Reliability Modeling – The RIAC Guide to Reliability Prediction, Assessment and Estimation

  • Reliability Modeling - The RIAC Guide to Reliability Prediction, Assessment and Estimation

Reliability Modeling – The RIAC Guide to Reliability Prediction, Assessment and Estimation

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This product is provided for free as a training resource for the upcoming course titled Reliability 301: RAM Modeling I. This course is offered Nov. 14-16, 2023 in Orlando, FL. Register for Reliability 301: RAM Modeling I today!

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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Product Description

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.

Additional information

ISBN:

978-1-933904-18-4

Product Format:

Download, Hardcopy

Table of Contents

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

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