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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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