IEC 61164:2004
(Main)Reliability growth - Statistical test and estimation methods
Reliability growth - Statistical test and estimation methods
IEC 61164:2004 gives models and numerical methods for reliability growth assessments based on failure data, which were generated in a reliability improvement programme. These procedures deal with growth, estimation, confidence intervals for product reliability and goodness-of-fit tests. The main changes with respect to the previous edition are:
- addition of two statistical models for reliability growth planning and tracking in the product design phase;
- statistical methods for the reliability growth programme in the design phase of IEC 61014;
- addition of the discrete reliability growth model for the test phase;
- addition of the fixed number of faults model for the test phase, clarification of the symbols used for various models;
- addition of real lif examples for most of the statistical models;
- numerical correction of tables in the reliability growth test example.
This publication is to be read in conjunction with IEC 61014:2003.
Croissance de la fiabilité - Tests et méthodes d'estimation statistiques
La CEI 61164:2004 fournit des modèles et méthodes numériques permettant d'effectuer des estimations de la croissance de la fiabilité basées sur des données de défaillance élaborées au cours d'un programme d'amélioration de la fiabilité. Ces procédures traitent de la croissance, de l'estimation et des intervalles de confiance pour les essais de fiabilité du produit et d'adéquation. Les principales modifications par rapport à l'édition précédente sont:
- ajout de deux modèles statistiques de planification et de suivi de la croissance de la fiabilité en phase de conception du produit;
- méthodes statistiques pour le programme relatif à la croissance de la fiabilité en phase de conception de la CEI 61014;
- ajout du modèle discret de croissance de la fiabilité pour la phase d'essai;
- ajout du nombre fixe de modèles de panne pour la phase d'essai;
- clarification des symboles utilisés pour les différents modèles;
- ajout d'exemples concrets pour la plupart des modèles statistiques;
- correction numérique des tableaux dans l'exemple de test de croissance de la fiabilité.
Cette publication doit être lue conjointement avec la CEI 61014:2003.
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INTERNATIONAL IEC
STANDARD 61164
Second edition
2004-03
Reliability growth –
Statistical test and estimation methods
Reference number
Publication numbering
As from 1 January 1997 all IEC publications are issued with a designation in the
60000 series. For example, IEC 34-1 is now referred to as IEC 60034-1.
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INTERNATIONAL IEC
STANDARD 61164
Second edition
2004-03
Reliability growth –
Statistical test and estimation methods
IEC 2004 Copyright - all rights reserved
No part of this publication may be reproduced or utilized in any form or by any means, electronic or
mechanical, including photocopying and microfilm, without permission in writing from the publisher.
International Electrotechnical Commission, 3, rue de Varembé, PO Box 131, CH-1211 Geneva 20, Switzerland
Telephone: +41 22 919 02 11 Telefax: +41 22 919 03 00 E-mail: inmail@iec.ch Web: www.iec.ch
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Международная Электротехническая Комиссия
For price, see current catalogue
– 2 – 61164 IEC:2004(E)
CONTENTS
FOREWORD.4
INTRODUCTION.6
1 Scope.7
2 Normative references.7
3 Terms and definitions .7
4 Symbols.8
5 Reliability growth models in design and test .12
6 Reliability growth models used for systems/products in design phase.13
6.1 Modified power law model for planning of reliability growth in product design
phase .13
6.2 Modified Bayesian IBM-Rosner model for planning reliability growth in design
phase .16
7 Reliability growth planning a tracking in the product reliability growth testing.18
7.1 Continuous reliability growth models .18
7.2 Discrete reliability growth model.20
8 Use of the power law model in planning reliability improvement test programmes.23
9 Statistical test and estimation procedures for continuous power law model.23
9.1 Overview.23
9.2 Growth tests and parameter estimation .23
9.3 Goodness-of-fit tests.27
9.4 Confidence intervals on the shape parameter.29
9.5 Confidence intervals on current MTBF.31
9.6 Projection technique.33
Annex A (informative) Examples for planning and analytical models used in design
and test phase of product development.37
Annex B (informative) The power law reliability growth model – Background
information.50
Bibliography.55
Figure 1 – Planned improvement of the average failure rate or reliability .12
Figure A.1 – Planned and achieved reliability growth – Example.40
Figure A.2 – Planned reliability growth using Bayesian reliability growth model.41
Figure A.3 − Scatter diagram of expected and observed test times at failure based on
data of Table A.2 with power law model .48
Figure A.4 − Observed and estimated accumulated failures/accumulated test time
based on data of Table A.2 with power law model.49
Table 1 – Categories of reliability growth models with clause references .13
Table 2 − Critical values for Cramér-von Mises goodness-of-fit test at 10 % level of
significance.34
Table 3 − Two-sided 90 % confidence intervals for MTBF from Type I testing .35
61164 IEC:2004(E) – 3 –
Table 4 − Two-sided 90 % confidence intervals for MTBF from Type II testing .36
Table A.1 – Calculation of the planning model for reliability growth in design phase .39
Table A.2 − Complete data − All relevant failures and accumulated test times for
Type I test .46
Table A.3 − Grouped data for Example 3 derived from Table A.2 .46
Table A.4 − Complete data for projected estimates in Example 4 − All relevant failures
and accumulated test times .47
Table A.5 − Distinct types of Category B failures, from Table A.4, with failure times,
time of first occurrence, number observed and effectiveness factors.47
– 4 – 61164 IEC:2004(E)
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
RELIABILITY GROWTH –
STATISTICAL TEST AND ESTIMATION METHODS
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, Publicly Available Specifications (PAS) 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 61164 has been prepared by IEC technical committee 56:
Dependability.
This second edition cancels and replaces the first edition, published in 1995, and constitutes
a technical revision.
The main changes with respect to the previous edition are listed below:
− addition of two statistical models for reliability growth planning and tracking in the product
design phase;
− statistical methods for the reliability growth programme in the design phase of IEC 61014;
− addition of the discrete reliability growth model for the test phase;
− addition of the fixed number of faults model for the test phase;
− clarification of the symbols used for various models;
− addition of real life examples for most of the statistical models;
− numerical correction of tables in the reliability growth test example.
61164 IEC:2004(E) – 5 –
This standard should be used in conjunction with IEC 61014.
The text of this standard is based on the following documents:
FDIS Report on voting
56/920/FDIS 56/939/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.
The committee has decided that the contents of this publication will remain unchanged until
2011. At this date, the publication will be
• reconfirmed;
• withdrawn;
• replaced by a revised edition, or
• amended.
– 6 – 61164 IEC:2004(E)
INTRODUCTION
This International Standard describes the power law reliability growth model and related
projection model and gives step-by-step directions for their use. There are several reliability
growth models available, the power law model being one of the most widely used. This
standard provides procedures to estimate some or all of the quantities listed in Clauses 4, 6
and 7 of IEC 61014.
Two types of input are required. The first one is for reliability growth planning through analysis
and design improvements in the design phase in terms of the design phase duration, initial
reliability, reliability goal, and planned design improvements, along with their expected
magnitude. The second input, for reliability growth in the project validation phase, is for a data
set of accumulated test times at which relevant failures occurred, or were observed, for a
single system, and the time of termination of the test, if different from the time of the final
failure. It is assumed that the collection of data as input for the model begins after the
completion of any preliminary tests, such as environmental stress screening, intended to
stabilize the product's initial failure intensity.
Model parameters estimated from previous test results may be used to plan and predict the
course of future reliability growth programmes, provided the conditions are similar.
Some of the procedures may require computer programs, but these are not unduly complex.
This standard presents algorithms for which computer programs should be easy to construct.
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IEC 61164 ®
Edition 2.0 2004-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Reliability growth – Statistical test and estimation methods
Croissance de la fiabilité – Tests et méthodes d'estimation statistiques
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IEC 61164 ®
Edition 2.0 2004-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Reliability growth – Statistical test and estimation methods
Croissance de la fiabilité – Tests et méthodes d'estimation statistiques
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
XA
CODE PRIX
ICS 03.120.01; 03.120.30 ISBN 978-2-8322-0050-6
– 2 – 61164 IEC:2004
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
4 Symbols . 8
5 Reliability growth models in design and test . 12
6 Reliability growth models used for systems/products in design phase . 13
6.1 Modified power law model for planning of reliability growth in product design
phase . 13
6.2 Modified Bayesian IBM-Rosner model for planning reliability growth in design
phase . 16
7 Reliability growth planning a tracking in the product reliability growth testing . 18
7.1 Continuous reliability growth models . 18
7.2 Discrete reliability growth model . 20
8 Use of the power law model in planning reliability improvement test programmes . 23
9 Statistical test and estimation procedures for continuous power law model . 23
9.1 Overview . 23
9.2 Growth tests and parameter estimation . 23
9.3 Goodness-of-fit tests . 27
9.4 Confidence intervals on the shape parameter . 29
9.5 Confidence intervals on current MTBF . 31
9.6 Projection technique . 32
Annex A (informative) Examples for planning and analytical models used in design
and test phase of product development . 37
Annex B (informative) The power law reliability growth model – Background
information. 50
Bibliography . 55
Figure 1 – Planned improvement of the average failure rate or reliability . 12
Figure A.1 – Planned and achieved reliability growth – Example . 40
Figure A.2 – Planned reliability growth using Bayesian reliability growth model . 41
Figure A.3 − Scatter diagram of expected and observed test times at failure based on
data of Table A.2 with power law model . 48
Figure A.4 − Observed and estimated accumulated failures/accumulated test time
based on data of Table A.2 with power law model . 49
Table 1 – Categories of reliability growth models with clause references . 13
Table 2 − Critical values for Cramér-von Mises goodness-of-fit test at 10 % level of
significance. 33
Table 3 − Two-sided 90 % confidence intervals for MTBF from Type I testing . 35
61164 IEC:2004 – 3 –
Table 4 − Two-sided 90 % confidence intervals for MTBF from Type II testing . 36
Table A.1 – Calculation of the planning model for reliability growth in design phase . 39
Table A.2 − Complete data − All relevant failures and accumulated test times for
Type I test . 46
Table A.3 − Grouped data for Example 3 derived from Table A.2 . 46
Table A.4 − Complete data for projected estimates in Example 4 − All relevant failures
and accumulated test times . 47
Table A.5 − Distinct types of Category B failures, from Table A.4, with failure times,
time of first occurrence, number observed and effectiveness factors . 47
– 4 – 61164 IEC:2004
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
RELIABILITY GROWTH –
STATISTICAL TEST AND ESTIMATION METHODS
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, Publicly Available Specifications (PAS) 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 61164 has been prepared by IEC technical committee 56:
Dependability.
This second edition cancels and replaces the first edition, published in 1995, and constitutes
a technical revision.
The main changes with respect to the previous edition are listed below:
− addition of two statistical models for reliability growth planning and tracking in the product
design phase;
− statistical methods for the reliability growth programme in the design phase of IEC 61014;
− addition of the discrete reliability growth model for the test phase;
− addition of th
...
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