1、BRITISH STANDARD BS IEC 61650:1997 Reliability data analysis techniques Procedures for comparison of two constant failure rates and two constant failure (event) intensities ICS 29.020BSIEC61650:1997 This British Standard, having been prepared under the directionof the Management Systems Sector Board
2、, was published under the authority ofthe Standards Board and comesinto effect on 15October1997 BSI 03-2000 ISBN 0 580 28097 7 National foreword This British Standard reproduces verbatim IEC61650:1997 and implements it as the UK national standard. The UK participation in its preparation was entruste
3、d by Technical CommitteeDS/1, Dependability and technology, to Subcommittee DS/1/1, Dependability, which has the responsibility to: aid enquirers to understand the text; present to the responsible international/European committee any enquiries on the interpretation, or proposals for change, and keep
4、 the UK interests informed; monitor related international and European developments and promulgate them in the UK. A list of organizations represented on this subcommittee can be obtained on request to its secretary. From 1January1997, all IEC publications have the number60000 added to the old numbe
5、r. For instance, IEC27-1 has been renumbered as IEC60027-1. 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 referr
6、ed to in this document may be found in the 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 co
7、ntract. Users of British Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover, pagesi andii, theIEC title page, pagesii toiv
8、, pages1 to11 and a back cover. This standard has been updated (see copyright date) and may have had amendments incorporated. This will be indicated in the amendment table on the inside front cover. Amendments issued since publication Amd. No. Date CommentsBSIEC61650:1997 BSI 03-2000 i Contents Page
9、 National foreword Inside front cover Foreword iii Text of IEC 61650 1ii blankBSIEC61650:1997 ii BSI 03-2000 Contents Page Foreword iii Introduction 1 1 Scope 1 2 Normative reference 1 3 Definitions 1 4 Symbols 1 5 Assumptions and area of application 2 6 Specification of input data 2 7 Calculation p
10、rocedures 3 Annex A (normative) Tables of the F distribution Graphs for comparison of two failure rates/intensities for T 1 *=T 2 * 5 Annex B (informative) Mathematical background 8 Annex C (informative) Examples 8 Annex D (informative) Bibliography 11 Figure 1 Example of calculation of T i * for on
11、e repaired item, T i * = t 1 + t 2 + t 3 + t 4 2 Figure 2 Example of calculation of T i * for five non-repaired items, T i * = t 1 + t 2 + t 3 + t 4 + t 5 3 Figure A.1 Comparison of two failure rates/intensities for T 1 *=T 2 * Significance levels 10%; 5%; 1%; 0,1%; 4k rk 130 6 Figure A.2 Comparison
12、 of two failure rates/intensities for T 1 *=T 2 * Significance levels 10%; 5%; 1%; 0,1%; 110k rk 250 7 Table 1 Decision criteria using the binomial distribution 3 Table 2 Decision criteria using the F distribution 4 Table 3 Decision criteria using the graphs, Figure A.1 orFigure A.2 inAnnex A 4 Tabl
13、e 4 Decision criteria using the standard normal distribution 4 Table 5 Significance levels (one-sided) using the standard normal distribution 4 Table A.1 0,90 fractiles of the F distribution F 0,90(5 1 , 5 2 ) 5 Table A.2 0,95 fractiles of the F distribution F 0,95 (5 1 , 5 2 ) 5BSIEC61650:1997 BSI
14、03-2000 iii Foreword 1) The IEC (International Electrotechnical 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 standa
15、rdization in the electrical and electronic fields. To this end and 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 w
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17、ns. 2) The formal decisions or agreements of the 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 National Committees. 3) The documents produced have the form
18、of recommendations for international use and are published in the form of standards, 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 tr
19、ansparently to the maximum extent possible 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 r
20、endered responsible for any equipment declared 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 p
21、atent rights. International Standard IEC61650 has been prepared by technical committee56: Dependability. The text of this standard is based on the following documents: Full information on the voting for the approval of this standard can be found in the report on voting indicated in the above table.
22、Annex A forms an integral part of this standard. Annex B, Annex C andAnnex D are for information only. FDIS Report on voting 56/533/FDIS 56/580/RVDiv blankBSIEC61650:1997 BSI 03-2000 1 Introduction It is often necessary to compare the reliability characteristics of systems and components when there
23、are technical or other reasons to believe that they might be different. For example, it might be necessary to compare the reliability of items produced by the same manufacturer over different periods of time, or of items produced by different manufacturers. Failure rate and failure intensity are oft
24、en used as reliability measures. This standard describes procedures for comparing two sets of observations of constant failure rate/constant failure intensity. Simple practical examples are provided to illustrate how the procedures can be applied. 1 Scope This International Standard specifies proced
25、ures to compare two observed failure rates; failure intensities; rates/intensities of relevant events. The procedures are used to determine whether an apparent difference between the two sets of observations can be considered statistically significant. It is assumed that the time intervals to/betwee
26、n the failures (events) are independent and identically exponentially distributed during the observation period (that is, the accumulated relevant test time). NOTEThis assumption implies that the failure rate/intensity is constant. It is furthermore assumed that there are technical or other reasons
27、to believe that a difference (either an improvement or deterioration) might exist between the observed reliability characteristic of the two sets of items under comparison. Some examples of typical applications are described in5.4. The methods are designed as hypothesis tests which state, with a spe
28、cified risk (the significance level), whether the two series of observations belong to the same population or the same process, that is they have the same true mean value. NOTEFailure rate, which is relevant to non-repaired items, is associated with a distribution of times to failure. Failure intens
29、ity, which is relevant to repaired items only, is associated with a point process describing a sequence of events, for example times between failures on a time axis. The procedures are not restricted to comparison of failure rate/intensity, but can be applied to observations of two series of any rel
30、evant events, provided the above assumptions are valid. NOTEThe two series of observations may be of items from the same population, or the same item under different conditions (for example environment and load), or just comparable series of events (for example car accidents on a road). Numerical me
31、thods and a graphical procedure are prescribed. The observation periods relevant to the two series do not need to be equal, but if they are, the methods are very simple. 2 Normative reference The following normative document contains provisions which, through reference in this text, constitute provi
32、sions of this International Standard. At the time of publication, the edition indicated was valid. All normative documents are subject to revision, and parties to agreements based on this International Standard are encouraged to investigate the possibility of applying the most recent edition of the
33、normative document indicated below. Members of IEC and ISO maintain registers of currently valid International Standards. IEC 60050(191):1990, International Electrotechnical Vocabulary (IEV) Chapter191: Dependability and quality of service. 3 Definitions For the purposes of this International Standa
34、rd, the terms and definitions of IEC60050(191) apply. 4 Symbols 4.1 List of symbols ! calculated significance level ! 0 given significance level 2 i true failure rate for series i 9(u) the cumulative standard normal distribution, 9(u!) = ! i 1 or 2, designation for the observation series f statistic
35、 when using the F distribution f c critical value for a given significance level using the F distribution F 1 ! (5 1 ,5 2 )the (1 !) fractile of the F(5 1 ,5 2 ) distribution with 5 1and 5 2degrees offreedom p ratio, p = T 1 */(T 1 *+T 2 *) r total number of failures, r = r 1 + r 2 r i number of fai
36、lures relevant to series i T i * accumulated relevant test time for series i u statistic when using the standard normal distributionBSIEC61650:1997 2 BSI 03-2000 4.2 Transformation of symbols Because the procedures in this International Standard are applicable to different reliability measures, the
37、generic symbol w is used for failure rate/intensity. Hence, for 5 Assumptions and area of application 5.1 Assumptions The tests are based on the assumption that the time intervals to/between the failures are independent and identically exponentially distributed during the observation period (accumul
38、ated relevant test time). This assumption implies constant failure rate and constant failure intensity, respectively. Because it is assumed that there are technical or other reasons to believe that a difference (either an improvement or deterioration) might exist between the observed reliability cha
39、racteristics of the two sets of items or observations under comparison, the one-sided test procedures indicated are valid. 5.2 Repaired items The procedures are applicable for comparing observations of failure intensity (as derived from repaired items), provided that within each period the following
40、 assumptions are true: the accumulated relevant test time is calculated as elapsed operating time (excluding repair times and other down times), seeFigure 1; the repaired items can be considered “as good as new”. 5.3 Non-repaired items The procedures are applicable for comparing observations of fail
41、ure rate derived from non-repaired items, provided that within each period the following assumptions are true: the accumulated relevant test time is calculated as the sum of the times to failure, or, in the case of no failure, the operating time for such items (seeFigure 2); all items belong to the
42、same population. 5.4 Examples of application Examples of observations to which the procedures described can be applied include the following: all kinds of failure rates relevant to components, circuit boards, etc., failure intensities relevant to equipments, units, systems, restarts, etc. The compar
43、ison may be applied to observations from the same item during different time periods, from the same kind of item from different manufacturers, from the same kind of item operating under different conditions, and from items before and after an improvement. NOTEThe statistical ability to detect a part
44、icular difference between two rates/intensities increases with the total number of observed failures (events). 6 Specification of input data In order to apply the procedures, the following data are required: the observed number of relevant failures r 1andr 2for the two observation periods; the accum
45、ulated relevant test times T 1 * andT 2 * for the two periods; the given (chosen) significance level ! 0 , if required. If additional analyses of statistical assumptions are required, the following data shall also be recorded: the time of occurrence for each failure. u! the ! fractile of the cumulat
46、ive standard normal distribution u c critical value for a given significance level using the standard normal distribution w true failure rate/intensity (see4.2) NOTEw is generally unknown. point estimate for failure rate/intensity for series i,= r i /T i z i true failure intensity for series i failu
47、re rate w = 2; failure intensity w = z. w i w i Figure 1 Example of calculation of T i * for one repaired item, T i * = t 1 + t 2 + t 3 + t 4BSIEC61650:1997 BSI 03-2000 3 7 Calculation procedures 7.1 Outline The null hypothesis is that the two rates/intensities are equal or H 0 : w 1 = w 2 . The alt
48、ernative hypothesis is that w 1is smaller than w 2or H 1 : w 1! 0 w 1= w 2BSIEC61650:1997 4 BSI 03-2000 b) Obtain f cfrom the F distribution Table A.1 (1(! 0 =0,90) or Table A.2 (1! 0 =0,95) inAnnex A: where 5 1 =2(r 1 +1); 5 2= 2 r 2 . c) Apply the decision criteria inTable 2. Table 2 Decision crit
49、eria using the F distribution Generally a significance level of ! 0 =5% or10% is recommended, corresponding to the 1! 0(0,95 or0,90) fractile of the F distribution. 7.3 Methods for the case T 1 *=T 2 * 7.3.1 Graphical method, r k 250 onFigure A.1 (if4k rk 130) orFigure A.2 (if110k rk 250) inAnnex A, and note whether the point falls above or below the curve for the stated significance level ! 0 . d) Apply the decision criteria inTable 3. Table 3 Decision criteria using the graphs, Figure A.1 orFigure
