Weibull analysis

IEC 61649:2008 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. The main changes with respect to the previous edition are as follows: the title has been shortened and simplified to read 'Weibull analysis'; and provision of methods for both analytical and graphical solutions have been added.

Weibull-Analyse

Analyse de Weibull

La CEI 61649:2008 fournit des méthodes pour analyser les données d'une distribution de Weibull en utilisant les paramètres continus tels que temps avant défaillance, nombre de cycles avant défaillance, contraintes mécaniques, etc. La présente norme est applicable dès que des données sur des paramètres cruciaux tels que temps avant défaillance, contraintes, etc. sont disponibles pour un échantillon aléatoire d'entités fonctionnant dans des conditions d'essais ou en service, afin d'estimer des mesures de performance de fiabilité de la population dont ces entités sont issues. Cette édition inclut les modifications techniques majeures suivantes par rapport à l'édition précédente: le titre a été raccourci et se lit maintenant comme 'Analyse de Weibull'; et des méthodes pour des solutions à la fois analytiques et graphiques ont été ajoutées.

Weibullova analiza (IEC 61649:2008)

General Information

Status
Published
Publication Date
06-Nov-2008
Technical Committee
Drafting Committee
Parallel Committee
Current Stage
6060 - Document made available
Due Date
07-Nov-2008
Completion Date
07-Nov-2008

Buy Standard

Standard
EN 61649:2009 - Standard ima barvne strani: PDF- 29-30!, natisnjeno za čitalnico (barvno)
English language
71 pages
sale 10% off
Preview
sale 10% off
Preview

e-Library read for
1 day

Standards Content (sample)

SLOVENSKI STANDARD
SIST EN 61649:2009
01-januar-2009
Weibullova analiza (IEC 61649:2008)
Weibull analysis (IEC 61649:2008)
Weibull-Analyse (IEC 61649:2008)
Analyse de Weibull (CEI 61649:2008)
Ta slovenski standard je istoveten z: EN 61649:2008
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
29.020 Elektrotehnika na splošno Electrical engineering in
general
SIST EN 61649:2009 en,fr

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
SIST EN 61649:2009
---------------------- Page: 2 ----------------------
SIST EN 61649:2009
EUROPEAN STANDARD
EN 61649
NORME EUROPÉENNE
November 2008
EUROPÄISCHE NORM
ICS 03.120.01; 03.120.30
English version
Weibull analysis
(IEC 61649:2008)
Analyse de Weibull Weibull-Analyse
(CEI 61649:2008) (IEC 61649:2008)

This European Standard was approved by CENELEC on 2008-10-01. CENELEC members are bound to comply

with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard

the status of a national standard without any alteration.

Up-to-date lists and bibliographical references concerning such national standards may be obtained on

application to the Central Secretariat or to any CENELEC member.

This European Standard exists in three official versions (English, French, German). A version in any other

language made by translation under the responsibility of a CENELEC member into its own language and notified

to the Central Secretariat has the same status as the official versions.

CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Cyprus, the

Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,

Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,

Sweden, Switzerland and the United Kingdom.
CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung
Central Secretariat: rue de Stassart 35, B - 1050 Brussels

© 2008 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.

Ref. No. EN 61649:2008 E
---------------------- Page: 3 ----------------------
SIST EN 61649:2009
EN 61649:2008 – 2 –
Foreword

The text of document 56/1269/FDIS, future edition 2 of IEC 61649, prepared by IEC TC 56,

Dependability, was submitted to the IEC-CENELEC parallel vote and was approved by CENELEC as

EN 61649 on 2008-10-01.
The following dates were fixed:
– latest date by which the EN has to be implemented
at national level by publication of an identical
national standard or by endorsement (dop) 2009-07-01
– latest date by which the national standards conflicting
with the EN have to be withdrawn (dow) 2011-10-01
Annex ZA has been added by CENELEC.
__________
Endorsement notice

The text of the International Standard IEC 61649:2008 was approved by CENELEC as a European

Standard without any modification.

In the official version, for Bibliography, the following notes have to be added for the standards indicated:

IEC 60300-1 NOTE Harmonized as EN 60300-1:2003 (not modified).
IEC 60300-2 NOTE Harmonized as EN 60300-2:2004 (not modified).
IEC 60300-3-1 NOTE Harmonized as EN 60300-3-1:2004 (not modified).
IEC 60300-3-2 NOTE Harmonized as EN 60300-3-2:2005 (not modified).
IEC 60300-3-4 NOTE Harmonized as EN 60300-3-4:2008 (not modified).
IEC 61703 NOTE Harmonized as EN 61703:2002 (not modified).
__________
---------------------- Page: 4 ----------------------
SIST EN 61649:2009
– 3 – EN 61649:2008
Annex ZA
(normative)
Normative references to international publications
with their corresponding European publications

The following referenced documents are indispensable for the application of this document. For dated

references, only the edition cited applies. For undated references, the latest edition of the referenced

document (including any amendments) applies.

NOTE When an international publication has been modified by common modifications, indicated by (mod), the relevant EN/HD

applies.
Publication Year Title EN/HD Year
IEC 60050-191 1990 International Electrotechnical Vocabulary - -
(IEV) -
Chapter 191: Dependability and quality of
service
IEC 60300-3-5 2001 Dependability management - - -
Part 3-5: Application guide - Reliability test
conditions and statistical test principles
1) 2)
IEC 61810-2 - Electromechanical elementary relays - EN 61810-2 2005
Part 2: Reliability
ISO 2854 1976 Statistical interpretation of data - Techniques - -
of estimation and tests relating to means and
variances
ISO 3534-1 2006 Statistics - Vocabulary and symbols - - -
Part 1: General statistical terms and terms
used in probability
Undated reference.
Valid edition at date of issue.
---------------------- Page: 5 ----------------------
SIST EN 61649:2009
---------------------- Page: 6 ----------------------
SIST EN 61649:2009
IEC 61649
Edition 2.0 2008-08
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Weibull analysis
Analyse de Weibull
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
CODE PRIX
ICS 03.120.01; 03.120.30 ISBN 2-8318-9954-0
® Registered trademark of the International Electrotechnical Commission
Marque déposée de la Commission Electrotechnique Internationale
---------------------- Page: 7 ----------------------
SIST EN 61649:2009
– 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

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

---------------------- Page: 8 ----------------------
SIST EN 61649:2009
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......................................................56

Annex H (informative) Three-parameter Weibull example.....................................................59

Annex I (informative) Constructing Weibull paper.................................................................61

Annex J (informative) Technical background and references................................................64

Bibliography..........................................................................................................................67

Figure 1 – The PDF shapes of the Weibull family for Ș = 1,0 .................................................12

Figure 2 – Total test time (in minutes)...................................................................................16

Figure 3 – Typical bathtub curve for an item .........................................................................19

---------------------- Page: 9 ----------------------
SIST EN 61649:2009
– 4 – 61649 © IEC:2008

Figure 4 – Weibull failure modes may be “masked” ...............................................................21

Figure 5 – Sample size: 10 ...................................................................................................21

Figure 6 – Sample size: 100 .................................................................................................22

Figure 7 – An example showing lack of fit with a two-parameter Weibull distribution .............23

Figure 8 – The same data plotted with a three-parameter Weibull distribution shows a

good fit with 3 months offset (location – 2,99 months)...........................................................24

Figure 9 – Example of estimating t by eye ...........................................................................25

Figure 10 – New compressor design WeiBayes versus old design ........................................35

Figure A.1 – Main oil pump low times....................................................................................38

Figure A.2 – Augmenter pump bearing failure .......................................................................39

β values hide problems ...........................................................................39

Figure A.3 – Steep

Figure B.1 – Plot of computations .........................................................................................41

Figure E.1 – Weibull plot for graphical analysis.....................................................................49

Figure E.2 – Weibull plot of censored data............................................................................51

Figure E.3 – Cumulative hazard plot for data of Table E.4 ....................................................52

Figure E.4 – Cumulative hazard plots for Table E.6 ..............................................................54

Figure H.1 – Steel-fracture toughness – Curved data............................................................59

Figure H.2 – t improves the fit of Figure H.1 data ................................................................60

Table 1 – Guidance for using this International Standard ......................................................11

Table 2 – Ranked flare failure rivet data ...............................................................................15

Table 3 – Adjusted ranks for suspended or censored data ....................................................16

Table 4 – Subgroup size to estimate time to X % failures using the sudden death

method .................................................................................................................................36

Table 5 – Chain data: cycles to failure ..................................................................................36

Table B.1 – Times to failure ..................................................................................................40

Table B.2 – Summary of results ............................................................................................41

Table D.1 – Values of the gamma function............................................................................47

Table D.2 – Fractiles of the normal distribution .....................................................................47

Table E.1 – Practical analysis example.................................................................................48

Table E.2 – Spreadsheet set-up for analysis of censored data ..............................................50

Table E.3 – Example of Weibull analysis for suspended data................................................50

Table E.4 – Example of Spreadsheet application for censored data ......................................51

Table E.5 – Example spreadsheet.........................................................................................52

Table E.6 – A relay data provided by ISO/TC94 and Hazard analysis for failure mode 1 .......53

Table I.1 – Construction of ordinate (Y).................................................................................62

Table I.2 – Construction of abscissa (t).................................................................................62

Table I.3 – Content of data entered into a spreadsheet.........................................................62

---------------------- Page: 10 ----------------------
SIST EN 61649:2009
61649 © IEC:2008 – 5 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
WEIBULL ANALYSIS
FOREWORD

1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising

all national electrotechnical committees (IEC National Committees). The object of IEC is to promote

international co-operation on all questions concerning standardization in the electrical and electronic fields. To

this end and in addition to other activities, IEC publishes International Standards, Technical Specifications,

Technical Reports, and Guides (hereafter referred to as “IEC Publication(s)”). Their preparation is entrusted to

technical committees; any IEC National Committee interested in the subject dealt with may participate in this

preparatory work. International, governmental and non-governmental organizations liaising with the IEC also

participate in this preparation. IEC collaborates closely with the International Organization for Standardization

(ISO) in accordance with conditions determined by agreement between the two organizations.

2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international

consensus of opinion on the relevant subjects since each technical committee has representation from all

interested IEC National Committees.

3) IEC Publications have the form of recommendations for international use and are accepted by IEC National

Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC

Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any

misinterpretation by any end user.

4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications

transparently to the maximum extent possible in their national and regional publications. Any divergence

between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in

the latter.

5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any

equipment declared to be in conformity with an IEC Publication.

6) All users should ensure that they have the latest edition of this publication.

7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and

members of its technical committees and IEC National Committees for any personal injury, property damage or

other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and

expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC

Publications.

8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is

indispensable for the correct application of this publication.

9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of

patent rights. IEC shall not be held responsible for identifying any or all such patent rights.

International Standard IEC 61649 has been prepared by IEC technical committee 56:

Dependability.

This second edition cancels and replaces the first edition, published in 1997, and constitutes

a technical revision.
The main changes with respect to the previous edition are as follows:
– the title has been shortened and simplified to read “Weibull analysis”;

– provision of methods for both analytical and graphical solutions have been added.

The text of this standard is based on the following documents:
FDIS Report on voting
56/1269/FDIS 56/1281/RVD

Full information on the voting for the approval of this standard can be found in the report on

voting indicated in the above table.

This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.

---------------------- Page: 11 ----------------------
SIST EN 61649:2009
– 6 – 61649 © IEC:2008

The committee has decided that the contents of this publication will remain unchanged until

the maintenance result date indicated on the IEC web site under "http://webstore.iec.ch" in

the data related to the specific publication. At this date, the publication will be

• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
---------------------- Page: 12 ----------------------
SIST EN 61649:2009
61649 © IEC:2008 – 7 –
INTRODUCTION

The Weibull distribution is used to model data regardless of whether the failure rate is

increasing, decreasing or constant. The Weibull distribution is flexible and adaptable to a wide

range of data. The time to failure, cycles to failure, mileage to failure, mechanical stress or

similar continuous parameters need to be recorded for all items. A life distribution can be

modelled even if not all the items have failed.

Guidance is given on how to perform an analysis using a spreadsheet program. Guidance is

also given on how to analyse different failure modes separately and identify a possible weak

population. Using the three-parameter Weibull distribution can give information on time to first

failure or minimum endurance in the sample.
---------------------- Page: 13 ----------------------
SIST EN 61649:2009
– 8 – 61649 © IEC:2008
WEIBULL ANALYSIS
1 Scope

This International Standard 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 (see 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.
2 Normative references

The following referenced documents are indispensable for the application of this document.

For dated references, only the edition cited applies. For undated references, the latest edition

of the referenced document (including any amendments) applies.

IEC 60050-191:1990, International Electrotechnical Vocabulary – Part 191: Dependability and

quality of service

IEC 60300-3-5:2001, Dependability management – Part 3-5: Application guide – Reliability

test conditions and statistical test principles
IEC 61810-2, Electromechanical elementary relays – Part 2: Reliability

ISO 2854:1976, Statistical interpretation of data – Techniques of estimations and tests

relating to means and variances

ISO 3534-1:2006, Statistics – Vocabulary and symbols – Part 1: General statistical terms and

terms in probability
3 Terms, definitions, abbreviations and symbols

For the purposes of this document, the definitions, abbreviations and symbols given in

IEC 60050-191 and ISO 3534-1 apply, together with the following.
3.1 Terms and definitions
3.1.1
censoring
terminating a test after either a given duration or a given number of failures

NOTE A test terminated when there are still unfailed items may be called a “censored test", and test time data

from such tests may be referred to as “censored data”.
---------------------- Page: 14 ----------------------
SIST EN 61649:2009
61649 © IEC:2008 – 9 –
3.1.2
suspended item
item upon which testing has been curtailed without relevant failure

NOTE 1 The item may not have failed, or it may have failed in a mode other than that under investigation.

NOTE 2 An “early suspension” is one that was suspended before the first failure. A “late suspension” is

suspended after the last failure.
3.1.3
life test
test conducted to estimate or verify the durability of a product

NOTE The end of the useful life will often be defined as the time when a certain percentage of the items have

failed for non-repairable items and as the time when the failure intensity has increased to a specified level for

repairable items.
3.1.4
non-repairable item

item that cannot, under given conditions, after a failure, be returned to a state in which it can

perform as required
NOTE The given conditions may be technical, economic, ecological and/or others.
3.1.5
operating time
time interval for which the item is in an operating state
NOTE ”Operating time” is generic, and should be ex
...

Questions, Comments and Discussion

Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.