Reliability Engineering
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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 PoF 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 PoF 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 ta,¿ of the t-Distribution 457
Appendix E: Percentage Points ¿2a,¿ of the Chi-Square Distribution 461
Appendix F: Percentage Points for the F-Distribution 467
Bibliography 473
Index 487
