Preface xiii -- List of Abbreviations xvii -- 1. Introduction 1 -- 2. Initial Considerations for Reliability Design 3 -- 2.1 The Challenge 3 -- 2.2 Initial Data Collection 3 -- 2.3 Where Do We Get MTBF Information? 5 -- 2.4 MTTR and Identifying Failures 6 -- 2.5 Summary 7 -- 3. A Game of Dice: An Introduction to Probability 8 -- 3.1 Introduction 8 -- 3.2 A Game of Dice 10 -- 3.3 Mutually Exclusive and Independent Events 10 -- 3.4 Dice Paradox Problem and Conditional Probability 15 -- 3.5 Flip a Coin 21 -- 3.6 Dice Paradox Revisited 23 -- 3.7 Probabilities for Multiple Dice Throws 24 -- 3.8 Conditional Probability Revisited 27 -- 3.9 Summary 29 -- 4. Discrete Random Variables 30 -- 4.1 Introduction 30 -- 4.2 Random Variables 31 -- 4.3 Discrete Probability Distributions 33 -- 4.4 Bernoulli Distribution 34 -- 4.5 Geometric Distribution 35 -- 4.6 Binomial Coeffi cients 38 -- 4.7 Binomial Distribution 40 -- 4.8 Poisson Distribution 43 -- 4.9 Negative Binomial Random Variable 48 -- 4.10 Summary 50 -- 5. Continuous Random Variables 51 -- 5.1 Introduction 51 -- 5.2 Uniform Random Variables 52 -- 5.3 Exponential Random Variables 53 -- 5.4 Weibull Random Variables 54 -- 5.5 Gamma Random Variables 55 -- 5.6 Chi-Square Random Variables 59 -- 5.7 Normal Random Variables 59 -- 5.8 Relationship between Random Variables 60 -- 5.9 Summary 61 -- 6. Random Processes 62 -- 6.1 Introduction 62 -- 6.2 Markov Process 63 -- 6.3 Poisson Process 63 -- 6.4 Deriving the Poisson Distribution 64 -- 6.5 Poisson Interarrival Times 69 -- 6.6 Summary 71 -- 7. Modeling and Reliability Basics 72 -- 7.1 Introduction 72 -- 7.2 Modeling 75 -- 7.3 Failure Probability and Failure Density 77 -- 7.4 Unreliability, F(t) 78 -- 7.5 Reliability, R(t) 79 -- 7.6 MTTF 79 -- 7.7 MTBF 79 -- 7.8 Repairable System 80 -- 7.9 Nonrepairable System 80 -- 7.10 MTTR 80 -- 7.11 Failure Rate 81 -- 7.12 Maintainability 81 -- 7.13 Operability 81 -- 7.14 Availability 82 -- 7.15 Unavailability 84 -- 7.16 Five 9s Availability 85.

7.17 Downtime 85 -- 7.18 Constant Failure Rate Model 85 -- 7.19 Conditional Failure Rate 88 -- 7.20 Bayes's Theorem 94 -- 7.21 Reliability Block Diagrams 98 -- 7.22 Summary 107 -- 8. Discrete-Time Markov Analysis 110 -- 8.1 Introduction 110 -- 8.2 Markov Process Defined 112 -- 8.3 Dynamic Modeling 116 -- 8.4 Discrete Time Markov Chains 116 -- 8.5 Absorbing Markov Chains 123 -- 8.6 Nonrepairable Reliability Models 129 -- 8.7 Summary 140 -- 9. Continuous-Time Markov Systems 141 -- 9.1 Introduction 141 -- 9.2 Continuous-Time Markov Processes 141 -- 9.3 Two-State Derivation 143 -- 9.4 Steps to Create a Markov Reliability Model 147 -- 9.5 Asymptotic Behavior (Steady-State Behavior) 148 -- 9.6 Limitations of Markov Modeling 154 -- 9.7 Markov Reward Models 154 -- 9.8 Summary 155 -- 10. Markov Analysis: Nonrepairable Systems 156 -- 10.1 Introduction 156 -- 10.2 One Component, No Repair 156 -- 10.3 Nonrepairable Systems: Parallel System with No Repair 165 -- 10.4 Series System with No Repair: Two Identical Components 172 -- 10.5 Parallel System with Partial Repair: Identical Components 176 -- 10.6 Parallel System with No Repair: Nonidentical Components 183 -- 10.7 Summary 192 -- 11. Markov Analysis: Repairable Systems 193 -- 11.1 Repairable Systems 193 -- 11.2 One Component with Repair 194 -- 11.3 Parallel System with Repair: Identical Component Failure and Repair Rates 204 -- 11.4 Parallel System with Repair: Different Failure and Repair Rates 217 -- 11.5 Summary 239 -- 12. Analyzing Confidence Levels 240 -- 12.1 Introduction 240 -- 12.2 pdf of a Squared Normal Random Variable 240 -- 12.3 pdf of the Sum of Two Random Variables 243 -- 12.4 pdf of the Sum of Two Gamma Random Variables 245 -- 12.5 pdf of the Sum of n Gamma Random Variables 246 -- 12.6 Goodness-of-Fit Test Using Chi-Square 249 -- 12.7 Confidence Levels 257 -- 12.8 Summary 264 -- 13. Estimating Reliability Parameters 266 -- 13.1 Introduction 266 -- 13.2 Bayes' Estimation 268 -- 13.3 Example of Estimating Hardware MTBF 273.

13.4 Estimating Software MTBF 273 -- 13.5 Revising Initial MTBF Estimates and Tradeoffs 274 -- 13.6 Summary 277 -- 14. Six Sigma Tools for Predictive Engineering 278 -- 14.1 Introduction 278 -- 14.2 Gathering Voice of Customer (VOC) 279 -- 14.3 Processing Voice of Customer 281 -- 14.4 Kano Analysis 282 -- 14.5 Analysis of Technical Risks 284 -- 14.6 Quality Function Deployment (QFD) or House of Quality 284 -- 14.7 Program Level Transparency of Critical Parameters 287 -- 14.8 Mapping DFSS Techniques to Critical Parameters 287 -- 14.9 Critical Parameter Management (CPM) 287 -- 14.10 First Principles Modeling 289 -- 14.11 Design of Experiments (DOE) 289 -- 14.12 Design Failure Modes and Effects Analysis (DFMEA) 289 -- 14.13 Fault Tree Analysis 290 -- 14.14 Pugh Matrix 290 -- 14.15 Monte Carlo Simulation 291 -- 14.16 Commercial DFSS Tools 291 -- 14.17 Mathematical Prediction of System Capability instead of “Gut Feel” 293 -- 14.18 Visualizing System Behavior Early in the Life Cycle 297 -- 14.19 Critical Parameter Scorecard 297 -- 14.20 Applying DFSS in Third-Party Intensive Programs 298 -- 14.21 Summary 300 -- 15. Design Failure Modes and Effects Analysis 302 -- 15.1 Introduction 302 -- 15.2 What Is Design Failure Modes and Effects Analysis (DFMEA)? 302 -- 15.3 Definitions 303 -- 15.4 Business Case for DFMEA 303 -- 15.5 Why Conduct DFMEA? 305 -- 15.6 When to Perform DFMEA 305 -- 15.7 Applicability of DFMEA 306 -- 15.8 DFMEA Template 306 -- 15.9 DFMEA Life Cycle 312 -- 15.10 The DFMEA Team 324 -- 15.11 DFMEA Advantages and Disadvantages 327 -- 15.12 Limitations of DFMEA 328 -- 15.13 DFMEAs, FTAs, and Reliability Analysis 328 -- 15.14 Summary 330 -- 16. Fault Tree Analysis 331 -- 16.1 What Is Fault Tree Analysis? 331 -- 16.2 Events 332 -- 16.3 Logic Gates 333 -- 16.4 Creating a Fault Tree 335 -- 16.5 Fault Tree Limitations 339 -- 16.6 Summary 339 -- 17. Monte Carlo Simulation Models 340 -- 17.1 Introduction 340 -- 17.2 System Behavior over Mission Time 344 -- 17.3 Reliability Parameter Analysis 344.

17.4 A Worked Example 348 -- 17.5 Component and System Failure Times Using Monte Carlo Simulations 359 -- 17.6 Limitations of Using Nontime-Based Monte Carlo Simulations 361 -- 17.7 Summary 365 -- 18. Updating Reliability Estimates: Case Study 367 -- 18.1 Introduction 367 -- 18.2 Overview of the Base Station Controller-Data Only (BSC-DO) System 367 -- 18.3 Downtime Calculation 368 -- 18.4 Calculating Availability from Field Data Only 371 -- 18.5 Assumptions Behind Using the Chi-Square Methodology 372 -- 18.6 Fault Tree Updates from Field Data 372 -- 18.7 Summary 376 -- 19. Fault Management Architectures 377 -- 19.1 Introduction 377 -- 19.2 Faults, Errors, and Failures 378 -- 19.3 Fault Management Design 381 -- 19.4 Repair versus Recovery 382 -- 19.5 Design Considerations for Reliability Modeling 383 -- 19.6 Architecture Techniques to Improve Availability 383 -- 19.7 Redundancy Schemes 384 -- 19.8 Summary 395 -- 20 Application of DFMEA to Real-Life Example 397 -- 20.1 Introduction 397 -- 20.2 Cage Failover Architecture Description 397 -- 20.3 Cage Failover DFMEA Example 399 -- 20.4 DFMEA Scorecard 401 -- 20.5 Lessons Learned 402 -- 20.6 Summary 403 -- 21. Application of FTA to Real-Life Example 404 -- 21.1 Introduction 404 -- 21.2 Calculating Availability Using Fault Tree Analysis 404 -- 21.3 Building the Basic Events 405 -- 21.4 Building the Fault Tree 406 -- 21.5 Steps for Creating and Estimating the Availability Using FTA 408 -- 21.6 Summary 416 -- 22. Complex High Availability System Analysis 420 -- 22.1 Introduction 420 -- 22.2 Markov Analysis of the Hardware Components 420 -- 22.3 Building a Fault Tree from the Hardware Markov Model 427 -- 22.4 Markov Analysis of the Software Components 427 -- 22.5 Markov Analysis of the Combined Hardware and Software Components 433 -- 22.6 Techniques for Simplifying Markov Analysis 437 -- 22.7 Summary 446 -- References 447 -- Index 450.