Reliability Engineering

An Integrated Approach to Product Development Reliability Engineering presents an integrated approach to the design, engineering, and management of reliability activities throughout the life cycle of a product, including concept, research and development, design, manufacturing, assembly, sales, and service. Containing illustrative guides that include worked problems, numerical examples, homework problems, a solutions manual, and class–tested materials, it demonstrates to product development and manufacturing professionals how to distribute key reliability practices throughout an organization. The authors explain how to integrate reliability methods and techniques in the Six Sigma process and Design for Six Sigma (DFSS). They also discuss relationships between warranty and reliability, as well as legal and liability issues. Other topics covered include: Reliability engineering in the 21 st Century Probability life distributions for reliability analysis Process control and process capability Failure modes, mechanisms, and effects analysis Health monitoring and prognostics Reliability tests and reliability estimation Reliability Engineering provides a comprehensive list of references on the topics covered in each chapter. It is an invaluable resource for those interested in gaining fundamental knowledge of the practical aspects of reliability in design, manufacturing, and testing. In addition, it is useful for implementation and management of reliability programs.

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 Failure36 2.4.3 Variance or the Second Moment about the Mean 36 2.4.4 Coeffi cient of Skewness    37 2.4.5 Coeffi cient 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 Distribution   75 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 Defi nition 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 Verifi cation 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 Defi ning 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 Specifi cations  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 Defi nition, 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 Qualifi cation and Testing   250 13.3.1 Input to PoF Qualifi cation 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 Qualifi cation 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 Confi dence 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 Variation297 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 08 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 Benefi ts 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 Charts323 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 Identifi cation 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 KAPUR, P H D, 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 PECHT, P H D, is the founder of CALCE (Center for Advanced Life Cycle Engineering) at the University of Maryland, which is funded by over 150 of the worlds 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.