Kailash C. Kapur & Michael G. Pecht 
Reliability Engineering [PDF ebook] 

Preface xv

1 Reliability Engineering in the Twenty-First Century 1

1.1 What Is Quality? 1

1.2 What Is Reliability? 2

1.2.1 The Ability to Perform as Intended 4

1.2.2 For a Specified Time 4

1.2.3 Life-Cycle Conditions 5

1.2.4 Reliability as a Relative Measure 5

1.3 Quality, Customer Satisfaction, and System Effectiveness 6

1.4 Performance, Quality, and Reliability 7

1.5 Reliability and the System Life Cycle 8

1.6 Consequences of Failure 12

1.6.1 Financial Loss 12

1.6.2 Breach of Public Trust 13

1.6.3 Legal Liability 15

1.6.4 Intangible Losses 15

1.7 Suppliers and Customers 16

1.8 Summary 16

Problems 17

2 Reliability Concepts 19

2.1 Basic Reliability Concepts 19

2.1.1 Concept of Probability Density Function 23

2.2 Hazard Rate 26

2.2.1 Motivation and Development of Hazard Rate 27

2.2.2 Some Properties of the Hazard Function 28

2.2.3 Conditional Reliability 31

2.3 Percentiles Product Life 33

2.4 Moments of Time to Failure 35

2.4.1 Moments about Origin and about the Mean 35

2.4.2 Expected Life or Mean Time to Failure 36

2.4.3 Variance or the Second Moment about the Mean 36

2.4.4 Coefficient of Skewness 37

2.4.5 Coefficient of Kurtosis 37

2.5 Summary 39

Problems 40

3 Probability and Life Distributions for Reliability Analysis 45

3.1 Discrete Distributions 45

3.1.1 Binomial Distribution 46

3.1.2 Poisson Distribution 50

3.1.3 Other Discrete Distributions 50

3.2 Continuous Distributions 51

3.2.1 Weibull Distribution 55

3.2.2 Exponential Distribution 61

3.2.3 Estimation of Reliability for Exponential Distribution 64

3.2.4 The Normal (Gaussian) Distribution 67

3.2.5 The Lognormal Distribution 73

3.2.6 Gamma Distribution75

3.3 Probability Plots 77

3.4 Summary 83

Problems 84

4 Design for Six Sigma 89

4.1 What Is Six Sigma? 89

4.2 Why Six Sigma? 90

4.3 How Is Six Sigma Implemented? 91

4.3.1 Steps in the Six Sigma Process 92

4.3.2 Summary of the Six Sigma Steps 97

4.4 Optimization Problems in the Six Sigma Process 98

4.4.1 System Transfer Function 99

4.4.2 Variance Transmission Equation 100

4.4.3 Economic Optimization and Quality Improvement 101

4.4.4 Tolerance Design Problem 102

4.5 Design for Six Sigma 103

4.5.1 Identify (I) 105

4.5.2 Characterize (C) 106

4.5.3 Optimize (O) 106

4.5.4 Verify (V) 106

4.6 Summary 108

Problems 108

5 Product Development 111

5.1 Product Requirements and Constraints 112

5.2 Product Life Cycle Conditions 113

5.3 Reliability Capability 114

5.4 Parts and Materials Selection 114

5.5 Human Factors and Reliability 115

5.6 Deductive versus Inductive Methods 117

5.7 Failure Modes, Effects, and Criticality Analysis 117

5.8 Fault Tree Analysis 119

5.8.1 Role of FTA in Decision-Making 121

5.8.2 Steps of Fault Tree Analysis 122

5.8.3 Basic Paradigms for the Construction of Fault Trees 122

5.8.4 Definition of the Top Event 122

5.8.5 Faults versus Failures 122

5.8.6 Minimal Cut Sets 127

5.9 Physics of Failure 128

5.9.1 Stress Margins 128

5.9.2 Model Analysis of Failure Mechanisms 129

5.9.3 Derating 129

5.9.4 Protective Architectures 130

5.9.5 Redundancy 131

5.9.6 Prognostics 131

5.10 Design Review 131

5.11 Qualification 132

5.12 Manufacture and Assembly 134

5.12.1 Manufacturability 134

5.12.2 Process Verification Testing 136

5.13 Analysis, Product Failure, and Root Causes 137

5.14 Summary 138

Problems 138

6 Product Requirements and Constraints 141

6.1 Defining Requirements 141

6.2 Responsibilities of the Supply Chain 142

6.2.1 Multiple-Customer Products 142

6.2.2 Single-Customer Products 143

6.2.3 Custom Products 144

6.3 The Requirements Document 144

6.4 Specifications 144

6.5 Requirements Tracking 146

6.6 Summary 147

Problems 147

7 Life-Cycle Conditions 149

7.1 Defining the Life-Cycle Profile 149

7.2 Life-Cycle Events 150

7.2.1 Manufacturing and Assembly 151

7.2.2 Testing and Screening 151

7.2.3 Storage 151

7.2.4 Transportation 151

7.2.5 Installation 151

7.2.6 Operation 152

7.2.7 Maintenance 152

7.3 Loads and Their Effects 152

7.3.1 Temperature 152

7.3.2 Humidity 155

7.3.3 Vibration and Shock 156

7.3.4 Solar Radiation 156

7.3.5 Electromagnetic Radiation 157

7.3.6 Pressure 157

7.3.7 Chemicals 158

7.3.8 Sand and Dust 159

7.3.9 Voltage 159

7.3.10 Current 159

7.3.11 Human Factors 160

7.4 Considerations and Recommendations for LCP Development 160

7.4.1 Extreme Specifications-Based Design (Global and Local Environments) 160

7.4.2 Standards-Based Profiles 161

7.4.3 Combined Load Conditions 161

7.4.4 Change in Magnitude and Rate of Change of Magnitude 165

7.5 Methods for Estimating Life-Cycle Loads 165

7.5.1 Market Studies and Standards Based Profiles as Sources of Data 165

7.5.2 In Situ Monitoring of Load Conditions 166

7.5.3 Field Trial Records, Service Records, and Failure Records 166

7.5.4 Data on Load Histories of Similar Parts, Assemblies, or Products 166

7.6 Summary 166

Problems 167

8 Reliability Capability 169

8.1 Capability Maturity Models 169

8.2 Key Reliability Practices 170

8.2.1 Reliability Requirements and Planning 170

8.2.2 Training and Development 171

8.2.3 Reliability Analysis 172

8.2.4 Reliability Testing 172

8.2.5 Supply-Chain Management 173

8.2.6 Failure Data Tracking and Analysis 173

8.2.7 Verification and Validation 174

8.2.8 Reliability Improvement 174

8.3 Summary 175

Problems 175

9 Parts Selection and Management 177

9.1 Part Assessment Process 177

9.1.1 Performance Assessment 178

9.1.2 Quality Assessment 179

9.1.3 Process Capability Index 179

9.1.4 Average Outgoing Quality 182

9.1.5 Reliability Assessment 182

9.1.6 Assembly Assessment 185

9.2 Parts Management 185

9.2.1 Supply Chain Management 185

9.2.2 Part Change Management 186

9.2.3 Industry Change Control Policies 187

9.3 Risk Management 188

9.4 Summary 190

Problems 191

10 Failure Modes, Mechanisms, and Effects Analysis 193

10.1 Development of FMMEA 193

10.2 Failure Modes, Mechanisms, and Effects Analysis 195

10.2.1 System Definition, Elements, and Functions 195

10.2.2 Potential Failure Modes 196

10.2.3 Potential Failure Causes 197

10.2.4 Potential Failure Mechanisms 197

10.2.5 Failure Models 197

10.2.6 Life-Cycle Profile 198

10.2.7 Failure Mechanism Prioritization 198

10.2.8 Documentation 200

10.3 Case Study 201

10.4 Summary 205

Problems 206

11 Probabilistic Design for Reliability and the Factor of Safety 207

11.1 Design for Reliability 207

11.2 Design of a Tension Element 208

11.3 Reliability Models for Probabilistic Design 209

11.4 Example of Probabilistic Design and Design for a Reliability Target 211

11.5 Relationship between Reliability, Factor of Safety, and Variability 212

11.6 Functions of Random Variables 215

11.7 Steps for Probabilistic Design 219

11.8 Summary 219

Problems 220

12 Derating and Uprating 223

12.1 Part Ratings 223

12.1.1 Absolute Maximum Ratings 224

12.1.2 Recommended Operating Conditions 224

12.1.3 Factors Used to Determine Ratings 225

12.2 Derating 225

12.2.1 How Is Derating Practiced? 225

12.2.2 Limitations of the Derating Methodology 231

12.2.3 How to Determine These Limits 238

12.3 Uprating 239

12.3.1 Parts Selection and Management Process 241

12.3.2 Assessment for Uprateability 241

12.3.3 Methods of Uprating 242

12.3.4 Continued Assurance 245

12.4 Summary 245

Problems 246

13 Reliability Estimation Techniques 247

13.1 Tests during the Product Life Cycle 247

13.1.1 Concept Design and Prototype 247

13.1.2 Performance Validation to Design Specification 248

13.1.3 Design Maturity Validation 248

13.1.4 Design and Manufacturing Process Validation 248

13.1.5 Preproduction Low Volume Manufacturing 248

13.1.6 High Volume Production 249

13.1.7 Feedback from Field Data 249

13.2 Reliability Estimation 249

13.3 Product Qualification and Testing 250

13.3.1 Input to Po F Qualification Methodology 250

13.3.2 Accelerated Stress Test Planning and Development 255

13.3.3 Specimen Characterization 257

13.3.4 Accelerated Life Tests 259

13.3.5 Virtual Testing 260

13.3.6 Virtual Qualification 261

13.3.7 Output 262

13.4 Case Study: System-in-Package Drop Test Qualification 263

13.4.1 Step 1: Accelerated Test Planning and Development 263

13.4.2 Step 2: Specimen Characterization 265

13.4.3 Step 3: Accelerated Life Testing 266

13.4.4 Step 4: Virtual Testing 270

13.4.5 Global FEA 271

13.4.6 Strain Distributions Due to Modal Contributions 272

13.4.7 Acceleration Curves 273

13.4.8 Local FEA 273

13.4.9 Step 5: Virtual Qualification 274

13.4.10 Po F Acceleration Curves 275

13.4.11 Summary of the Methodology for Qualification 276

13.5 Basic Statistical Concepts 276

13.5.1 Confidence Interval 277

13.5.2 Interpretation of the Confidence Level 277

13.5.3 Relationship between Confidence Interval and Sample Size 279

13.6 Confidence Interval for Normal Distribution 279

13.6.1 Unknown Mean with a Known Variance for Normal Distribution 279

13.6.2 Unknown Mean with an Unknown Variance for Normal Distribution 280

13.6.3 Differences in Two Population Means with Variances Known 281

13.7 Confidence Intervals for Proportions 282

13.8 Reliability Estimation and Confidence Limits for Success–Failure Testing 283

13.8.1 Success Testing 286

13.9 Reliability Estimation and Confidence Limits for Exponential Distribution 287

13.10 Summary 292

Problems 292

14 Process Control and Process Capability 295

14.1 Process Control System 295

14.1.1 Control Charts: Recognizing Sources of Variation 297

14.1.2 Sources of Variation 297

14.1.3 Use of Control Charts for Problem Identification 297

14.2 Control Charts 299

14.2.1 Control Charts for Variables 306

14.2.2 X-Bar and R Charts 306

14.2.3 Moving Range Chart Example 308

14.2.4 X-Bar and S Charts 311

14.2.5 Control Charts for Attributes 312

14.2.6 p Chart and np Chart 312

14.2.7 np Chart Example 313

14.2.8 c Chart and u Chart 314

14.2.9 c Chart Example 315

14.3 Benefits of Control Charts 316

14.4 Average Outgoing Quality 317

14.4.1 Process Capability Studies 318

14.5 Advanced Control Charts 323

14.5.1 Cumulative Sum Control Charts 323

14.5.2 Exponentially Weighted Moving Average Control Charts 324

14.5.3 Other Advanced Control Charts 325

14.6 Summary 325

Problems 326

15 Product Screening and Burn-In Strategies 331

15.1 Burn-In Data Observations 332

15.2 Discussion of Burn-In Data 333

15.3 Higher Field Reliability without Screening 334

15.4 Best Practices 335

15.5 Summary 336

Problems 337

16 Analyzing Product Failures and Root Causes 339

16.1 Root-Cause Analysis Processes 341

16.1.1 Preplanning 341

16.1.2 Collecting Data for Analysis and Assessing Immediate Causes 343

16.1.3 Root-Cause Hypothesization 344

16.1.4 Analysis and Interpretation of Evidence 348

16.1.5 Root-Cause Identification and Corrective Actions 348

16.1.6 Assessment of Corrective Actions 350

16.2 No-Fault-Found 351

16.2.1 An Approach to Assess NFF 353

16.2.2 Common Mode Failure 355

16.2.3 Concept of Common Mode Failure 356

16.2.4 Modeling and Analysis for Dependencies for Reliability Analysis 360

16.2.5 Common Mode Failure Root Causes 362

16.2.6 Common Mode Failure Analysis 364

16.2.7 Common Mode Failure Occurrence and Impact Reduction 366

16.3 Summary 373

Problems 374

17 System Reliability Modeling 375

17.1 Reliability Block Diagram 375

17.2 Series System 376

17.3 Products with Redundancy 381

17.3.1 Active Redundancy 381

17.3.2 Standby Systems 385

17.3.3 Standby Systems with Imperfect Switching 387

17.3.4 Shared Load Parallel Models 390

17.3.5 (k, n) Systems 391

17.3.6 Limits of Redundancy 393

17.4 Complex System Reliability 393

17.4.1 Complete Enumeration Method 393

17.4.2 Conditional Probability Method 395

17.4.3 Concept of Coherent Structures 396

17.5 Summary 401

Problems 402

18 Health Monitoring and Prognostics 409

18.1 Conceptual Model for Prognostics 410

18.2 Reliability and Prognostics 412

18.3 PHM for Electronics 414

18.4 PHM Concepts and Methods 417

18.4.1 Fuses and Canaries 418

18.5 Monitoring and Reasoning of Failure Precursors 420

18.5.1 Monitoring Environmental and Usage Profiles for Damage Modeling 424

18.6 Implementation of PHM in a System of Systems 429

18.7 Summary 431

Problems 431

19 Warranty Analysis 433

19.1 Product Warranties 434

19.2 Warranty Return Information 435

19.3 Warranty Policies 436

19.4 Warranty and Reliability 437

19.5 Warranty Cost Analysis 439

19.5.1 Elements of Warranty Cost Models 440

19.5.2 Failure Distributions 440

19.5.3 Cost Modeling Calculation 440

19.5.4 Modeling Assumptions and Notation 441

19.5.5 Cost Models Examples 442

19.5.6 Information Needs 444

19.5.7 Other Cost Models 446

19.6 Warranty and Reliability Management 448

19.7 Summary 449

Problems 449

Appendix A: Some Useful Integrals 451

Appendix B: Table for Gamma Function 453

Appendix C: Table for Cumulative Standard Normal Distribution 455

Appendix D: Values for the Percentage Points tα, ν of the t-Distribution 457

Appendix E: Percentage Points χ2α, ν of the Chi-Square Distribution 461

Appendix F: Percentage Points for the F-Distribution 467

Bibliography 473

Index 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.