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1、BRITISH STANDARD BS IEC 60605-4:2001 Equipment reliability testing Part 4: Statistical procedures for exponential distribution Point estimates, confidence intervals, prediction intervals and tolerance intervals ICS 29.020; 03.120.01 NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT
2、LAW Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 14:35:31 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS IEC 60605-4:2001 This British Standard, having been prepared under the direction of the Management Systems Sector Policy and Strategy Committee, was published under the authority of the
3、Standards Policy and Strategy Committee on 31 August 2001 BSI 31 August 2001 ISBN 0 580 38414 4 National foreword This British Standard reproduces verbatim IEC 60605-4:2001 and implements it as the UK national standard. The UK participation in its preparation was entrusted to Technical Committee DS/
4、1, Dependability and terotechnology, which has the responsibility to: A list of organizations represented on this committee can be obtained on request to its secretary. From 1 January 1997, all IEC publications have the number 60000 added to the old number. For instance, IEC 27-1 has been renumbered
5、 as IEC 60027-1. For a period of time during the change over from one numbering system to the other, publications may contain identifiers from both systems. Cross-references The British Standards which implement international or European publications referred to in this document may be found in the
6、BSI Standards Catalogue under the section entitled “International Standards Correspondence Index”, or by using the “Find” facility of the BSI Standards Electronic Catalogue. A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are resp
7、onsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. aid enquirers to understand the text; present to the responsible international/European committee any enquiries on the interpretation, or proposals for change, and kee
8、p the UK interests informed; monitor related international and European developments and promulgate them in the UK. Summary of pages This document comprises a front cover, an inside front cover, the IEC title page, pages 2 to 33 and a back cover. The BSI copyright date displayed in this document ind
9、icates when the document was last issued. Amendments issued since publication Amd. No. DateComments Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 14:35:31 GMT+00:00 2006, Uncontrolled Copy, (c) BSI NORME INTERNATIONALE CEI IEC INTERNATIONAL STANDARD 60605-4 Deuxime dition Second edition 200
10、1-08 Essai de fiabilit des quipements Partie 4: Mthodes statistiques de distribution exponentielle Estimateurs ponctuels, intervalles de confiance, intervalles de prdiction et intervalles de tolrance Equipment reliability testing Part 4: Statistical procedures for exponential distribution Point esti
11、mates, confidence intervals, prediction intervals and tolerance intervals Numro de rfrence Reference number CEI/IEC 60605-4:2001 BS IEC 606054:2001 Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 14:35:31 GMT+00:00 2006, Uncontrolled Copy, (c) BSI 60605-4 ? IEC:2001 2 CONTENTS FOREWORD 4 1Sco
12、pe 6 2Normative references. 6 3Definitions and symbols . 7 3.1Definitions 7 3.2Symbols 7 4Assumptions and requirements 8 4.1Assumptions and information required for point estimates and confidence intervals . 9 4.2Assumptions and requirements for prediction intervals 9 4.3Assumptions and requirements
13、 for tolerance intervals . 9 5Procedure for calculating point estimates and confidence intervals 10 5.1Time terminated tests 11 5.1.1Point estimates 11 5.1.2Confidence limits11 5.2Analytical procedure Failure terminated tests.15 5.2.1Point estimate15 5.2.2Confidence intervals.15 6Prediction interval
14、s for the number of failures in a future period.17 6.1Two-sided prediction intervals L2 rand U2 r.17 6.2One-sided prediction interval17 7Procedure for assigning tolerance intervals .17 7.1Upper Poisson tolerance bound17 7.2Lower Poisson tolerance bound18 Annex A (informative) Examples.19 A.1 Point e
15、stimate of MTTF.19 A.2 Application of lower one-sided 90 % confidence limit on mean time to failure (MTTF).19 A.3 Application of two-sided 90 % confidence limits on MTTF 19 A.4 Application of a two-sided 90 % prediction interval.20 A.5 Application of upper 90 % tolerance bound at 95 % confidence20 A
16、.6 Application of lower 90 % tolerance bound at 95 % confidence 20 Annex B (informative) Relation between confidence, prediction and tolerance intervals .22 B.1Confidence intervals.22 B.2Prediction intervals.22 B.3Tolerance intervals.23 BS IEC 606054:2001 BSI 31 August 20012 BS IEC 606054:2001 BSI 3
17、1 August 20012 BS IEC 606054:2001 BSI 31 August 20012 Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 14:35:31 GMT+00:00 2006, Uncontrolled Copy, (c) BSI 60605-4 ? IEC:2001 3 Annex C (normative) Computation of accumulated test time * T24 C.1Case 1, one repaired item with constant failure inte
18、nsity .24 C.2Case 2, more than one repaired item with identical constant failure intensities 25 C.3Case 3, non-repaired items 26 Annex D (normative) Tables of fractiles of the chi-squared distribution:)( 2 ?27 Annex E (normative) Integral of the chi-squared distribution and cumulative Poisson distri
19、bution .29 Annex F (normative) 0,95 fractiles of the F distribution32 Bibliography 33 BS IEC 606054:2001 BSI 31 August 20013 BS IEC 606054:2001 BSI 31 August 20013 BS IEC 606054:2001 BSI 31 August 20013 Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 14:35:31 GMT+00:00 2006, Uncontrolled Copy
20、, (c) BSI 60605-4 ? IEC:2001 4 INTERNATIONAL ELECTROTECHNICAL COMMISSION _ EQUIPMENT RELIABILITY TESTING Part 4: Statistical procedures for exponential distribution Point estimates, confidence intervals, prediction intervals and tolerance intervals FOREWORD 1)The IEC (International Electrotechnical
21、Commission) is a worldwide organization for standardization comprising all national electrotechnical committees (IEC National Committees). The object of the IEC is to promote international co-operation on all questions concerning standardization in the electrical and electronic fields. To this end a
22、nd in addition to other activities, the IEC publishes International Standards. 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 organizati
23、ons liaising with the IEC also participate in this preparation. The 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 the IEC on technical
24、 matters express, as nearly as possible, an international consensus of opinion on the relevant subjects since each technical committee has representation from all interested National Committees. 3)The documents produced have the form of recommendations for international use and are published in the
25、form of standards, technical specifications, technical reports or guides and they are accepted by the National Committees in that sense. 4)In order to promote international unification, IEC National Committees undertake to apply IEC International Standards transparently to the maximum extent possibl
26、e in their national and regional standards. Any divergence between the IEC Standard and the corresponding national or regional standard shall be clearly indicated in the latter. 5)The IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any equipment decl
27、ared to be in conformity with one of its standards. 6) Attention is drawn to the possibility that some of the elements of this International Standard may be the subject of patent rights. The IEC shall not be held responsible for identifying any or all such patent rights. International Standard IEC 6
28、0605-4 has been prepared by IEC technical committee 56: Dependability. This second edition cancels and replaces the first edition published in 1986 and its amendment 1 (1989), of which it constitutes a technical revision. The text of this standard is based on the following documents: FDISReport on v
29、oting 56/737/FDIS56/756/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 3. Annexes A and B are for information only. Annexes C, D,
30、 E and F form an integral part of this standard. BS IEC 606054:2001 BSI 31 August 20014 BS IEC 606054:2001 BSI 31 August 20014 BS IEC 606054:2001 BSI 31 August 20014 Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 14:35:31 GMT+00:00 2006, Uncontrolled Copy, (c) BSI 60605-4 ? IEC:2001 5 The co
31、mmittee has decided that the contents of this publication will remain unchanged until 2006. At this date, the publication will be ? reconfirmed; ? withdrawn; ? replaced by a revised edition, or ? amended. BS IEC 606054:2001 BSI 31 August 20015 BS IEC 606054:2001 BSI 31 August 20015 BS IEC 606054:200
32、1 BSI 31 August 20015 Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 14:35:31 GMT+00:00 2006, Uncontrolled Copy, (c) BSI 60605-4 ? IEC:2001 6 EQUIPMENT RELIABILITY TESTING Part 4: Statistical procedures for exponential distribution Point estimates, confidence intervals, prediction intervals
33、and tolerance intervals 1 Scope This International Standard provides statistical methods for evaluating point estimates, confidence intervals, prediction intervals and tolerance intervals for the failure rate of items, whose time to failure follows an exponential distribution. This implies that the
34、failure rate (see IEV 191-12-02) is constant with respect to time. It should be noted that although reference is made above to failure rate, the numerical methods to be described are equally applicable to other event rates provided the times to the occurrence of the event follow an exponential distr
35、ibution. Thus, with this qualification, the numerical methods will apply, for example, to constant failure intensities and constant repair rates (see IEV 191-12-04 and IEV 191-13-02 respectively). For convenience, however, and to avoid unnecessary repetition, reference will be made in what follows o
36、nly to failures and failure rates. Use of the procedures in this standard should be supported by tests to confirm the validity of the assumption of constant failure rate or failure intensity (see IEC 60605-6). This standard is also applicable whenever a random sample of items is subjected to a test
37、of times to failure for the purpose of estimating measures of reliability performance. 2 Normative references The following normative documents contain provisions which, through reference in this text, constitute provisions of this part of IEC 60605. For dated references, subsequent amendments to, o
38、r revisions of, any of these publications do not apply. However, parties to agreements based on this part of IEC 60605 are encouraged to investigate the possibility of applying the most recent editions of the normative documents indicated below. For undated references, the latest edition of the norm
39、ative document referred to applies. Members of IEC and ISO maintain registers of currently valid International Standards. IEC 60050(191):1990, International Electrotechnical Vocabulary (IEV) Chapter 191: Depend- ability and quality of service IEC 60605-6:1997, Equipment reliability testing Part 6: T
40、ests for the validity of the constant failure rate or constant failure intensity assumptions ISO 3534-1:1993, Statistics Vocabulary and symbols Part 1: Probability and general statistical terms ISO 3534-2:1993, Statistics Vocabulary and symbols Part 2: Statistical quality control BS IEC 606054:2001
41、BSI 31 August 20016 BS IEC 606054:2001 BSI 31 August 20016 BS IEC 606054:2001 BSI 31 August 20016 Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 14:35:31 GMT+00:00 2006, Uncontrolled Copy, (c) BSI 60605-4 ? IEC:2001 7 3 Definitions and symbols For the purposes of this International Standard,
42、 the terms and definitions of IEC 60050(191), ISO 3534-1 and ISO 3534-2 apply, together with the following definitions and symbols. Additional constants and functions are defined in the text. 3.1 Definitions 3.1.1 two-sided confidence interval (see ISO 3534-1, 2.57) when L2 m and U2 m are two functi
43、ons of the observed values such that, m being a population parameter to be estimated, the probability )(Pr 2U2L mmm? is at least equal to )1(? (where )1(? is a fixed number, positive and less than 1), the interval between 2L m and 2U m is a two- sided )1(?confidence interval for m 3.1.2 one-sided co
44、nfidence interval (see ISO 3534-1, 2.58) when 1U m (or L1 m) is a function of the observed values such that, m being a population parameter to be estimated, the probability )(Pr 1U mm? (or the probability )(Pr 1L mm?) is at least equal to )1(? (where )1(?is a fixed number, positive and less than 1),
45、 the interval from the smallest possible value of m up to 1U m (or the interval from L1 m up to the largest possible value of m) is a one-sided )1(? confidence interval for m NOTESee annex B for further discussion. 3.1.3 tolerance limits (see ISO 3534-2, 1.4.3) two limits L2 ? and U2 ? on the observ
46、ed number of failures between which at least a proportion P of the population may be asserted (with probability ?1) to lie NOTEThe interval L2 ? to U2 ? is known as the tolerance interval. 3.1.4 (see ISO 3534-2, 1.4.4) tolerance difference between the upper and lower tolerance limits. NOTEMore descr
47、iptive definitions of the above quantities and their relationship to one another are given in annex B. 3.2 Symbols clLower or upper one-sided confidence limit on a dependability parameter, such as MTTF (mean time to failure), failure rate, reliability, etc. ?Significance level: )1(100? % is the conf
48、idence level at which confidence intervals and limits are calculated ?L1, ?U1Lower and upper one-sided values of a )1(100? % tolerance interval ?L2, ?U2Lower and upper two-sided values of a )2/1(100? % tolerance interval ?True constant failure rate BS IEC 606054:2001 BSI 31 August 20017 BS IEC 60605
49、4:2001 BSI 31 August 20017 BS IEC 606054:2001 BSI 31 August 20017 Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 14:35:31 GMT+00:00 2006, Uncontrolled Copy, (c) BSI 60605-4 ? IEC:2001 8 ? Estimated constant failure rate U11L ,?Lower and upper one-sided confidence limit on true failure rate U22L ,?Lower and upper two-sided confidence limit on true failure rate mTrue mean time to failure m Estimated mean time to failure U11L ,mmLower an