AS/NZS IEC 61649:2020
Weibull analysis
Standard adopts IEC 61649:2008 which provides methods for analysing data from a Weibull distribution using continuous parameters such as time to failure, cycles to failure, mechanical stress, etc. This Standard is applicable whenever data on strength parameters, e.g. times to failure, cycles, stress, etc. are available for a random sample of items operating under test conditions or in-service, for the purpose of estimating measures of reliability performance of the population from which these items were drawn. This Standard is applicable when the data being analysed are independently, identically distributed. This should either be tested or assumed to be true (refer to IEC 60300-3-5). In this Standard, numerical methods and graphical methods are described to plot data, to make a goodness-of-fit test, to estimate the parameters of the two- or three-parameter Weibull distribution and to plot confidence limits. Guidance is given on how to interpret the plot in terms of risk as a function of time, failure modes and possible weak population and time to first failure or minimum endurance. The proposed standard is identical with, and will be reproduced from, IEC 61649:2008 Weibull analysis.
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AS/NZS IEC 61649:2020 Weibull analysis
CONTENTS
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 – point estimates of the distribution parameters β and η
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 β
10.2 Interval estimation of η
10.3 MRR Beta-binomial bounds
10.4 Fisher's matrix bounds
10.5 Lower confidence limit for B10
10.6 Lower confidence limit for R
11 Comparison of median rank regression (MRR) and maximum likelihood estimation (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 β
11.5 Confidence intervals
11.6 Single failure
11.7 Mathematical rigour
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
Figures
Figure 1 – The PDF shapes of the Weibull family for η = 1,0
Figure 2 – Total test time (in minutes)
Figure 3 – Typical bathtub curve for an item
Figure 4 – Weibull failure modes may be “masked”
Figure 5 – Sample size: 10
Figure 6 – Sample size: 100
Figure 7 – An example showing lack of fit with a two-parameter Weibull distribution
Figure 8 – The same data plotted with a three-parameter Weibull distribution shows a good fit with 3 months offset (location – 2,99 months)
Figure 9 – Example of estimating t0 by eye
Figure 10 – New compressor design WeiBayes versus old design
Figure A.1 – Main oil pump low times
Figure A.2 – Augmenter pump bearing failure
Figure A.3 – Steep β values hide problems
Figure B.1 – Plot of computations
Figure E.1 – Weibull plot for graphical analysis
Figure E.2 – Weibull plot of censored data
Figure E.3 – Cumulative hazard plot for data of Table E.4
Figure E.4 – Cumulative hazard plots for Table E.6
Figure H.1 – Steel-fracture toughness – Curved data
Figure H.2 – t0 improves the fit of Figure H.1 data
Tables
Table 1 – Guidance for using IEC 61649
Table 2 – Ranked flare failure rivet data
Table 3 – Adjusted ranks for suspended or censored data
Table 4 – Subgroup size to estimate time to X % failures using the sudden death method
Table 5 – Chain data – Cycles to failure
Table B.1 – Times to failure
Table B.2 – Summary of results
Table D.1 – Values of the gamma function
Table D.2 – Fractiles of the normal distribution
Table E.1 – Practical analysis example
Table E.2 – Spreadsheet set-up for analysis of censored data
Table E.3 – Example of Weibull analysis for suspended data
Table E.4 – Example of spreadsheet application for censored data
Table E.5 – Example spreadsheet
Table E.6 – A relay data provided by ISO/TC94 and Hazard analysis for failure mode 1
Table I.1 – Construction of ordinate (Y)
Table I.2 – Construction of abscissa (t)
Table I.3 – Content of data entered into a spreadsheet
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AS/NZS IEC 61649:2020 Weibull analysis
CONTENTS
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 – point estimates of the distribution parameters β and η
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 β
10.2 Interval estimation of η
10.3 MRR Beta-binomial bounds
10.4 Fisher's matrix bounds
10.5 Lower confidence limit for B10
10.6 Lower confidence limit for R
11 Comparison of median rank regression (MRR) and maximum likelihood estimation (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 β
11.5 Confidence intervals
11.6 Single failure
11.7 Mathematical rigour
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
Figures
Figure 1 – The PDF shapes of the Weibull family for η = 1,0
Figure 2 – Total test time (in minutes)
Figure 3 – Typical bathtub curve for an item
Figure 4 – Weibull failure modes may be “masked”
Figure 5 – Sample size: 10
Figure 6 – Sample size: 100
Figure 7 – An example showing lack of fit with a two-parameter Weibull distribution
Figure 8 – The same data plotted with a three-parameter Weibull distribution shows a good fit with 3 months offset (location – 2,99 months)
Figure 9 – Example of estimating t0 by eye
Figure 10 – New compressor design WeiBayes versus old design
Figure A.1 – Main oil pump low times
Figure A.2 – Augmenter pump bearing failure
Figure A.3 – Steep β values hide problems
Figure B.1 – Plot of computations
Figure E.1 – Weibull plot for graphical analysis
Figure E.2 – Weibull plot of censored data
Figure E.3 – Cumulative hazard plot for data of Table E.4
Figure E.4 – Cumulative hazard plots for Table E.6
Figure H.1 – Steel-fracture toughness – Curved data
Figure H.2 – t0 improves the fit of Figure H.1 data
Tables
Table 1 – Guidance for using IEC 61649
Table 2 – Ranked flare failure rivet data
Table 3 – Adjusted ranks for suspended or censored data
Table 4 – Subgroup size to estimate time to X % failures using the sudden death method
Table 5 – Chain data – Cycles to failure
Table B.1 – Times to failure
Table B.2 – Summary of results
Table D.1 – Values of the gamma function
Table D.2 – Fractiles of the normal distribution
Table E.1 – Practical analysis example
Table E.2 – Spreadsheet set-up for analysis of censored data
Table E.3 – Example of Weibull analysis for suspended data
Table E.4 – Example of spreadsheet application for censored data
Table E.5 – Example spreadsheet
Table E.6 – A relay data provided by ISO/TC94 and Hazard analysis for failure mode 1
Table I.1 – Construction of ordinate (Y)
Table I.2 – Construction of abscissa (t)
Table I.3 – Content of data entered into a spreadsheet
AS/NZS IEC 61649:2020
Online Library subscription pricing
The cost of your subscription will depend on which standards you want to access, and how many people in your organisation need to be able to access the Online Library subscription at the same time (concurrent users). During your subscription period, we are also able to make any necessary changes and ensure you are aware of any pricing changes that result. For a quote, contact our Online Library team by emailing onlinelibrary@standards.govt.nz.