EN 61710:2013
(Main)Power law model - Goodness-of-fit tests and estimation methods
Power law model - Goodness-of-fit tests and estimation methods
IEC 61710:2013 specifies procedures to estimate the parameters of the power law model, to provide confidence intervals for the failure intensity, to provide prediction intervals for the times to future failures, and to test the goodness-of-fit of the power law model to data from repairable items. It is assumed that the time to failure data have been collected from an item, or some identical items operating under the same conditions (e.g. environment and load). This second edition cancels and replaces the first edition, published in 2000, and constitutes a technical revision. The main changes with respect to the previous edition are listed below: the inclusion of an additional Annex C on Bayesian estimation for the power law model. Keywords: power law model, Bayesian estimation, reliability of repairable items
Potenzgesetz-Modell - Anpassungstests und Schätzverfahren
Modèle de loi en puissance - Essais d'adéquation et méthodes d'estimation des paramètres
La CEI 61710:2013 spécifie les procédures pour l'estimation des paramètres du modèle de loi en puissance en fournissant les intervalles de confiance pour l'intensité de défaillance, les intervalles de prédiction pour les défaillances futures et pour déterminer l'adéquation du modèle de loi en puissance avec les données relatives aux entités réparables. L'hypothèse prise est que les données de durées avant défaillance ont été collectées à partir d'une ou de plusieurs entités identiques fonctionnant dans les mêmes conditions (par exemple d'environnement et de charge). Cette deuxième édition annule et remplace la première édition parue en 2000. Cette édition constitue une révision technique. Les modifications principales par rapport à l'édition précédente sont les suivantes: Introduction d'une Annexe supplémentaire C traitant de l'estimation bayésienne pour le modèle de loi en puissance. Mots clés: modèle de loi en puissance, l'estimation bayésienne, fiabilité des entités réparables
Model eksponentnega pravila - Preskusi ujemanja in metode vrednotenja (IEC 61710:2013)
Ta mednarodni standard določa postopke za vrednotenje parametrov modela eksponentnega pravila, ugotavljanje intervalov zaupanja za intenzivnost odpovedi, ugotavljanje napovednih intervalov za čas delovanja do prihodnje odpovedi in preskušanje ujemanja modela eksponentnega pravila s podatki na podlagi popravljivih elementov. Predvideva se, da so bili podatki o času delovanja do odpovedi zbrani na podlagi dela ali drugih identičnih delov, ki delujejo v istih pogojih (npr. okolje in obremenitev).
General Information
Standards Content (Sample)
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Model eksponentnega pravila - Preskusi ujemanja in metode vrednotenja (IEC 61710:2013)Modèle de loi en puissance - Essai d'adéquation et méthodes d'estimation des paramètresPower law model - Goodness-of-fit tests and estimation methods29.020Elektrotehnika na splošnoElectrical engineering in general03.120.30Application of statistical methodsICS:Ta slovenski standard je istoveten z:EN 61710:2013SIST EN 61710:2014en01-maj-2014SIST EN 61710:2014SLOVENSKI
STANDARD
EUROPEAN STANDARD EN 61710 NORME EUROPÉENNE
EUROPÄISCHE NORM September 2013
CENELEC European Committee for Electrotechnical Standardization Comité Européen de Normalisation Electrotechnique Europäisches Komitee für Elektrotechnische Normung
CEN-CENELEC Management Centre: Avenue Marnix 17, B - 1000 Brussels
© 2013 CENELEC -
All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.
Ref. No. EN 61710:2013 E
ICS 03.120.01; 03.120.30
English version
Power law model -
Goodness-of-fit tests and estimation methods (IEC 61710:2013)
Modèle de loi en puissance -
Essais d'adéquation et méthodes d'estimation des paramètres (CEI 61710:2013)
Potenzgesetz-Modell -
Anpassungstests und Schätzverfahren (IEC 61710:2013)
This European Standard was approved by CENELEC on 2013-06-26. 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 CEN-CENELEC Management Centre 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 CEN-CENELEC Management Centre has the same status as the official versions.
CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Croatia, Cyprus, the Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
Foreword The text of document 56/1500/FDIS, future edition 2 of IEC 61710, prepared by IEC/TC 56 "Dependability" was submitted to the IEC-CENELEC parallel vote and approved by CENELEC as EN 61710:2013.
The following dates are fixed: • latest date by which the document has to be implemented at national level by publication of an identical national standard or by endorsement (dop) 2014-03-26 • latest date by which the national standards conflicting with the document have to be withdrawn (dow) 2016-06-26
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. CENELEC [and/or CEN] shall not be held responsible for identifying any or all such patent rights.
Endorsement notice The text of the International Standard IEC 61710:2013 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 61703 NOTE Harmonised as EN 61703. IEC 61164:2004 NOTE Harmonised as EN 61164:2004 (not modified). SIST EN 61710:2014
- 3 - EN 61710:2013
Annex ZA
(normative)
Normative references to international publications with their corresponding European publications
The following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. 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 61710 Edition 2.0 2013-05 INTERNATIONAL STANDARD NORME INTERNATIONALE Power law model – Goodness-of-fit tests and estimation methods
Modèle de loi en puissance – Essais d'adéquation et méthodes d'estimation
des paramètres
INTERNATIONAL ELECTROTECHNICAL COMMISSION COMMISSION ELECTROTECHNIQUE INTERNATIONALE XA ICS 03.120.01; 03.120.30 PRICE CODE CODE PRIX ISBN 978-2-83220-797-0
– 2 – 61710 © IEC:2013
CONTENTS FOREWORD . 5 INTRODUCTION . 7 1 Scope . 8 2 Normative references . 8 3 Terms and definitions . 8 4 Symbols and abbreviations . 8 5 Power law model . 9 6 Data requirements . 10 6.1 General . 10 6.1.1 Case 1 – Time data for every relevant failure for one or more copies
from the same population . 10 6.1.2 Case 1a) – One repairable item . 10 6.1.3 Case 1b) – Multiple items of the same kind of repairable item observed for the same length of time . 11 6.1.4 Case 1c) – Multiple repairable items of the same kind observed for different lengths of time . 11 6.2 Case 2 – Time data for groups of relevant failures for one or more repairable items from the same population . 12 6.3 Case 3 – Time data for every relevant failure for more than one repairable item from different populations . 12 7 Statistical estimation and test procedures . 13 7.1 Overview . 13 7.2 Point estimation . 13 7.2.1 Case 1a) and 1b) – Time data for every relevant failure . 13 7.2.2 Case 1c) – Time data for every relevant failure . 14 7.2.3 Case 2 – Time data for groups of relevant failures . 15 7.3 Goodness-of-fit tests . 16 7.3.1 Case 1 – Time data for every relevant failure. 16 7.3.2 Case 2 – Time data for groups of relevant failures . 17 7.4 Confidence intervals for the shape parameter . 18 7.4.1 Case 1 – Time data for every relevant failure. 18 7.4.2 Case 2 – Time data for groups of relevant failures . 19 7.5 Confidence intervals for the failure intensity . 20 7.5.1 Case 1 – Time data for every relevant failure. 20 7.5.2 Case 2 – Time data for groups of relevant failures . 20 7.6 Prediction intervals for the length of time to future failures of a single item . 21 7.6.1 Prediction interval for length of time to next failure for case 1 –
Time data for every relevant failure . 21 7.6.2 Prediction interval for length of time to Rth future failure for case 1 –
Time data for every relevant failure . 22 7.7 Test for the equality of the shape parameters kβββ ., ,,21 . 23 7.7.1 Case 3 – Time data for every relevant failure for two items from different populations . 23 7.7.2 Case 3 – Time data for every relevant failure for three or more items from different populations . 24 Annex A (informative)
The power law model – Background information . 30 Annex B (informative)
Numerical examples . 31 SIST EN 61710:2014
61710 © IEC:2013 – 3 –
Annex C (informative)
Bayesian estimation for the power law model . 41 Bibliography . 56
Figure 1 – One repairable item . 10 Figure 2 – Multiple items of the same kind of repairable item
observed for same length of time . 11 Figure 3 – Multiple repairable items of the same kind observed for different lengths of time . 12 Figure B.1 – Accumulated number of failures against accumulated time for software system . 32 Figure B.2 – Expected against observed accumulated times to failure for software system . 32 Figure B.3 – Accumulated number of failures against accumulated time for five copies of a system . 35 Figure B.4 – Accumulated number of failures against accumulated time
for an OEM product from vendors A and B . 37 Figure B.5 – Accumulated number of failures against time for generators . 38 Figure B.6 – Expected against observed accumulated
number of failures for generators . 39 Figure C.1 – Plot of fitted Gamma prior (6,7956, 0,0448) . 47 for the shape parameter of the power law model . 47 Figure C.2 – Plot of fitted Gamma prior (17,756 6, 1447,408)
for the expected number of failures parameter of the power law model . 47 Figure C.3 – Subjective distribution of number of failures. 51 Figure C.4 – Plot of the posterior probability distribution
for the number of future failures, M . 54 Figure C.5 – Plot of the posterior cumulative distribution
for the number of future failures, M . 55
Table 1 – Critical values for Cramer-von-Mises goodness-of-fit test at 10 % level of significance. 25 Table 2 – Fractiles of the Chi-square distribution . 26 Table 3 – Multipliers for two-sided 90 % confidence intervals for intensity function for time terminated data . 27 Table 4 – Multipliers for two-sided 90 % confidence intervals for intensity function for failure terminated data . 28 Table 5 – 0,95 fractiles of the F distribution . 29 Table B.1 – All relevant failures and accumulated times for software system . 31 Table B.2 – Calculation of expected accumulated times to failure for Figure B.2 . 33 Table B.3 – Accumulated times for all relevant failures for five copies of a system (labelled A, B, C, D, E) . 34 Table B.4 – Combined accumulated times
for multiple items of the same kind of a system . 34 Table B.5 – Accumulated operating hours to failure for OEM product from vendors A and B . 36 Table B.6 – Group
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