IEC 61649 : 2.0

WEIBULL ANALYSIS

International Electrotechnical Committee

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FOREWORD
INTRODUCTION
1 Scope
2 Normative references
3 Terms, definitions, abbreviations and symbols
   3.1 Terms and definitions
   3.2 Abbreviations
   3.3 Symbols
4 Application of the techniques
5 The Weibull distribution
   5.1 The two-parameter Weibull distribution
   5.2 The three-parameter Weibull distribution
6 Data considerations
   6.1 Data types
   6.2 Time to first failure
   6.3 Material characteristics and the Weibull distribution
   6.4 Sample size
   6.5 Censored and suspended data
7 Graphical methods and goodness-of-fit
   7.1 Overview
   7.2 How to make the probability plot
   7.3 Hazard plotting
8 Interpreting the Weibull probability plot
   8.1 The bathtub curve
   8.2 Unknown Weibull modes may be 'masked'
   8.3 Small samples
   8.4 Outliers
   8.5 Interpretation of non-linear plots
9 Computational methods and goodness-of-fit
   9.1 Introduction
   9.2 Assumptions and conditions
   9.3 Limitations and accuracy
   9.4 Input and output data
   9.5 Goodness-of-fit test
   9.6 MLE - pont estimates of the distribution parameters
        beta and eta
   9.7 Point estimate of the mean time to failure
   9.8 Point estimate of the fractile (10%)of the time to
        failure
   9.9 Point estimate of the reliability at time t (t <= T)
   9.10 Software programs
10 Confidence intervals
   10.1 Interval estimation of beta
   10.2 Interval estimation of eta
   10.3 MRR Beta-binomial bounds
   10.4 Fisher's Matrix bounds
   10.5 Lower confidence limit for B[10]
   10.6 Lower confidence limit for R
11 Comparison of median rank regression (MRR)and maximum
   likelihood (MLE) estimation methods
   11.1 Graphical display
   11.2 B life estimates sometimes known as B or L percentiles
   11.3 Small samples
   11.4 Shape parameter beta
   11.5 Confidence intervals
   11.6 Single failure
   11.7 Mathematical rigor
   11.8 Presentation of results
12 WeiBayes approach
   12.1 Description
   12.2 Method
   12.3 WeiBayes without failures
   12.4 WeiBayes with failures
   12.5 WeiBayes case study
13 Sudden death method
14 Other distributions
Annex A (informative) Examples and case studies
Annex B (informative) Example of computations
Annex C (informative) Median rank tables
Annex D (normative) Statistical Tables
Annex E (informative) Spreadsheet example
Annex F (informative) Example of Weibull probability paper
Annex G (informative) Mixtures of several failure modes
Annex H (informative) Three-parameter Weibull example
Annex I (informative) Constructing Weibull paper
Annex J (informative) Technical background and references
Bibliography

Abstract

Describes methods for analysing data from a Weibull distribution using continuous parameters such as time to failure, cycles to failure, mechanical stress, etc.