Alec Feinberg, DfR Software Company, Raleigh, NC, USA Dr. Feinberg has a Ph.D. in Physics and provides engineering services in all areas of reliability. He also provides consultancy services for: Reliability Test and Analysis, Accelerated Testing, HALT, FMEA, Quality statistics, corrosion analysis and Thermodynamic Modeling. Alec has presented numerous technical papers and won the 2003 RAMS Alan O. Plait best tutorial award for the topic, Thermodynamic Reliability Engineering.

• List of Figures xiiiList of Tables xviAbout the Author xviiPreface xviii1 Equilibrium Thermodynamic Degradation Science 11.1 Introduction to a New Science 11.2 Categorizing Physics of Failure Mechanisms 21.3 Entropy Damage Concept 31.3.1 The System (Device) and its Environment 41.3.2 Irreversible Thermodynamic Processes Cause Damage 51.4 Thermodynamic Work 61.5 Thermodynamic State Variables and their Characteristics 71.6 Thermodynamic Second Law in Terms of System Entropy Damage 91.6.1 Thermodynamic Entropy Damage Axiom 111.6.2 Entropy and Free Energy 131.7 Work, Resistance, Generated Entropy, and the Second Law 141.8 Thermodynamic Catastrophic and Parametric Failure 161.8.1 Equilibrium and Non-Equilibrium Aging States in Terms of the Free Energy or Entropy Change 161.9 Repair Entropy 171.9.1 Example 1.1: Repair Entropy: Relating Non-Damage Entropy Flow to Entropy Damage 17Summary 18References 222 Applications of Equilibrium Thermodynamic Degradation to Complex and Simple Systems: Entropy Damage, Vibration, Temperature, Noise Analysis, and Thermodynamic Potentials 232.1 Cumulative Entropy Damage Approach in Physics of Failure 232.1.1 Example 2.1: Miner’s Rule Derivation 252.1.2 Example 2.2: Miner’s Rule Example 262.1.3 Non-Cyclic Applications of Cumulative Damage 272.2 Measuring Entropy Damage Processes 272.3 Intermediate Thermodynamic Aging States and Sampling 292.4 Measures for System-Level Entropy Damage 292.4.1 Measuring System Entropy Damage with Temperature 292.4.2 Example 2.3: Resistor Aging 302.4.3 Example 2.4: Complex Resistor Bank 312.4.4 System Entropy Damage with Temperature Observations 322.4.5 Example 2.5: Temperature Aging of an Operating System 322.4.6 Comment on High-Temperature Aging for Operating and Non-Operating Systems 322.5 Measuring Randomness due to System Entropy Damage with Mesoscopic Noise Analysis in an Operating System 332.5.1 Example 2.6: Gaussian Noise Vibration Damage 352.5.2 Example 2.7: System Vibration Damage Observed with Noise Analysis 362.6 How System Entropy Damage Leads to Random Processes 372.6.1 Stationary versus Non-Stationary Entropy Process 402.7 Example 2.8: Human Heart Rate Noise Degradation 412.8 Entropy Damage Noise Assessment Using Autocorrelation and the Power Spectral Density 422.8.1 Noise Measurements Rules of Thumb for the PSD and R 432.8.2 Literature Review of Traditional Noise Measurement 442.8.3 Literature Review for Resistor Noise 482.9 Noise Detection Measurement System 482.9.1 System Noise Temperature 492.9.2 Environmental Noise Due to Pollution 502.9.3 Measuring System Entropy Damage using Failure Rate 502.10 Entropy Maximize Principle: Combined First and Second Law 512.10.1 Example 2.9: Thermal Equilibrium 522.10.2 Example 2.10: Equilibrium with Charge Exchange 532.10.3 Example 2.11: Diffusion Equilibrium 552.10.4 Example 2.12: Available Work 552.11 Thermodynamic Potentials and Energy States 572.11.1 The Helmholtz Free Energy 582.11.2 The Enthalpy Energy State 602.11.3 The Gibbs Free Energy 602.11.4 Summary of Common Thermodynamic State Energies 622.11.5 Example 2.13: Work, Entropy Damage, and Free Energy Change 622.11.6 Example 2.14: System in Contact with a Reservoir 65Summary 68References 763 NE Thermodynamic Degradation Science Assessment Using the Work Concept 773.1 Equilibrium versus Non-Equilibrium Aging Approach 773.1.1 Conjugate Work and Free Energy Approach to Understanding Non-Equilibrium Thermodynamic Degradation 783.2 Application to Cyclic Work and Cumulative Damage 793.3 Cyclic Work Process, Heat Engines, and the Carnot Cycle 813.4 Example 3.1: Cyclic Engine Damage Quantified Using Efficiency 843.5 The Thermodynamic Damage Ratio Method for Tracking Degradation 863.6 Acceleration Factors from the Damage Ratio Principle 87Summary 89References 924 Applications of NE Thermodynamic Degradation Science to Mechanical Systems: Accelerated Test and CAST Equations, Miner’s Rule, and FDS 934.1 Thermodynamic Work Approach to Physics of Failure Problems 934.2 Example 4.1: Miner’s Rule 934.2.1 Acceleration Factor Modification of Miner’s Damage Rule 954.3 Assessing Thermodynamic Damage in Mechanical Systems 964.3.1 Example 4.2: Creep Cumulative Damage and Acceleration Factors 964.3.2 Example 4.3: Wear Cumulative Damage and Acceleration Factors 994.3.3 Example 4.4: Thermal Cycle Fatigue and Acceleration Factors 1014.3.4 Example 4.5: Mechanical Cycle Vibration Fatigue and Acceleration Factors 1024.3.5 Example 4.6: Cycles to Failure under a Resonance Condition: Q Effect 1054.4 Cumulative Damage Accelerated Stress Test Goal: Environmental Profiling and Cumulative Accelerated Stress Test (CAST) Equations 1074.5 Fatigue Damage Spectrum Analysis for Vibration Accelerated Testing 1084.5.1 Fatigue Damage Spectrum for Sine Vibration Accelerated Testing 1094.5.2 Fatigue Damage Spectrum for Random Vibration Accelerated Testing 110Summary 111References 1175 Corrosion Applications in NE Thermodynamic Degradation 1185.1 Corrosion Damage in Electrochemistry 1185.1.1 Example 5.1: Miner’s Rule for Secondary Batteries 1195.2 Example 5.2: Chemical Corrosion Processes 1215.2.1 Example 5.3: Numerical Example of Linear Corrosion 1235.2.2 Example 5.4: Corrosion Rate Comparison of Different Metals 1245.2.3 Thermal Arrhenius Activation and Peukert’s Law 1245.3 Corrosion Current in Primary Batteries 1265.3.1 Equilibrium Thermodynamic Condition: Nernst Equation 1275.4 Corrosion Rate in Microelectronics 1285.4.1 Corrosion and Chemical Rate Processes Due to Temperature 129Summary 130References 1336 Thermal Activation Free Energy Approach 1346.1 Free Energy Roller Coaster 1346.2 Thermally Activated Time-Dependent (TAT) Degradation Model 1356.2.1 Arrhenius Aging Due to Small Parametric Change 1366.3 Free Energy Use in Parametric Degradation and the Partition Function 1386.4 Parametric Aging at End of Life Due to the Arrhenius Mechanism: Large Parametric Change 140Summary 141References 1437 TAT Model Applications: Wear, Creep, and Transistor Aging 1447.1 Solving Physics of Failure Problems with the TAT Model 1447.2 Example 7.1: Activation Wear 1447.3 Example 7.2: Activation Creep Model 1467.4 Transistor Aging 1487.4.1 Bipolar Transistor Beta Aging Mechanism 1487.4.2 Capacitor Leakage Model for Base Leakage Current 1497.4.3 Thermally Activated Time-Dependent Model for Transistors and Dielectric Leakage 1507.4.4 Field-Effect Transistor Parameter Degradation 152Summary 154References 1568 Diffusion 1578.1 The Diffusion Process 1578.2 Example 8.1: Describing Diffusion Using Equilibrium Thermodynamics 1578.3 Describing Diffusion Using Probability 1598.4 Diffusion Acceleration Factor with and without Temperature Dependence 1618.5 Diffusion Entropy Damage 1618.5.1 Example 8.2: Package Moisture Diffusion 1628.6 General Form of the Diffusion Equation 163Summary 164Reference 1669 How Aging Laws Influence Parametric and Catastrophic Reliability Distributions 1679.1 Physics of Failure Influence on Reliability Distributions 1679.2 Log Time Aging (or Power Aging Laws) and the Lognormal Distribution 1689.3 Aging Power Laws and the Weibull Distribution: Influence on Beta 1719.4 Stress and Life Distributions 1759.4.1 Example 9.1: Cumulative Distribution Function as a Function of Stress 1769.5 Time- (or Stress-) Dependent Standard Deviation 177Summary 178References 18010 The Theory of Organization: Final Thoughts 181Special Topics A: Key Reliability Statistics 183A.1 Introduction 183A.1.1 Reliability and Accelerated Testing Software to Aid the Reader 183A.2 The Key Reliability Functions 184A.3 More Information on the Failure Rate 186A.4 The Bathtub Curve and Reliability Distributions 187A.4.1 Exponential Distribution 188A.4.2 Weibull Distribution 190A.4.3 Normal (Gaussian) Distribution 191A.4.4 The Lognormal Reliability Function 194A.5 Confidence Interval for Normal Parametric Analysis 195A.5.1 Example A.4: Power Amplifier Confidence Interval 196A.6 Central Limit Theorem and Cpk Analysis 197A.6.1 Cpk Analysis 197A.6.2 Example A.5: Cpk and Yield for the Power Amplifiers 197A.7 Catastrophic Analysis 199A.7.1 Censored Data 199A.7.2 Example A.6: Weibull and Lognormal Analysis of Semiconductors 199A.7.3 Example A.7: Mixed Modal Analysis Inflection Point Method 201A.8 Reliability Objectives and Confidence Testing 203A.8.1 Chi-Squared Confidence Test Planning for Few Failures: The Exponential Case 204A.8.2 Example A.8: Chi-Squared Accelerated Test Plan 205A.9 Comprehensive Accelerated Test Planning 205References 206Special Topics B: Applications to Accelerated Testing 207B.1 Introduction 207B.1.1 Reliability and Accelerated Testing Software to Aid the Reader 208B.1.2 Using the Arrhenius Acceleration Model for Temperature 209B.1.3 Example B.2: Estimating the Activation Energy 211B.1.4 Example B.3: Estimating Mean Time to Failure from Life Test 212B.2 Power Law Acceleration Factors 212B.2.1 Example B.4: Generalized Power Law Acceleration Factors 214B.3 Temperature–Humidity Life Test Model 214B.3.1 Temperature–Humidity Bias and Local Relative Humidity 215B.4 Temperature Cycle Testing 216B.4.1 Example B.6: Using the Temperature Cycle Model 217B.5 Vibration Acceleration 217B.5.1 Example B.7: Accelerated Testing Using Sine and Random Vibration 220B.6 Multiple-Stress Accelerated Test Plans for Demonstrating Reliability 220B.6.1 Example B.8: Designing Multi-Accelerated Tests Plans: Failure-Free 221B.7 Cumulative Accelerated Stress Test (CAST) Goals and Equations Usage in Environmental Profiling 222B.7.1 Example B.9: Cumulative Accelerated Stress Test (CAST) Goals and Equation in Environmental Profiling 222References 223Special Topics C: Negative Entropy and the Perfect Human Engine 224C.1 Spontaneous Negative Entropy: Growth and Repair 224C.2 The Perfect Human Engine: How to Live Longer 225C.2.1 Differences and Similarities of the Human Engine to Other Systems 226C.2.2 Knowledge of Cyclic Work to Improve Our Chances of a Longer Life 226C.2.3 Example C.1: Exercise and the Human Heart Life Cycle 228C.3 Growth and Self-Repair Part of the Human Engine 229C.3.1 Example C.2: Work for Human Repair 230C.4 Act of Spontaneous Negative Entropy 231C.4.1 Repair Aging Rate: An RC Electrical Model 232References 233Overview of New Terms, Equations, and Concepts 234Index 236

Alec Feinberg, DfR Software Company, Raleigh, NC, USA Dr. Feinberg has a Ph.D. in Physics and provides engineering services in all areas of reliability. He also provides consultancy services for: Reliability Test and Analysis, Accelerated Testing, HALT, FMEA, Quality statistics, corrosion analysis and Thermodynamic Modeling. Alec has presented numerous technical papers and won the 2003 RAMS Alan O. Plait best tutorial award for the topic, Thermodynamic Reliability Engineering.

• List of Figures xiiiList of Tables xviAbout the Author xviiPreface xviii1 Equilibrium Thermodynamic Degradation Science 11.1 Introduction to a New Science 11.2 Categorizing Physics of Failure Mechanisms 21.3 Entropy Damage Concept 31.3.1 The System (Device) and its Environment 41.3.2 Irreversible Thermodynamic Processes Cause Damage 51.4 Thermodynamic Work 61.5 Thermodynamic State Variables and their Characteristics 71.6 Thermodynamic Second Law in Terms of System Entropy Damage 91.6.1 Thermodynamic Entropy Damage Axiom 111.6.2 Entropy and Free Energy 131.7 Work, Resistance, Generated Entropy, and the Second Law 141.8 Thermodynamic Catastrophic and Parametric Failure 161.8.1 Equilibrium and Non-Equilibrium Aging States in Terms of the Free Energy or Entropy Change 161.9 Repair Entropy 171.9.1 Example 1.1: Repair Entropy: Relating Non-Damage Entropy Flow to Entropy Damage 17Summary 18References 222 Applications of Equilibrium Thermodynamic Degradation to Complex and Simple Systems: Entropy Damage, Vibration, Temperature, Noise Analysis, and Thermodynamic Potentials 232.1 Cumulative Entropy Damage Approach in Physics of Failure 232.1.1 Example 2.1: Miner’s Rule Derivation 252.1.2 Example 2.2: Miner’s Rule Example 262.1.3 Non-Cyclic Applications of Cumulative Damage 272.2 Measuring Entropy Damage Processes 272.3 Intermediate Thermodynamic Aging States and Sampling 292.4 Measures for System-Level Entropy Damage 292.4.1 Measuring System Entropy Damage with Temperature 292.4.2 Example 2.3: Resistor Aging 302.4.3 Example 2.4: Complex Resistor Bank 312.4.4 System Entropy Damage with Temperature Observations 322.4.5 Example 2.5: Temperature Aging of an Operating System 322.4.6 Comment on High-Temperature Aging for Operating and Non-Operating Systems 322.5 Measuring Randomness due to System Entropy Damage with Mesoscopic Noise Analysis in an Operating System 332.5.1 Example 2.6: Gaussian Noise Vibration Damage 352.5.2 Example 2.7: System Vibration Damage Observed with Noise Analysis 362.6 How System Entropy Damage Leads to Random Processes 372.6.1 Stationary versus Non-Stationary Entropy Process 402.7 Example 2.8: Human Heart Rate Noise Degradation 412.8 Entropy Damage Noise Assessment Using Autocorrelation and the Power Spectral Density 422.8.1 Noise Measurements Rules of Thumb for the PSD and R 432.8.2 Literature Review of Traditional Noise Measurement 442.8.3 Literature Review for Resistor Noise 482.9 Noise Detection Measurement System 482.9.1 System Noise Temperature 492.9.2 Environmental Noise Due to Pollution 502.9.3 Measuring System Entropy Damage using Failure Rate 502.10 Entropy Maximize Principle: Combined First and Second Law 512.10.1 Example 2.9: Thermal Equilibrium 522.10.2 Example 2.10: Equilibrium with Charge Exchange 532.10.3 Example 2.11: Diffusion Equilibrium 552.10.4 Example 2.12: Available Work 552.11 Thermodynamic Potentials and Energy States 572.11.1 The Helmholtz Free Energy 582.11.2 The Enthalpy Energy State 602.11.3 The Gibbs Free Energy 602.11.4 Summary of Common Thermodynamic State Energies 622.11.5 Example 2.13: Work, Entropy Damage, and Free Energy Change 622.11.6 Example 2.14: System in Contact with a Reservoir 65Summary 68References 763 NE Thermodynamic Degradation Science Assessment Using the Work Concept 773.1 Equilibrium versus Non-Equilibrium Aging Approach 773.1.1 Conjugate Work and Free Energy Approach to Understanding Non-Equilibrium Thermodynamic Degradation 783.2 Application to Cyclic Work and Cumulative Damage 793.3 Cyclic Work Process, Heat Engines, and the Carnot Cycle 813.4 Example 3.1: Cyclic Engine Damage Quantified Using Efficiency 843.5 The Thermodynamic Damage Ratio Method for Tracking Degradation 863.6 Acceleration Factors from the Damage Ratio Principle 87Summary 89References 924 Applications of NE Thermodynamic Degradation Science to Mechanical Systems: Accelerated Test and CAST Equations, Miner’s Rule, and FDS 934.1 Thermodynamic Work Approach to Physics of Failure Problems 934.2 Example 4.1: Miner’s Rule 934.2.1 Acceleration Factor Modification of Miner’s Damage Rule 954.3 Assessing Thermodynamic Damage in Mechanical Systems 964.3.1 Example 4.2: Creep Cumulative Damage and Acceleration Factors 964.3.2 Example 4.3: Wear Cumulative Damage and Acceleration Factors 994.3.3 Example 4.4: Thermal Cycle Fatigue and Acceleration Factors 1014.3.4 Example 4.5: Mechanical Cycle Vibration Fatigue and Acceleration Factors 1024.3.5 Example 4.6: Cycles to Failure under a Resonance Condition: Q Effect 1054.4 Cumulative Damage Accelerated Stress Test Goal: Environmental Profiling and Cumulative Accelerated Stress Test (CAST) Equations 1074.5 Fatigue Damage Spectrum Analysis for Vibration Accelerated Testing 1084.5.1 Fatigue Damage Spectrum for Sine Vibration Accelerated Testing 1094.5.2 Fatigue Damage Spectrum for Random Vibration Accelerated Testing 110Summary 111References 1175 Corrosion Applications in NE Thermodynamic Degradation 1185.1 Corrosion Damage in Electrochemistry 1185.1.1 Example 5.1: Miner’s Rule for Secondary Batteries 1195.2 Example 5.2: Chemical Corrosion Processes 1215.2.1 Example 5.3: Numerical Example of Linear Corrosion 1235.2.2 Example 5.4: Corrosion Rate Comparison of Different Metals 1245.2.3 Thermal Arrhenius Activation and Peukert’s Law 1245.3 Corrosion Current in Primary Batteries 1265.3.1 Equilibrium Thermodynamic Condition: Nernst Equation 1275.4 Corrosion Rate in Microelectronics 1285.4.1 Corrosion and Chemical Rate Processes Due to Temperature 129Summary 130References 1336 Thermal Activation Free Energy Approach 1346.1 Free Energy Roller Coaster 1346.2 Thermally Activated Time-Dependent (TAT) Degradation Model 1356.2.1 Arrhenius Aging Due to Small Parametric Change 1366.3 Free Energy Use in Parametric Degradation and the Partition Function 1386.4 Parametric Aging at End of Life Due to the Arrhenius Mechanism: Large Parametric Change 140Summary 141References 1437 TAT Model Applications: Wear, Creep, and Transistor Aging 1447.1 Solving Physics of Failure Problems with the TAT Model 1447.2 Example 7.1: Activation Wear 1447.3 Example 7.2: Activation Creep Model 1467.4 Transistor Aging 1487.4.1 Bipolar Transistor Beta Aging Mechanism 1487.4.2 Capacitor Leakage Model for Base Leakage Current 1497.4.3 Thermally Activated Time-Dependent Model for Transistors and Dielectric Leakage 1507.4.4 Field-Effect Transistor Parameter Degradation 152Summary 154References 1568 Diffusion 1578.1 The Diffusion Process 1578.2 Example 8.1: Describing Diffusion Using Equilibrium Thermodynamics 1578.3 Describing Diffusion Using Probability 1598.4 Diffusion Acceleration Factor with and without Temperature Dependence 1618.5 Diffusion Entropy Damage 1618.5.1 Example 8.2: Package Moisture Diffusion 1628.6 General Form of the Diffusion Equation 163Summary 164Reference 1669 How Aging Laws Influence Parametric and Catastrophic Reliability Distributions 1679.1 Physics of Failure Influence on Reliability Distributions 1679.2 Log Time Aging (or Power Aging Laws) and the Lognormal Distribution 1689.3 Aging Power Laws and the Weibull Distribution: Influence on Beta 1719.4 Stress and Life Distributions 1759.4.1 Example 9.1: Cumulative Distribution Function as a Function of Stress 1769.5 Time- (or Stress-) Dependent Standard Deviation 177Summary 178References 18010 The Theory of Organization: Final Thoughts 181Special Topics A: Key Reliability Statistics 183A.1 Introduction 183A.1.1 Reliability and Accelerated Testing Software to Aid the Reader 183A.2 The Key Reliability Functions 184A.3 More Information on the Failure Rate 186A.4 The Bathtub Curve and Reliability Distributions 187A.4.1 Exponential Distribution 188A.4.2 Weibull Distribution 190A.4.3 Normal (Gaussian) Distribution 191A.4.4 The Lognormal Reliability Function 194A.5 Confidence Interval for Normal Parametric Analysis 195A.5.1 Example A.4: Power Amplifier Confidence Interval 196A.6 Central Limit Theorem and Cpk Analysis 197A.6.1 Cpk Analysis 197A.6.2 Example A.5: Cpk and Yield for the Power Amplifiers 197A.7 Catastrophic Analysis 199A.7.1 Censored Data 199A.7.2 Example A.6: Weibull and Lognormal Analysis of Semiconductors 199A.7.3 Example A.7: Mixed Modal Analysis Inflection Point Method 201A.8 Reliability Objectives and Confidence Testing 203A.8.1 Chi-Squared Confidence Test Planning for Few Failures: The Exponential Case 204A.8.2 Example A.8: Chi-Squared Accelerated Test Plan 205A.9 Comprehensive Accelerated Test Planning 205References 206Special Topics B: Applications to Accelerated Testing 207B.1 Introduction 207B.1.1 Reliability and Accelerated Testing Software to Aid the Reader 208B.1.2 Using the Arrhenius Acceleration Model for Temperature 209B.1.3 Example B.2: Estimating the Activation Energy 211B.1.4 Example B.3: Estimating Mean Time to Failure from Life Test 212B.2 Power Law Acceleration Factors 212B.2.1 Example B.4: Generalized Power Law Acceleration Factors 214B.3 Temperature–Humidity Life Test Model 214B.3.1 Temperature–Humidity Bias and Local Relative Humidity 215B.4 Temperature Cycle Testing 216B.4.1 Example B.6: Using the Temperature Cycle Model 217B.5 Vibration Acceleration 217B.5.1 Example B.7: Accelerated Testing Using Sine and Random Vibration 220B.6 Multiple-Stress Accelerated Test Plans for Demonstrating Reliability 220B.6.1 Example B.8: Designing Multi-Accelerated Tests Plans: Failure-Free 221B.7 Cumulative Accelerated Stress Test (CAST) Goals and Equations Usage in Environmental Profiling 222B.7.1 Example B.9: Cumulative Accelerated Stress Test (CAST) Goals and Equation in Environmental Profiling 222References 223Special Topics C: Negative Entropy and the Perfect Human Engine 224C.1 Spontaneous Negative Entropy: Growth and Repair 224C.2 The Perfect Human Engine: How to Live Longer 225C.2.1 Differences and Similarities of the Human Engine to Other Systems 226C.2.2 Knowledge of Cyclic Work to Improve Our Chances of a Longer Life 226C.2.3 Example C.1: Exercise and the Human Heart Life Cycle 228C.3 Growth and Self-Repair Part of the Human Engine 229C.3.1 Example C.2: Work for Human Repair 230C.4 Act of Spontaneous Negative Entropy 231C.4.1 Repair Aging Rate: An RC Electrical Model 232References 233Overview of New Terms, Equations, and Concepts 234Index 236

Alec Feinberg, DfR Software Company, Raleigh, NC, USA Dr. Feinberg has a Ph.D. in Physics and provides engineering services in all areas of reliability. He also provides consultancy services for: Reliability Test and Analysis, Accelerated Testing, HALT, FMEA, Quality statistics, corrosion analysis and Thermodynamic Modeling. Alec has presented numerous technical papers and won the 2003 RAMS Alan O. Plait best tutorial award for the topic, Thermodynamic Reliability Engineering.

• List of Figures xiiiList of Tables xviAbout the Author xviiPreface xviii1 Equilibrium Thermodynamic Degradation Science 11.1 Introduction to a New Science 11.2 Categorizing Physics of Failure Mechanisms 21.3 Entropy Damage Concept 31.3.1 The System (Device) and its Environment 41.3.2 Irreversible Thermodynamic Processes Cause Damage 51.4 Thermodynamic Work 61.5 Thermodynamic State Variables and their Characteristics 71.6 Thermodynamic Second Law in Terms of System Entropy Damage 91.6.1 Thermodynamic Entropy Damage Axiom 111.6.2 Entropy and Free Energy 131.7 Work, Resistance, Generated Entropy, and the Second Law 141.8 Thermodynamic Catastrophic and Parametric Failure 161.8.1 Equilibrium and Non-Equilibrium Aging States in Terms of the Free Energy or Entropy Change 161.9 Repair Entropy 171.9.1 Example 1.1: Repair Entropy: Relating Non-Damage Entropy Flow to Entropy Damage 17Summary 18References 222 Applications of Equilibrium Thermodynamic Degradation to Complex and Simple Systems: Entropy Damage, Vibration, Temperature, Noise Analysis, and Thermodynamic Potentials 232.1 Cumulative Entropy Damage Approach in Physics of Failure 232.1.1 Example 2.1: Miner’s Rule Derivation 252.1.2 Example 2.2: Miner’s Rule Example 262.1.3 Non-Cyclic Applications of Cumulative Damage 272.2 Measuring Entropy Damage Processes 272.3 Intermediate Thermodynamic Aging States and Sampling 292.4 Measures for System-Level Entropy Damage 292.4.1 Measuring System Entropy Damage with Temperature 292.4.2 Example 2.3: Resistor Aging 302.4.3 Example 2.4: Complex Resistor Bank 312.4.4 System Entropy Damage with Temperature Observations 322.4.5 Example 2.5: Temperature Aging of an Operating System 322.4.6 Comment on High-Temperature Aging for Operating and Non-Operating Systems 322.5 Measuring Randomness due to System Entropy Damage with Mesoscopic Noise Analysis in an Operating System 332.5.1 Example 2.6: Gaussian Noise Vibration Damage 352.5.2 Example 2.7: System Vibration Damage Observed with Noise Analysis 362.6 How System Entropy Damage Leads to Random Processes 372.6.1 Stationary versus Non-Stationary Entropy Process 402.7 Example 2.8: Human Heart Rate Noise Degradation 412.8 Entropy Damage Noise Assessment Using Autocorrelation and the Power Spectral Density 422.8.1 Noise Measurements Rules of Thumb for the PSD and R 432.8.2 Literature Review of Traditional Noise Measurement 442.8.3 Literature Review for Resistor Noise 482.9 Noise Detection Measurement System 482.9.1 System Noise Temperature 492.9.2 Environmental Noise Due to Pollution 502.9.3 Measuring System Entropy Damage using Failure Rate 502.10 Entropy Maximize Principle: Combined First and Second Law 512.10.1 Example 2.9: Thermal Equilibrium 522.10.2 Example 2.10: Equilibrium with Charge Exchange 532.10.3 Example 2.11: Diffusion Equilibrium 552.10.4 Example 2.12: Available Work 552.11 Thermodynamic Potentials and Energy States 572.11.1 The Helmholtz Free Energy 582.11.2 The Enthalpy Energy State 602.11.3 The Gibbs Free Energy 602.11.4 Summary of Common Thermodynamic State Energies 622.11.5 Example 2.13: Work, Entropy Damage, and Free Energy Change 622.11.6 Example 2.14: System in Contact with a Reservoir 65Summary 68References 763 NE Thermodynamic Degradation Science Assessment Using the Work Concept 773.1 Equilibrium versus Non-Equilibrium Aging Approach 773.1.1 Conjugate Work and Free Energy Approach to Understanding Non-Equilibrium Thermodynamic Degradation 783.2 Application to Cyclic Work and Cumulative Damage 793.3 Cyclic Work Process, Heat Engines, and the Carnot Cycle 813.4 Example 3.1: Cyclic Engine Damage Quantified Using Efficiency 843.5 The Thermodynamic Damage Ratio Method for Tracking Degradation 863.6 Acceleration Factors from the Damage Ratio Principle 87Summary 89References 924 Applications of NE Thermodynamic Degradation Science to Mechanical Systems: Accelerated Test and CAST Equations, Miner’s Rule, and FDS 934.1 Thermodynamic Work Approach to Physics of Failure Problems 934.2 Example 4.1: Miner’s Rule 934.2.1 Acceleration Factor Modification of Miner’s Damage Rule 954.3 Assessing Thermodynamic Damage in Mechanical Systems 964.3.1 Example 4.2: Creep Cumulative Damage and Acceleration Factors 964.3.2 Example 4.3: Wear Cumulative Damage and Acceleration Factors 994.3.3 Example 4.4: Thermal Cycle Fatigue and Acceleration Factors 1014.3.4 Example 4.5: Mechanical Cycle Vibration Fatigue and Acceleration Factors 1024.3.5 Example 4.6: Cycles to Failure under a Resonance Condition: Q Effect 1054.4 Cumulative Damage Accelerated Stress Test Goal: Environmental Profiling and Cumulative Accelerated Stress Test (CAST) Equations 1074.5 Fatigue Damage Spectrum Analysis for Vibration Accelerated Testing 1084.5.1 Fatigue Damage Spectrum for Sine Vibration Accelerated Testing 1094.5.2 Fatigue Damage Spectrum for Random Vibration Accelerated Testing 110Summary 111References 1175 Corrosion Applications in NE Thermodynamic Degradation 1185.1 Corrosion Damage in Electrochemistry 1185.1.1 Example 5.1: Miner’s Rule for Secondary Batteries 1195.2 Example 5.2: Chemical Corrosion Processes 1215.2.1 Example 5.3: Numerical Example of Linear Corrosion 1235.2.2 Example 5.4: Corrosion Rate Comparison of Different Metals 1245.2.3 Thermal Arrhenius Activation and Peukert’s Law 1245.3 Corrosion Current in Primary Batteries 1265.3.1 Equilibrium Thermodynamic Condition: Nernst Equation 1275.4 Corrosion Rate in Microelectronics 1285.4.1 Corrosion and Chemical Rate Processes Due to Temperature 129Summary 130References 1336 Thermal Activation Free Energy Approach 1346.1 Free Energy Roller Coaster 1346.2 Thermally Activated Time-Dependent (TAT) Degradation Model 1356.2.1 Arrhenius Aging Due to Small Parametric Change 1366.3 Free Energy Use in Parametric Degradation and the Partition Function 1386.4 Parametric Aging at End of Life Due to the Arrhenius Mechanism: Large Parametric Change 140Summary 141References 1437 TAT Model Applications: Wear, Creep, and Transistor Aging 1447.1 Solving Physics of Failure Problems with the TAT Model 1447.2 Example 7.1: Activation Wear 1447.3 Example 7.2: Activation Creep Model 1467.4 Transistor Aging 1487.4.1 Bipolar Transistor Beta Aging Mechanism 1487.4.2 Capacitor Leakage Model for Base Leakage Current 1497.4.3 Thermally Activated Time-Dependent Model for Transistors and Dielectric Leakage 1507.4.4 Field-Effect Transistor Parameter Degradation 152Summary 154References 1568 Diffusion 1578.1 The Diffusion Process 1578.2 Example 8.1: Describing Diffusion Using Equilibrium Thermodynamics 1578.3 Describing Diffusion Using Probability 1598.4 Diffusion Acceleration Factor with and without Temperature Dependence 1618.5 Diffusion Entropy Damage 1618.5.1 Example 8.2: Package Moisture Diffusion 1628.6 General Form of the Diffusion Equation 163Summary 164Reference 1669 How Aging Laws Influence Parametric and Catastrophic Reliability Distributions 1679.1 Physics of Failure Influence on Reliability Distributions 1679.2 Log Time Aging (or Power Aging Laws) and the Lognormal Distribution 1689.3 Aging Power Laws and the Weibull Distribution: Influence on Beta 1719.4 Stress and Life Distributions 1759.4.1 Example 9.1: Cumulative Distribution Function as a Function of Stress 1769.5 Time- (or Stress-) Dependent Standard Deviation 177Summary 178References 18010 The Theory of Organization: Final Thoughts 181Special Topics A: Key Reliability Statistics 183A.1 Introduction 183A.1.1 Reliability and Accelerated Testing Software to Aid the Reader 183A.2 The Key Reliability Functions 184A.3 More Information on the Failure Rate 186A.4 The Bathtub Curve and Reliability Distributions 187A.4.1 Exponential Distribution 188A.4.2 Weibull Distribution 190A.4.3 Normal (Gaussian) Distribution 191A.4.4 The Lognormal Reliability Function 194A.5 Confidence Interval for Normal Parametric Analysis 195A.5.1 Example A.4: Power Amplifier Confidence Interval 196A.6 Central Limit Theorem and Cpk Analysis 197A.6.1 Cpk Analysis 197A.6.2 Example A.5: Cpk and Yield for the Power Amplifiers 197A.7 Catastrophic Analysis 199A.7.1 Censored Data 199A.7.2 Example A.6: Weibull and Lognormal Analysis of Semiconductors 199A.7.3 Example A.7: Mixed Modal Analysis Inflection Point Method 201A.8 Reliability Objectives and Confidence Testing 203A.8.1 Chi-Squared Confidence Test Planning for Few Failures: The Exponential Case 204A.8.2 Example A.8: Chi-Squared Accelerated Test Plan 205A.9 Comprehensive Accelerated Test Planning 205References 206Special Topics B: Applications to Accelerated Testing 207B.1 Introduction 207B.1.1 Reliability and Accelerated Testing Software to Aid the Reader 208B.1.2 Using the Arrhenius Acceleration Model for Temperature 209B.1.3 Example B.2: Estimating the Activation Energy 211B.1.4 Example B.3: Estimating Mean Time to Failure from Life Test 212B.2 Power Law Acceleration Factors 212B.2.1 Example B.4: Generalized Power Law Acceleration Factors 214B.3 Temperature–Humidity Life Test Model 214B.3.1 Temperature–Humidity Bias and Local Relative Humidity 215B.4 Temperature Cycle Testing 216B.4.1 Example B.6: Using the Temperature Cycle Model 217B.5 Vibration Acceleration 217B.5.1 Example B.7: Accelerated Testing Using Sine and Random Vibration 220B.6 Multiple-Stress Accelerated Test Plans for Demonstrating Reliability 220B.6.1 Example B.8: Designing Multi-Accelerated Tests Plans: Failure-Free 221B.7 Cumulative Accelerated Stress Test (CAST) Goals and Equations Usage in Environmental Profiling 222B.7.1 Example B.9: Cumulative Accelerated Stress Test (CAST) Goals and Equation in Environmental Profiling 222References 223Special Topics C: Negative Entropy and the Perfect Human Engine 224C.1 Spontaneous Negative Entropy: Growth and Repair 224C.2 The Perfect Human Engine: How to Live Longer 225C.2.1 Differences and Similarities of the Human Engine to Other Systems 226C.2.2 Knowledge of Cyclic Work to Improve Our Chances of a Longer Life 226C.2.3 Example C.1: Exercise and the Human Heart Life Cycle 228C.3 Growth and Self-Repair Part of the Human Engine 229C.3.1 Example C.2: Work for Human Repair 230C.4 Act of Spontaneous Negative Entropy 231C.4.1 Repair Aging Rate: An RC Electrical Model 232References 233Overview of New Terms, Equations, and Concepts 234Index 236