IEC 61649:2008

IEC 61649
Edition 2.0 2008-08
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Weibull analysis
Analyse de Weibull
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IEC 61649
Edition 2.0 2008-08
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Weibull analysis
Analyse de Weibull
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
XB
CODE PRIX
ICS 03.120.01; 03.120.30 ISBN 2-8318-9954-0
– 2 – 61649 © IEC:2008
CONTENTS
FOREWORD.5
INTRODUCTION.7
1 Scope.8
2 Normative references .8
3 Terms, definitions, abbreviations and symbols.8
3.1 Terms and definitions .8
3.2 Abbreviations .10
3.3 Symbols .10
4 Application of the techniques.11
5 The Weibull distribution .11
5.1 The two-parameter Weibull distribution.11
5.2 The three-parameter Weibull distribution .13
6 Data considerations.13
6.1 Data types.13
6.2 Time to first failure .13
6.3 Material characteristics and the Weibull distribution .13
6.4 Sample size .13
6.5 Censored and suspended data .14
7 Graphical methods and goodness-of-fit .14
7.1 Overview .14
7.2 How to make the probability plot.14
7.2.1 Ranking.15
7.2.2 The Weibull probability plot .15
7.2.3 Dealing with suspensions or censored data .15
7.2.4 Probability plotting.17
7.2.5 Checking the fit .17
7.3 Hazard plotting.18
8 Interpreting the Weibull probability plot.19
8.1 The bathtub curve .19
8.1.1 General .19
8.1.2 β < 1 – Implies early failures.19
8.1.3 β = 1 – Implies constant instantaneous failure rate.20
8.1.4 > 1 – Implies wear-out.20
β
8.2 Unknown Weibull modes may be "masked".20
8.3 Small samples.21
8.4 Outliers .22
8.5 Interpretation of non-linear plots.22
8.5.1 Distributions other than the Weibull .25
8.5.2 Data inconsistencies and multimode failures .25
9 Computational methods and goodness-of-fit .25
9.1 Introduction .25
9.2 Assumptions and conditions .26
9.3 Limitations and accuracy .26
9.4 Input and output data .26

61649 © IEC:2008 – 3 –
9.5 Goodness-of-fit test.27
9.6 MLE – point estimates of the distribution parameters β and η .27
9.7 Point estimate of the mean time to failure.28
9.8 Point estimate of the fractile (10 %) of the time to failure.28
9.9 Point estimate of the reliability at time t (t ≤ T).28
9.10 Software programs .28
10 Confidence intervals.28
10.1 Interval estimation of β .28
10.2 Interval estimation of η .29
10.3 MRR Beta-binomial bounds .30
10.4 Fisher's Matrix bounds .30
10.5 Lower confidence limit for B .31
10.6 Lower confidence limit for R .31
11 Comparison of median rank regression (MRR) and maximum likelihood (MLE)
estimation methods .31
11.1 Graphical display.31
11.2 B life estimates sometimes known as B or L percentiles .31
11.3 Small samples.32
11.4 Shape parameter β.32
11.5 Confidence intervals.32
11.6 Single failure .32
11.7 Mathematical rigor.32
11.8 Presentation of results .32
12 WeiBayes approach.33
12.1 Description.33
12.2 Method.33
12.3 WeiBayes without failures .33
12.4 WeiBayes with failures .33
12.5 WeiBayes case study .34
13 Sudden death method .35
14 Other distributions .37
Annex A (informative) Examples and case studies .38
Annex B (informative) Example of computations .40
Annex C (informative) Median rank tables.42
Annex D (normative) Statistical Tables .47
Annex E (informative) Spreadsheet example.48
Annex F (informative) Example of Weibull probability paper.55
Annex G (informative) Mixtures of several failure modes.
...