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The intent of this book is to provide guidance on modeling techniques that can be used to quantify the reliability of a product or system. In this context, reliability modeling is the process of constructing a mathematical model that is used to estimate the reliability characteristics of a product.
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The intent of this book is to provide guidance on modeling techniques that can be used to quantify the reliability of a product or system. In this context, reliability modeling is the process of constructing a mathematical model that is used to estimate the reliability characteristics of a product. There are many ways in which this can be accomplished, depending on the product or system and the type of information that is available, or practical to obtain. This book reviews possible approaches, summarizes their advantages and disadvantages, and provides guidance on selecting a methodology based on the specific goals and constraints of the analyst. While this book will not discuss the use of specific published methodologies, in cases where examples are provided, tools and methodologies with which the author has personal experience in their development are used, such as life modeling, NPRD, MIL-HDBK-217 and the RIAC 217Plus methodology.
| ISBN: | 978-1-933904-18-4 |
|---|---|
| Product Format: | Download, Hardcopy |
| 1. INTRODUCTION | 1 |
| 1.1. Scope | 2 |
| 1.2. Book Organization | 5 |
| 1.3. Reliability Program Elements | 7 |
| 1.4. The History of Reliability Prediction | 11 |
| 1.5. Acronyms | 17 |
| 1.6. References | 18 |
| 2. GENERAL ASSESSMENT APPROACH | 19 |
| 2.1. Define System | 20 |
| 2.2. Identify the Purpose of the Model | 22 |
| 2.3. Determine the Appropriate Level at Which to Perform the Modeling | 25 |
| 2.3.1. Level vs. Data Needed | 26 |
| 2.3.2. Using an FMEA as the basis for a reliability model | 28 |
| 2.3.3. Model Form vs. Level | 34 |
| 2.4. Assess Data Available | 36 |
| 2.5. Determine and Execute Appropriate Approach | 38 |
| 2.5.1. Empirical | 44 |
| 2.5.1.1. Test | 44 |
| 2.5.1.2. Field Data | 77 |
| 2.5.2. Physics | 106 |
| 2.5.2.1. Stress/Strength Modeling | 106 |
| 2.5.2.2. First Principles | 111 |
| 2.6. Combine Data | 114 |
| 2.6.1. Bayesian Inference | 121 |
| 2.7. Develop System Model | 123 |
| 2.7.1. Monte Carlo Analysis | 127 |
| 2.8. References | 133 |
| 3. FUNDAMENTAL CONCEPTS | 135 |
| 3.1. Reliability Theory Concepts | 135 |
| 3.2. Probability concepts | 142 |
| 3.2.1. Covariance | 142 |
| 3.2.2. Correlation Coefficient | 142 |
| 3.2.3. Permutations and Combinations | 143 |
| 3.2.4. Mutual Exclusivity | 144 |
| 3.2.5. Independent Events | 144 |
| 3.2.6. Non‐independent (Dependent) Events | 145 |
| 3.2.7. Non‐independent (Dependent) Events: Bayes Theorem | 146 |
| 3.2.8. System Models | 146 |
| 3.2.9. K‐out‐of‐N Configurations | 151 |
| 3.3. Distributions | 153 |
| 3.3.1. Exponential | 159 |
| 3.3.2. Weibull | 160 |
| 3.3.3. Lognormal | 166 |
| 3.4. References | 169 |
| 4. DOE‐BASED APPROACHES TO RELIABILITY MODELING | 171 |
| 4.1. Determine the Feature to be Assessed | 172 |
| 4.2. Determine Factors | 172 |
| 4.3. Determine the Factor Levels | 172 |
| 4.4. Design the Tests | 174 |
| 4.5. Perform Tests and Measurements | 180 |
| 4.6. Analyze the Data | 181 |
| 4.7. Develop the Life Model | 183 |
| 4.8. References | 183 |
| 5. LIFE DATA MODELING | 185 |
| 5.1. Selecting a Distribution | 185 |
| 5.2. Parameter Estimation Overview | 186 |
| 5.2.1. Closed Form Parameter Approximations | 189 |
| 5.2.2. Least Squares Regression | 190 |
| 5.2.3. Parameter Estimation Using MLE | 192 |
| 5.2.3.1. Brief Historical Remarks | 193 |
| 5.2.3.2. Likelihood Function | 193 |
| 5.2.3.3. Maximum Likelihood Estimator (MLE) | 195 |
| 5.2.4. Confidence Bounds and Uncertainty | 198 |
| 5.2.4.1. Confidence Bounds with MLE | 198 |
| 5.2.4.2. Confidence Bounds Approximations | 199 |
| 5.3. Acceleration Models | 206 |
| 5.3.1. Fundamental Acceleration Models | 207 |
| 5.3.1.1. Examples | 208 |
| 5.3.2. Combined Models | 210 |
| 5.3.3. Cumulative Damage Model | 214 |
| 5.4. MLE Equations | 216 |
| 5.4.1. Likelihood Functions | 217 |
| 5.5. References | 221 |
| 6. INTERPRETATION OF RELIABILITY ESTIMATES | 223 |
| 6.1. Bathtub Curve | 223 |
| 6.2. Common Cause vs. Special Cause | 225 |
| 6.3. Confidence Bounds | 238 |
| 6.3.1. Traditional Techniques for Confidence Bounds | 238 |
| 6.3.2. Uncertainty in Reliability Prediction Estimates | 240 |
| 6.4. Failure Rate vs pdf | 243 |
| 6.5. Practical Aspects of Reliability Assessments | 245 |
| 6.6. Weibayes | 245 |
| 6.7. Weibull Closure Property | 246 |
| 6.8. Estimating Event‐Related Reliability | 247 |
| 6.9. Combining Different Types of Assessments at Different Levels | 248 |
| 6.10. Estimating the Number of Failures | 250 |
| 6.11. Calculation of Equivalent Failure Rates | 251 |
| 6.12. Failure Rate Units | 252 |
| 6.13. Factors to be Considered When Developing Models | 253 |
| 6.13.1. Causes of Electronic System Failure | 253 |
| 6.13.2. Selection of Factors | 255 |
| 6.13.3. Reliability Growth of Components | 257 |
| 6.13.4. Relative vs. Absolute Humidity | 259 |
| 6.14. Addressing Data with No Failures | 259 |
| 6.15. Reliability of Components Used Outside of Their Rating | 261 |
| 6.16. References | 262 |
| 7. EXAMPLES | 263 |
| 7.1. MIL‐HDBK‐217 Model Development Methodology | 264 |
| 7.1.1. Identify Possible Variables | 266 |
| 7.1.2. Develop Theoretical Model | 266 |
| 7.1.3. Collect and QC Data | 267 |
| 7.1.4. Correlation Coefficient Analysis | 268 |
| 7.1.5. Stepwise Multiple Regression Analysis | 270 |
| 7.1.6. Goodness‐of‐Fit Analysis | 271 |
| 7.1.7. Extreme Case Analysis | 272 |
| 7.1.8. Model Validation | 272 |
| 7.2. 217Plus Reliability Prediction Models | 273 |
| 7.2.1. Background | 273 |
| 7.2.2. System Reliability Prediction Model | 274 |
| 7.2.2.1. 217Plus Background | 274 |
| 7.2.2.2. Methodology Overview | 277 |
| 7.2.2.3. System Reliability Model | 278 |
| 7.2.2.4. Initial Failure Rate Estimate | 279 |
| 7.2.2.5. Process Grading Factors | 280 |
| 7.2.2.6. Basis Data for the Model | 281 |
| 7.2.2.7. Uncertainty in Traditional Approach Estimates | 281 |
| 7.2.2.8. System Failure Causes | 282 |
| 7.2.2.9. Environmental Factor | 287 |
| 7.2.2.10. Reliability Growth | 291 |
| 7.2.2.11. Infant Mortality | 292 |
| 7.2.2.12. Combining Predicted Failure Rate with Empirical Data | 292 |
| 7.2.3. Development of Component Reliability Models | 292 |
| 7.2.3.1. Model Form | 292 |
| 7.2.3.2. Acceleration Factors | 294 |
| 7.2.3.3. Time Basis of Models | 294 |
| 7.2.3.4. Failure Mode to Failure Cause Mapping | 295 |
| 7.2.3.5. Derivation of Base Failure Rates | 296 |
| 7.2.3.6. Combining the Predicted Failure Rate with Empirical Data | 296 |
| 7.2.3.7. Estimating Confidence Levels | 298 |
| 7.2.3.8. Using the 217Plus Model in a Top-Down Analysis | 298 |
| 7.2.3.9. Capacitor Model Example | 299 |
| 7.2.3.10. Default Values | 301 |
| 7.2.4. Photonic Model Development Example | 303 |
| 7.2.4.1. Introduction | 303 |
| 7.2.4.2. Model development methodology and results | 306 |
| 7.2.4.3. Uncertainty Analysis | 322 |
| 7.2.4.4. Comments on Part Quality Levels | 325 |
| 7.2.4.5. Explanation of Failure Rate Units | 325 |
| 7.2.5. System‐Level Model | 326 |
| 7.2.5.1. Model Presentation | 326 |
| 7.2.5.2. 217Plus Process Grading Criteria | 328 |
| 7.2.5.3. Design Process Grade Factor Questions | 330 |
| 7.2.5.4. Manufacturing Process Grade Factor Questions | 336 |
| 7.2.5.5. Part Quality Process Grade Factor Questions | 340 |
| 7.2.5.6. System Management Process Grade Factor Questions | 342 |
| 7.2.5.7. Can Not Duplicate (CND) Process Grade Factor Questions | 346 |
| 7.2.5.8. Induced Process Grade Factor Questions | 347 |
| 7.2.5.9. Wearout Process Grade Factor Questions | 348 |
| 7.2.5.10. Growth Process Grade Factor Questions | 349 |
| 7.3. Life Modeling Example | 350 |
| 7.3.1. Introduction | 350 |
| 7.3.2. Approach | 350 |
| 7.3.3. Reliability Test Plan | 350 |
| 7.3.4. Results | 352 |
| 7.3.4.1. Times to Failure Summary | 352 |
| 7.3.4.2. Life Models | 354 |
| 7.4. NPRD Description | 357 |
| 7.4.1. Data Collection | 358 |
| 7.4.2. Data Interpretation | 361 |
| 7.4.3. Document Overview | 366 |
| 7.4.3.1. “Part Summaries” Overview | 366 |
| 7.4.3.2. “Part Details” Overview | 373 |
| 7.4.3.3. Section 4 “Data Sources” Overview | 374 |
| 7.4.3.4. Section 5 “Part Number/MIL Number” Index | 374 |
| 7.4.3.5. Section 6 “National Stock Number Index with Federal Stock Class” | 375 |
| 7.4.3.6. Section 7 “National Stock Number Index without Federal Stock Class Prefix” |
375 |
| 7.5. References | 375 |
| 8. THE USE OF FMEA IN RELIABILITY MODELING | 377 |
| 8.1. Introduction | 377 |
| 8.2. Definitions | 381 |
| 8.3. FMEA Logistics | 383 |
| 8.3.1. When initiated | 383 |
| 8.3.2. FMEA Team | 383 |
| 8.3.3. FMEA Facilitation | 384 |
| 8.3.4. Implementation | 385 |
| 8.4. How to Perform an FMEA | 385 |
| 8.5. Identify System Hierarchy | 387 |
| 8.6. Function Analysis | 388 |
| 8.7. IPOUND Analysis | 388 |
| 8.8. Identify the Severity | 390 |
| 8.9. Identify the Possible Effect(s) that Result from Occurrence of Each Failure Mode | 392 |
| 8.10. Identify Potential Causes of Each Failure Mode | 392 |
| 8.11. Identify Factors for Each Failure Cause | 398 |
| 8.11.1. Accelerating Stress(es) or Potential Tests | 398 |
| 8.11.2. Occurrence | 398 |
| 8.11.2.1. Occurrence Rankings | 398 |
| 8.11.3. Preventions | 401 |
| 8.11.4. Detections | 401 |
| 8.11.5. Detectability | 401 |
| 8.12. Calculate the RPN | 404 |
| 8.13. Determine Appropriate Corrective Action | 405 |
| 8.14. Update the RPN | 408 |
| 8.15. Using Quality Function Deployment to Feed the FMEA | 408 |
| 8.16. References | 410 |
| 9. CONCLUDING REMARKS | 411 |
