TECHNICAL REPORT CISPR 16-4-3 2004 AMENDMENT 1 2006-10 INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE Amedmet 1 Specificatio for radio disturbace ad immuity measurig apparatus ad methods Part 4-3: Ucertaities, statistics ad limit modellig Statistical cosideratios i the determiatio of EMC compliace of mass-produced products IEC 2006 Droits de reproductio réservés Copyright - all rights reserved Iteratioal Electrotechical Commissio, 3, rue de Varembé, PO Box 131, CH-1211 Geeva 20, Switzerlad Telephoe: +41 22 919 02 11 Telefax: +41 22 919 03 00 E-mail: imail@iec.ch Web: www.iec.ch Commissio Electrotechique Iteratioale Iteratioal Electrotechical Commissio Международная Электротехническая Комиссия PRICE CODE For price, see curret catalogue H
2 TR CISPR 16-4-3 Amed. 1 IEC:2006(E) FOREWORD This amedmet has bee prepared by CISPR subcommittee A: Radio iterferece measuremets ad statistical methods. The text of this amedmet is based o the followig documets: DTR CISPR/A/666/DTR Report o votig CISPR/A/691/RVC Full iformatio o the votig for the approval of this amedmet ca be foud i the report o votig idicated i the above table. The committee has decided that the cotets of this amedmet ad the base publicatio will remai uchaged util the maiteace result date idicated o the IEC web site uder "http://webstore.iec.ch" i the data related to the specific publicatio. At this date, the publicatio will be recofirmed, withdraw, replaced by a revised editio, or ameded. Page 2 CONTENTS Add the title of ew Aex D as follows: Aex D (iformative) Estimatio of the acceptace probability of a sample Page 7 5.1.1.2 Number of sub-rages Replace the formula i NOTE 4, o page 8, by the followig: f i fupp log N = low low 10 f f Page 8 5.1.1.3 Normalizatio of the measured disturbace levels Replace the existig text of the subclause by the followig: The average value ad the stadard deviatio of the measured values i a frequecy subrage shall be compared to the limit. Because the limit may ot be costat over the frequecy sub-rage, it is ecessary to ormalize the measured values.
TR CISPR 16-4-3 Amed. 1 IEC:2006(E) 3 For ormalizatio, the differece, d f, betwee the measured level, x f, ad the limit level, L f, shall be determied at the specific frequecy f that has the largest differece, usig Equatio (3). The differece is egative as log as the measured value is below the limit. where d f = the gap to the limit at the specific frequecy i db; x f = the measured level i db(μv or pw or μv/m); L f = the limit at the specific frequecy i db(μv or pw or μv/m). d f = x f L f (3) 5.1.1.4 Tests based o the o-cetral t-distributio with frequecy sub-rages After Equatio (4) replace the lie begiig " =..." by the followig: " = the umber of items i the sample" Page 30 Add, after Aex C, the followig ew aex: Aex D (iformative) Estimatio of the acceptace probability of a sample D.1 Itroductio The followig cosideratios are iteded for use by maufacturers to estimate the real acceptace probability of a sample, i.e. the maufacturers risk to fail a market surveillace test. These cosideratios are based o the assumptio that a realistic stadard deviatio for the specific type of equipmet uder test ca be estimated based o the experiece of the maufacturer with a specific class of products. The cosideratios i this aex ca also be used to estimate a margi to the limit, which is eeded to achieve a desired acceptace probability. It is emphasized that the purpose of this aex is to provide tools to maufacturers for estimatio of their ow risk, but without itroducig additioal requiremets. For both the realistic stadard deviatio ad the target acceptace probability, exact values ca be defied oly by the maufacturer. Therefore, these methods caot be used to add a additioal margi to the limit as a Pass/Fail criterio for tests performed by orgaizatios other tha the maufacturers. The acceptace probability relatioships provided i this documet do ot iclude cosideratio of measuremet ucertaities, as described i CISPR 16-4-1 ad CISPR 16-4-2. I some cases, these ucertaities ca domiate iterlaboratory comparisos. As such, the acceptace probability calculatios below are valid oly whe results differig from each other withi the measuremet ucertaity of the origial test are cosidered to be equivalet. Figure D.1 shows the ormalized (stadard deviatio σ = 1,0) distributio of the amplitude desity of the disturbace values for a populatio exactly at the acceptace limit, which meas 80 % of the values are uder the disturbace limit, ad 20 % are over the disturbace limit. I this figure the disturbace limit has bee shifted to the origi of the coordiate system, to allow easier calculatio of the differece from the limit.
4 TR CISPR 16-4-3 Amed. 1 IEC:2006(E) To pass a statistical evaluatio based o the biomial distributio, for seve devices take radomly out of this populatio, the largest measured value must still be below the iterferece limit. The curve labeled = 7 i Figure D.1 shows this probability, which is just 20 % at the disturbace limit (the origi of the coordiate system) for the give populatio. I this case the acceptace probability is 20 %. NOTE A acceptace probability of exactly 20 % i this case is ot coicidetal it comes from the requiremet to guaratee a 80 % cofidece level for the method, based o the biomial distributio. Applicatio of the biomial distributio: if the populatio is at the limit of the 80 %/80 % rule, this meas a acceptace probability of 20 % 1,0 1 0,8 The iterferece limit has bee shifted to the origi Distributio largest of 7 Amplitude desity of the disturbace values of a populatio exactly at the acceptace limit 0,6 0,4 0,2 K A = 1,33 0-5 5 4-4 3-3 2-2 1-1 0 1 2 3 4 Normalized emissio values (σ = 1,0) IEC 1679/06 Figure D.1 Normalized distributio (stadard deviatio σ = 1,0) for the amplitude desity of the disturbace values The black arrows idicate how a additioal distace to the limit could be selected to icrease the acceptace probability. To realize a acceptace probability of about 90 % for a test with a sample size of seve, all ormalized emissio values should be reduced by a value K A of about 1,33, which would shift both curves to the left by 1,33. The the curve labeled = 7 would itersect the ordiate at about 0,9, meaig the probability that all values are below zero is about 90 %. This approach is similar to the methodology used i [4] 1), ad i CISPR 16-4-3, 5.3 ad Aex C, respectively. The problem with the precedig approach is that kowledge about the true values for the average ad the stadard deviatio of the populatio are assumed. But the maufacturer does ot kow the true values, oly the results from the sample tested. These results have the same radom variatio as a later sample would, whe beig tested for market surveillace purposes. I practice, the maufacturer has to ifer from the sample tested what results ca be expected for a possible sample tested later. Therefore, aother approach has bee chose for the estimatio of the acceptace probability, described i Clause D.2. 1) Figures i square brackets refer to the referece documets i Clause D.6.
TR CISPR 16-4-3 Amed. 1 IEC:2006(E) 5 D.2 Estimatio of the acceptace probability The followig approach is recommeded to ifer from existig sample test results what results ca be expected for a possible sample tested later. Usig a assumptio of a ormal distributio for the disturbace values, it is possible by simulatio, or itegratio over the distributio fuctios, to determie the distributio of the differece betwee the maximum values of both samples. Cosequetly the acceptace probability for the secod sample ca be obtaied, as show i Figure D.2 ad described i the followig. I Figure D.2, ad also the subsequet Table D.1, 1 is the umber of EUTs tested i the first sample (i.e. i the testig doe by the maufacturer), 2 is the umber of EUTs tested i the secod sample (e.g. durig a market surveillace), ad k s is a factor used for the estimatio of the acceptace probability. The curves show are ormalized, with stadard deviatio σ = 1,0. The term 1 i Figure D.2, ad Table D.1, represets the umber of EUTs tested. If the EUTs are from the same populatio ad are tested uder the same coditios, the probability is exactly 50 % that a secod sample tested is at least as good as the first. Therefore a maufacturer ca assume a acceptace probability of 50 % for a later test, if the maufacturer s sample is exactly at the acceptace limit, i.e. where the requiremets i the stadard are just fulfilled. If the sample tested by the maufacturer is better, the the acceptace probability for a later sample is higher tha 50 %. The curve labeled A i Figure D.1, havig 1 = 5 ad 2 = 5, is calculated assumig that both samples are tested accordig to the same method, ad based o the calculatio for a additioal, differet acceptace limit. Calculatios ca also be doe for differet sample sizes. Figure D.2 shows also the curve B ( 1 = 5, 2 = 7), which is applicable whe a later market surveillace is based o the biomial distributio. Fially, curve C ( 1 = 1, 2 = 7) may be iterestig for a maufacturer who has tested oly oe prototype, ad is useful to estimate the acceptace probability of a sample durig a later market surveillace. Acceptace probability for a secod sample 100 90 80 70 60 50 40 30 20 10 0 4 Iferece from first to secod sample (σ =1) 3 2 1 0 1 2 3 4 A B C Key A 1 = 5; 2 = 5 B 1 = 5; 2 = 7 C 1 = 1; 2 = 7 k s IEC 1680/06 Figure D.2 Acceptace probability for a secod sample Table D.1 shows the values for a factor k S which ca be used to estimate the acceptace probability for a secod sample followig a test o a first sample with 1 = 5 or 1 = 1. The factor k s ca be used i two differet ways:
6 TR CISPR 16-4-3 Amed. 1 IEC:2006(E) to estimate the acceptace probability for a repeated statistical evaluatio after evaluatig a first sample; to defie a margi to the limit, ecessary to reach a desired acceptace probability. Examples showig both applicatios are give i D.4. I these applicatios, a estimatio of a realistic stadard deviatio, σ R, is eeded for the type of EUT beig ivestigated, which must be obtaied by the maufacturer based o experiece with similar products. Table D.1 Values of the factor k S used to obtai acceptace probabilities Row k S for a acceptace probability of: 99 % 98 % 97 % 95 % 90 % 85 % 80 % 75 % 70 % 60 % 50 % A 1 = 5, 2 = 5 B 1 = 5, 2 = 7 C 1 = 1, 2 = 7 2,22 1,95 1,78 1,55 1,21 0,97 0,79 0,63 0,49 0,24 0,00 2,34 2,08 1,91 1,69 1,35 1,13 0,95 0,80 0,66 0,42 0,19 4,15 3,81 3,59 3,31 2,87 2,57 2,34 2,14 1,96 1,64 1,34 NOTE The calculatio with 2 = 5 is based o the ew method with a additioal acceptace limit, itroduced i CISPR 16-4-3, while the calculatio with 2 = 7 is based o the use of the biomial distributio. D.3 Derivatio of the factor k s The values for the factor k s i Table D.1 were derived as follows. Assume, the measured values are ormally distributed with desity g(x) ad distributio fuctio G(x). The i the sample 1 take by the maufacturer, the distributio fuctio for the highest value is give by [ G(x) ] 1 1 ad its desity is therefore 1g( x ) [ G( x )] 1 testig authority, the distributio fuctio of the highest value is give by [ G( y )] 2 1 desity is therefore [ ] 2 g( y ) G( y ). 2. Similarly, i the sample 2 take by the ad its Settig y = x + δ, the desity of the distributio of δ (the differece betwee the highest result of the maufacturer ad the highest result of the testig authority) is therefore f ( δ ) = 1 2 g( x ) [ G( x )] 1 1 1 g( x + δ ) [ G( x + δ )] 2 dx Thus, if the highest result of the maufacturer is a margi D below the limit, the probability of the highest result of the testig authority beig below the limit (i.e. test successful) is give by D f ( δ ) dδ To obtai the precedig table ad figure, this itegral was evaluated umerically. D.4 Emissios ear the limit at more tha oe frequecy The calculatios i this aex are based o the use of the biomial distributio, i.e. o the method described i 5.3 of CISPR 16-4-3 (test based o a additioal acceptace limit). For this coditio, oly the sigle emissio value earest to the limit is cosidered. If results are ear the limit at more tha oe frequecy, the frequecy havig the worst-case result shall be