.2.3 Reliability Analysis 1728.2.4 Reliability Testing 1728.2.5 Supply-Chain Management 1738.2.6 Failure Data Tracking and Analysis 1738.2.7 Verification and Validation 1748.2.8 Reliability Improvement 1748.3 Summary 175Problems 1759 Parts Selection and Management 1779.1 Part Assessment Process 1779.1.1 Performance Assessment 1789.1.2 Quality Assessment 1799.1.3 Process Capability Index 1799.1.4 Average Outgoing Quality 1829.1.5 Reliability Assessment 1829.1.6 Assembly Assessment 1859.2 Parts Management 1859.2.1 Supply Chain Management 1859.2.2 Part Change Management 1869.2.3 Industry Change Control Policies 1879.3 Risk Management 1889.4 Summary 190Problems 19110 Failure Modes, Mechanisms, and Effects Analysis 19310.1 Development of FMMEA 19310.2 Failure Modes, Mechanisms, and Effects Analysis 19510.2.1 System Definition, Elements, and Functions 19510.2.2 Potential Failure Modes 19610.2.3 Potential Failure Causes 19710.2.4 Potential Failure Mechanisms 19710.2.5 Failure Models 19710.2.6 Life-Cycle Profile 19810.2.7 Failure Mechanism Prioritization 19810.2.8 Documentation 20010.3 Case Study 20110.4 Summary 205Problems 20611 Probabilistic Design for Reliability and the Factor of Safety 20711.1 Design for Reliability 20711.2 Design of a Tension Element 20811.3 Reliability Models for Probabilistic Design 20911.4 Example of Probabilistic Design and Design for a Reliability Target 21111.5 Relationship between Reliability, Factor of Safety, and Variability 21211.6 Functions of Random Variables 21511.7 Steps for Probabilistic Design 21911.8 Summary 219Problems 22012 Derating and Uprating 22312.1 Part Ratings 22312.1.1 Absolute Maximum Ratings 22412.1.2 Recommended Operating Conditions 22412.1.3 Factors Used to Determine Ratings 22512.2 Derating 22512.2.1 How Is Derating Practiced? 22512.2.2 Limitations of the Derating Methodology 23112.2.3 How to Determine These Limits 23812.3 Uprating 23912.3.1 Parts Selection and Management Process 24112.3.2 Assessment for Uprateability 24112.3.3 Methods of Uprating 24212.3.4 Continued Assurance 24512.4 Summary 245Problems 24613 Reliability Estimation Techniques 24713.1 Tests during the Product Life Cycle 24713.1.1 Concept Design and Prototype 24713.1.2 Performance Validation to Design Specification 24813.1.3 Design Maturity Validation 24813.1.4 Design and Manufacturing Process Validation 24813.1.5 Preproduction Low Volume Manufacturing 24813.1.6 High Volume Production 24913.1.7 Feedback from Field Data 24913.2 Reliability Estimation 24913.3 Product Qualification and Testing 25013.3.1 Input to PoF Qualification Methodology 25013.3.2 Accelerated Stress Test Planning and Development 25513.3.3 Specimen Characterization 25713.3.4 Accelerated Life Tests 25913.3.5 Virtual Testing 26013.3.6 Virtual Qualification 26113.3.7 Output 26213.4 Case Study: System-in-Package Drop Test Qualification 26313.4.1 Step 1: Accelerated Test Planning and Development 26313.4.2 Step 2: Specimen Characterization 26513.4.3 Step 3: Accelerated Life Testing 26613.4.4 Step 4: Virtual Testing 27013.4.5 Global FEA 27113.4.6 Strain Distributions Due to Modal Contributions 27213.4.7 Acceleration Curves 27313.4.8 Local FEA 27313.4.9 Step 5: Virtual Qualification 27413.4.10 PoF Acceleration Curves 27513.4.11 Summary of the Methodology for Qualification 27613.5 Basic Statistical Concepts 27613.5.1 Confidence Interval 27713.5.2 Interpretation of the Confidence Level 27713.5.3 Relationship between Confidence Interval and Sample Size 27913.6 Confidence Interval for Normal Distribution 27913.6.1 Unknown Mean with a Known Variance for Normal Distribution 27913.6.2 Unknown Mean with an Unknown Variance for Normal Distribution 28013.6.3 Differences in Two Population Means with Variances Known 28113.7 Confidence Intervals for Proportions 28213.8 Reliability Estimation and Confidence Limits for Success–Failure Testing 28313.8.1 Success Testing 28613.9 Reliability Estimation and Confidence Limits for Exponential Distribution 28713.10 Summary 292Problems 29214 Process Control and Process Capability 29514.1 Process Control System 29514.1.1 Control Charts: Recognizing Sources of Variation 29714.1.2 Sources of Variation 29714.1.3 Use of Control Charts for Problem Identification 29714.2 Control Charts 29914.2.1 Control Charts for Variables 30614.2.2 X-Bar and R Charts 30614.2.3 Moving Range Chart Example 30814.2.4 X-Bar and S Charts 31114.2.5 Control Charts for Attributes 31214.2.6 p Chart and np Chart 31214.2.7 np Chart Example 31314.2.8 c Chart and u Chart 31414.2.9 c Chart Example 31514.3 Benefits of Control Charts 31614.4 Average Outgoing Quality 31714.4.1 Process Capability Studies 31814.5 Advanced Control Charts 32314.5.1 Cumulative Sum Control Charts 32314.5.2 Exponentially Weighted Moving Average Control Charts 32414.5.3 Other Advanced Control Charts 32514.6 Summary 325Problems 32615 Product Screening and Burn-In Strategies 33115.1 Burn-In Data Observations 33215.2 Discussion of Burn-In Data 33315.3 Higher Field Reliability without Screening 33415.4 Best Practices 33515.5 Summary 336Problems 33716 Analyzing Product Failures and Root Causes 33916.1 Root-Cause Analysis Processes 34116.1.1 Preplanning 34116.1.2 Collecting Data for Analysis and Assessing Immediate Causes 34316.1.3 Root-Cause Hypothesization 34416.1.4 Analysis and Interpretation of Evidence 34816.1.5 Root-Cause Identification and Corrective Actions 34816.1.6 Assessment of Corrective Actions 35016.2 No-Fault-Found 35116.2.1 An Approach to Assess NFF 35316.2.2 Common Mode Failure 35516.2.3 Concept of Common Mode Failure 35616.2.4 Modeling and Analysis for Dependencies for Reliability Analysis 36016.2.5 Common Mode Failure Root Causes 36216.2.6 Common Mode Failure Analysis 36416.2.7 Common Mode Failure Occurrence and Impact Reduction 36616.3 Summary 373Problems 37417 System Reliability Modeling 37517.1 Reliability Block Diagram 37517.2 Series System 37617.3 Products with Redundancy 38117.3.1 Active Redundancy 38117.3.2 Standby Systems 38517.3.3 Standby Systems with Imperfect Switching 38717.3.4 Shared Load Parallel Models 39017.3.5 (k, n) Systems 39117.3.6 Limits of Redundancy 39317.4 Complex System Reliability 39317.4.1 Complete Enumeration Method 39317.4.2 Conditional Probability Method 39517.4.3 Concept of Coherent Structures 39617.5 Summary 401Problems 40218 Health Monitoring and Prognostics 40918.1 Conceptual Model for Prognostics 41018.2 Reliability and Prognostics 41218.3 PHM for Electronics 41418.4 PHM Concepts and Methods 41718.4.1 Fuses and Canaries 41818.5 Monitoring and Reasoning of Failure Precursors 42018.5.1 Monitoring Environmental and Usage Profiles for Damage Modeling 42418.6 Implementation of PHM in a System of Systems 42918.7 Summary 431Problems 43119 Warranty Analysis 43319.1 Product Warranties 43419.2 Warranty Return Information 43519.3 Warranty Policies 43619.4 Warranty and Reliability 43719.5 Warranty Cost Analysis 43919.5.1 Elements of Warranty Cost Models 44019.5.2 Failure Distributions 44019.5.3 Cost Modeling Calculation 44019.5.4 Modeling Assumptions and Notation 44119.5.5 Cost Models Examples 44219.5.6 Information Needs 44419.5.7 Other Cost Models 44619.6 Warranty and Reliability Management 44819.7 Summary 449Problems 449Appendix A: Some Useful Integrals 451Appendix B: Table for Gamma Function 453Appendix C: Table for Cumulative Standard Normal Distribution 455Appendix D: Values for the Percentage Points tα,ν of the t-Distribution 457Appendix E: Percentage Points χ2α,ν of the Chi-Square Distribution 461Appendix F: Percentage Points for the F-Distribution 467Bibliography 473Index 487

KAILASH C. KAPUR, PHD, is a Professor of Industrial & Systems Engineering at the University of Washington, where he was also the Director from 1993 to 1999. Dr. Kapur has worked with General Motors Research Laboratories as a senior research engineer, Ford Motor Company as a visiting scholar, and the U.S. Army, Tank-Automotive Command as a reliability engineer. He is a Fellow of ASQ and IIE, and a registered professional engineer.MICHAEL G. PECHT, PHD, is the founder of CALCE (Center for Advanced Life Cycle Engineering) at the University of Maryland, which is funded by over 150 of the world’s leading electronics companies. He is also a Chair Professor in Mechanical Engineering and a Professor in Applied Mathematics at the University of Maryland. He consults for twenty-two major international electronics companies.

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• Preface xv1 Reliability Engineering in the Twenty-First Century 11.1 What Is Quality? 11.2 What Is Reliability? 21.2.1 The Ability to Perform as Intended 41.2.2 For a Specified Time 41.2.3 Life-Cycle Conditions 51.2.4 Reliability as a Relative Measure 51.3 Quality, Customer Satisfaction, and System Effectiveness 61.4 Performance, Quality, and Reliability 71.5 Reliability and the System Life Cycle 81.6 Consequences of Failure 121.6.1 Financial Loss 121.6.2 Breach of Public Trust 131.6.3 Legal Liability 151.6.4 Intangible Losses 151.7 Suppliers and Customers 161.8 Summary 16Problems 172 Reliability Concepts 192.1 Basic Reliability Concepts 192.1.1 Concept of Probability Density Function 232.2 Hazard Rate 262.2.1 Motivation and Development of Hazard Rate 272.2.2 Some Properties of the Hazard Function 282.2.3 Conditional Reliability 312.3 Percentiles Product Life 332.4 Moments of Time to Failure 352.4.1 Moments about Origin and about the Mean 352.4.2 Expected Life or Mean Time to Failure 362.4.3 Variance or the Second Moment about the Mean 362.4.4 Coefficient of Skewness 372.4.5 Coefficient of Kurtosis 372.5 Summary 39Problems 403 Probability and Life Distributions for Reliability Analysis 453.1 Discrete Distributions 453.1.1 Binomial Distribution 463.1.2 Poisson Distribution 503.1.3 Other Discrete Distributions 503.2 Continuous Distributions 513.2.1 Weibull Distribution 553.2.2 Exponential Distribution 613.2.3 Estimation of Reliability for Exponential Distribution 643.2.4 The Normal (Gaussian) Distribution 673.2.5 The Lognormal Distribution 733.2.6 Gamma Distribution753.3 Probability Plots 773.4 Summary 83Problems 844 Design for Six Sigma 894.1 What Is Six Sigma? 894.2 Why Six Sigma? 904.3 How Is Six Sigma Implemented? 914.3.1 Steps in the Six Sigma Process 924.3.2 Summary of the Six Sigma Steps 974.4 Optimization Problems in the Six Sigma Process 984.4.1 System Transfer Function 994.4.2 Variance Transmission Equation 1004.4.3 Economic Optimization and Quality Improvement 1014.4.4 Tolerance Design Problem 1024.5 Design for Six Sigma 1034.5.1 Identify (I) 1054.5.2 Characterize (C) 1064.5.3 Optimize (O) 1064.5.4 Verify (V) 1064.6 Summary 108Problems 1085 Product Development 1115.1 Product Requirements and Constraints 1125.2 Product Life Cycle Conditions 1135.3 Reliability Capability 1145.4 Parts and Materials Selection 1145.5 Human Factors and Reliability 1155.6 Deductive versus Inductive Methods 1175.7 Failure Modes, Effects, and Criticality Analysis 1175.8 Fault Tree Analysis 1195.8.1 Role of FTA in Decision-Making 1215.8.2 Steps of Fault Tree Analysis 1225.8.3 Basic Paradigms for the Construction of Fault Trees 1225.8.4 Definition of the Top Event 1225.8.5 Faults versus Failures 1225.8.6 Minimal Cut Sets 1275.9 Physics of Failure 1285.9.1 Stress Margins 1285.9.2 Model Analysis of Failure Mechanisms 1295.9.3 Derating 1295.9.4 Protective Architectures 1305.9.5 Redundancy 1315.9.6 Prognostics 1315.10 Design Review 1315.11 Qualification 1325.12 Manufacture and Assembly 1345.12.1 Manufacturability 1345.12.2 Process Verification Testing 1365.13 Analysis, Product Failure, and Root Causes 1375.14 Summary 138Problems 1386 Product Requirements and Constraints 1416.1 Defining Requirements 1416.2 Responsibilities of the Supply Chain 1426.2.1 Multiple-Customer Products 1426.2.2 Single-Customer Products 1436.2.3 Custom Products 1446.3 The Requirements Document 1446.4 Specifications 1446.5 Requirements Tracking 1466.6 Summary 147Problems 1477 Life-Cycle Conditions 1497.1 Defining the Life-Cycle Profile 1497.2 Life-Cycle Events 1507.2.1 Manufacturing and Assembly 1517.2.2 Testing and Screening 1517.2.3 Storage 1517.2.4 Transportation 1517.2.5 Installation 1517.2.6 Operation 1527.2.7 Maintenance 1527.3 Loads and Their Effects 1527.3.1 Temperature 1527.3.2 Humidity 1557.3.3 Vibration and Shock 1567.3.4 Solar Radiation 1567.3.5 Electromagnetic Radiation 1577.3.6 Pressure 1577.3.7 Chemicals 1587.3.8 Sand and Dust 1597.3.9 Voltage 1597.3.10 Current 1597.3.11 Human Factors 1607.4 Considerations and Recommendations for LCP Development 1607.4.1 Extreme Specifications-Based Design (Global and Local Environments) 1607.4.2 Standards-Based Profiles 1617.4.3 Combined Load Conditions 1617.4.4 Change in Magnitude and Rate of Change of Magnitude 1657.5 Methods for Estimating Life-Cycle Loads 1657.5.1 Market Studies and Standards Based Profiles as Sources of Data 1657.5.2 In Situ Monitoring of Load Conditions 1667.5.3 Field Trial Records, Service Records, and Failure Records 1667.5.4 Data on Load Histories of Similar Parts, Assemblies, or Products 1667.6 Summary 166Problems 1678 Reliability Capability 1698.1 Capability Maturity Models 1698.2 Key Reliability Practices 1708.2.1 Reliability Requirements and Planning 1708.2.2 Training and Development 1718.2.3 Reliability Analysis 1728.2.4 Reliability Testing 1728.2.5 Supply-Chain Management 1738.2.6 Failure Data Tracking and Analysis 1738.2.7 Verification and Validation 1748.2.8 Reliability Improvement 1748.3 Summary 175Problems 1759 Parts Selection and Management 1779.1 Part Assessment Process 1779.1.1 Performance Assessment 1789.1.2 Quality Assessment 1799.1.3 Process Capability Index 1799.1.4 Average Outgoing Quality 1829.1.5 Reliability Assessment 1829.1.6 Assembly Assessment 1859.2 Parts Management 1859.2.1 Supply Chain Management 1859.2.2 Part Change Management 1869.2.3 Industry Change Control Policies 1879.3 Risk Management 1889.4 Summary 190Problems 19110 Failure Modes, Mechanisms, and Effects Analysis 19310.1 Development of FMMEA 19310.2 Failure Modes, Mechanisms, and Effects Analysis 19510.2.1 System Definition, Elements, and Functions 19510.2.2 Potential Failure Modes 19610.2.3 Potential Failure Causes 19710.2.4 Potential Failure Mechanisms 19710.2.5 Failure Models 19710.2.6 Life-Cycle Profile 19810.2.7 Failure Mechanism Prioritization 19810.2.8 Documentation 20010.3 Case Study 20110.4 Summary 205Problems 20611 Probabilistic Design for Reliability and the Factor of Safety 20711.1 Design for Reliability 20711.2 Design of a Tension Element 20811.3 Reliability Models for Probabilistic Design 20911.4 Example of Probabilistic Design and Design for a Reliability Target 21111.5 Relationship between Reliability, Factor of Safety, and Variability 21211.6 Functions of Random Variables 21511.7 Steps for Probabilistic Design 21911.8 Summary 219Problems 22012 Derating and Uprating 22312.1 Part Ratings 22312.1.1 Absolute Maximum Ratings 22412.1.2 Recommended Operating Conditions 22412.1.3 Factors Used to Determine Ratings 22512.2 Derating 22512.2.1 How Is Derating Practiced? 22512.2.2 Limitations of the Derating Methodology 23112.2.3 How to Determine These Limits 23812.3 Uprating 23912.3.1 Parts Selection and Management Process 24112.3.2 Assessment for Uprateability 24112.3.3 Methods of Uprating 24212.3.4 Continued Assurance 24512.4 Summary 245Problems 24613 Reliability Estimation Techniques 24713.1 Tests during the Product Life Cycle 24713.1.1 Concept Design and Prototype 24713.1.2 Performance Validation to Design Specification 24813.1.3 Design Maturity Validation 24813.1.4 Design and Manufacturing Process Validation 24813.1.5 Preproduction Low Volume Manufacturing 24813.1.6 High Volume Production 24913.1.7 Feedback from Field Data 24913.2 Reliability Estimation 24913.3 Product Qualification and Testing 25013.3.1 Input to PoF Qualification Methodology 25013.3.2 Accelerated Stress Test Planning and Development 25513.3.3 Specimen Characterization 25713.3.4 Accelerated Life Tests 25913.3.5 Virtual Testing 26013.3.6 Virtual Qualification 26113.3.7 Output 26213.4 Case Study: System-in-Package Drop Test Qualification 26313.4.1 Step 1: Accelerated Test Planning and Development 26313.4.2 Step 2: Specimen Characterization 26513.4.3 Step 3: Accelerated Life Testing 26613.4.4 Step 4: Virtual Testing 27013.4.5 Global FEA 27113.4.6 Strain Distributions Due to Modal Contributions 27213.4.7 Acceleration Curves 27313.4.8 Local FEA 27313.4.9 Step 5: Virtual Qualification 27413.4.10 PoF Acceleration Curves 27513.4.11 Summary of the Methodology for Qualification 27613.5 Basic Statistical Concepts 27613.5.1 Confidence Interval 27713.5.2 Interpretation of the Confidence Level 27713.5.3 Relationship between Confidence Interval and Sample Size 27913.6 Confidence Interval for Normal Distribution 27913.6.1 Unknown Mean with a Known Variance for Normal Distribution 27913.6.2 Unknown Mean with an Unknown Variance for Normal Distribution 28013.6.3 Differences in Two Population Means with Variances Known 28113.7 Confidence Intervals for Proportions 28213.8 Reliability Estimation and Confidence Limits for Success–Failure Testing 28313.8.1 Success Testing 28613.9 Reliability Estimation and Confidence Limits for Exponential Distribution 28713.10 Summary 292Problems 29214 Process Control and Process Capability 29514.1 Process Control System 29514.1.1 Control Charts: Recognizing Sources of Variation 29714.1.2 Sources of Variation 29714.1.3 Use of Control Charts for Problem Identification 29714.2 Control Charts 29914.2.1 Control Charts for Variables 30614.2.2 X-Bar and R Charts 30614.2.3 Moving Range Chart Example 30814.2.4 X-Bar and S Charts 31114.2.5 Control Charts for Attributes 31214.2.6 p Chart and np Chart 31214.2.7 np Chart Example 31314.2.8 c Chart and u Chart 31414.2.9 c Chart Example 31514.3 Benefits of Control Charts 31614.4 Average Outgoing Quality 31714.4.1 Process Capability Studies 31814.5 Advanced Control Charts 32314.5.1 Cumulative Sum Control Charts 32314.5.2 Exponentially Weighted Moving Average Control Charts 32414.5.3 Other Advanced Control Charts 32514.6 Summary 325Problems 32615 Product Screening and Burn-In Strategies 33115.1 Burn-In Data Observations 33215.2 Discussion of Burn-In Data 33315.3 Higher Field Reliability without Screening 33415.4 Best Practices 33515.5 Summary 336Problems 33716 Analyzing Product Failures and Root Causes 33916.1 Root-Cause Analysis Processes 34116.1.1 Preplanning 34116.1.2 Collecting Data for Analysis and Assessing Immediate Causes 34316.1.3 Root-Cause Hypothesization 34416.1.4 Analysis and Interpretation of Evidence 34816.1.5 Root-Cause Identification and Corrective Actions 34816.1.6 Assessment of Corrective Actions 35016.2 No-Fault-Found 35116.2.1 An Approach to Assess NFF 35316.2.2 Common Mode Failure 35516.2.3 Concept of Common Mode Failure 35616.2.4 Modeling and Analysis for Dependencies for Reliability Analysis 36016.2.5 Common Mode Failure Root Causes 36216.2.6 Common Mode Failure Analysis 36416.2.7 Common Mode Failure Occurrence and Impact Reduction 36616.3 Summary 373Problems 37417 System Reliability Modeling 37517.1 Reliability Block Diagram 37517.2 Series System 37617.3 Products with Redundancy 38117.3.1 Active Redundancy 38117.3.2 Standby Systems 38517.3.3 Standby Systems with Imperfect Switching 38717.3.4 Shared Load Parallel Models 39017.3.5 (k, n) Systems 39117.3.6 Limits of Redundancy 39317.4 Complex System Reliability 39317.4.1 Complete Enumeration Method 39317.4.2 Conditional Probability Method 39517.4.3 Concept of Coherent Structures 39617.5 Summary 401Problems 40218 Health Monitoring and Prognostics 40918.1 Conceptual Model for Prognostics 41018.2 Reliability and Prognostics 41218.3 PHM for Electronics 41418.4 PHM Concepts and Methods 41718.4.1 Fuses and Canaries 41818.5 Monitoring and Reasoning of Failure Precursors 42018.5.1 Monitoring Environmental and Usage Profiles for Damage Modeling 42418.6 Implementation of PHM in a System of Systems 42918.7 Summary 431Problems 43119 Warranty Analysis 43319.1 Product Warranties 43419.2 Warranty Return Information 43519.3 Warranty Policies 43619.4 Warranty and Reliability 43719.5 Warranty Cost Analysis 43919.5.1 Elements of Warranty Cost Models 44019.5.2 Failure Distributions 44019.5.3 Cost Modeling Calculation 44019.5.4 Modeling Assumptions and Notation 44119.5.5 Cost Models Examples 44219.5.6 Information Needs 44419.5.7 Other Cost Models 44619.6 Warranty and Reliability Management 44819.7 Summary 449Problems 449Appendix A: Some Useful Integrals 451Appendix B: Table for Gamma Function 453Appendix C: Table for Cumulative Standard Normal Distribution 455Appendix D: Values for the Percentage Points tα,ν of the t-Distribution 457Appendix E: Percentage Points χ2α,ν of the Chi-Square Distribution 461Appendix F: Percentage Points for the F-Distribution 467Bibliography 473Index 487