© ISO 2016 Application of ISO 5725 for the determination of repeatability and reproducibility of precision tests performed in standardization work for chemical analysis of steel Application de la norm[.]
TECHNICAL REPORT ISO/TR 21074 First edition 2016-10-15 Application of ISO 5725 for the determination of repeatability and reproducibility of precision tests performed in standardization work for chemical analysis of steel Application de la norme ISO 5725 pour la détermination de la répétabilité et la reproductibilité des essais de précision réalisés en travaux de normalisation pour l’analyse chimique de l’acier Reference number ISO/TR 21074:2016(E) © ISO 2016 ISO/TR 074: 01 6(E) COPYRIGHT PROTECTED DOCUMENT © ISO 2016, Published in Switzerland All rights reserved Unless otherwise specified, no part o f this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission Permission can be requested from either ISO at the address below or ISO’s member body in the country o f the requester ISO copyright o ffice Ch de Blandonnet • CP 401 CH-1214 Vernier, Geneva, Switzerland Tel +41 22 749 01 11 Fax +41 22 749 09 47 copyright@iso.org www.iso.org ii © ISO 2016 – All rights reserved ISO/TR 21074:2016(E) Contents Page Foreword iv Scope Normative references Terms and definitions Precision test 4.1 4.3 Structure of the precision test f Number of laboratories and number of levels 5.1 5.2 5.3 General Table of results and number of decimal places Graphical representation of the data 5.3.1 General 5.3.2 Data plot H o mo geneity o s amp les Representation of the experimental results Statistical evaluation 6.1 6.2 6.3 6.4 6.5 6.6 Cochran’s test Grubbs’ test 6.2.1 General 6.2.2 Grubbs’ test for one outlier observation 6.2.3 Grubbs’ test for two outlier observations Treatment of outlier observations Calculation of precision Representation of the results of the statistical evaluations Functions linking the level and the precision parameters 13 Determining smoothed precision and scope 15 Bibliography 16 © ISO 2016 – All rights reserved iii ISO/TR 21074:2016(E) Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies) The work o f preparing International Standards is normally carried out through ISO technical committees Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters o f electrotechnical standardization The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part In particular the different approval criteria needed for the di fferent types o f ISO documents should be noted This document was dra fted in accordance with the editorial rules of the ISO/IEC Directives, Part (see www.iso.org/directives) Attention is drawn to the possibility that some o f the elements o f this document may be the subject o f patent rights ISO shall not be held responsible for identi fying any or all such patent rights Details o f any patent rights identified during the development o f the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso.org/patents) Any trade name used in this document is in formation given for the convenience o f users and does not constitute an endorsement For an explanation on the meaning o f ISO specific terms and expressions related to formity assessment, as well as information about ISO’s adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following URL: www.iso.org/iso/foreword.html The committee responsible for this document is ISO/TC 17, Steel, Subcommittee SC 1, Methods of determination of chemical composition iv © ISO 2016 – All rights reserved TECHNICAL REPORT ISO/TR 21074:2016(E) Application of ISO 5725 for the determination of repeatability and reproducibility of precision tests performed in standardization work for chemical analysis of steel Scope T h i s c u ment de s crib e s how to de term i ne the rep e atabi l ity a nd repro ducibi l ity o f pre ci s ion te s ts p er forme d with i n s tandard i z ation work u s i ng the chem ica l ana lys i s me tho d Sp e c i fic a l ly, th i s c u ment explains the procedure for calculating precision, using precision test data of ISO 5725-3:1994, Table D.2 for the precision test in ISO 9647:1989 as an example The procedure of the international test for determining precision is described in ISO 5725-2 and ISO 5725-3 Normative references There are no normative references in this document Terms and definitions No term s and defi nition s a re l i s te d i n th i s c ument ISO and IEC maintain terminological databases for use in standardization at the following addresses: — IEC Electropedia: available at http://www.electropedia.org/ — ISO Online browsing platform: available at http://www.iso.org/obp Precision test 4.1 Structure of the precision test T he s truc tu re o f the pre c i s ion tes t norma l ly u s e d with i n s ta ndard i z ation work u s i ng chem ic a l a na lys i s is a 3-factor, staggered-nested structure, as shown in Figure Day A Day B C Figure — Structure of the precision test © ISO 2016 – All rights reserved ISO/TR 21074:2016(E) a) Both A and B (Day 1) are obtained under repeatability where independent test results are obtained with the same method on identical items in the same laboratory by the same operator using the same equipment within short intervals of time b) C (Day 2) is obtained under time-di fferent intermediate precision conditions, except for the time factor The measurement is per formed by the same operator and, in addition, the measurements at a given level are performed using the same sample and equipment throughout 4.2 Homogeneity of samples For a precision test it is important to use homogeneous samples There fore, it is necessary to control the homogeneity o f the samples selected for each precision test, i f the samples are not certified re ference materials, be fore starting a test in order to be sure that the heterogeneity level o f the sample can be included in the expected precision values 4.3 Number of laboratories and number of levels In principle, the number of laboratories that participate in an international cooperative test is decided on the basis o f the required precision As this approach is o ften di fficult to implement, the practical rule typically followed is the selection o f to 15 (or more) laboratories see ISO 5725-1:1994, 6.3.4, pre ferably in countries The number of levels depends on the range and scope of the method to be tested A minimum o f two levels by decade with the scheme (for example, 1–10) is required, and in the case o f limited application ranges, three or more levels by decade (for example, 1–2–5–10) can be selected NOTE Fully-nested experiments o ffer higher reliability o f repeatability than staggered-nested experiments However, it will not improve the reliability o f reproducibility significantly From the standpoint o f improving reliability, it is e ffective to increase the number o f participating laboratories Representation of the experimental results 5.1 General First, on the basis of precision test results, prepare the following tables and graphs 5.2 Table of results and number of decimal places Prepare a list of precision data In the list of data, the number of decimal places is the number required in the experiment plus one according to the convenor’s requirement Table shows an example of a list of data The data obtained by laboratory are indicated by y ij ( = 1, 2, 3) i j The symbol p represents the number o f laboratories participating in the experiment (It should be noted that the number changes if outliers are deleted.) © ISO 2016 – All rights reserved ISO/TR 21074:2016(E) Table — Original results Lab no — i — p B y12 Day C y13 yi1 yi2 yi3 yp1 yp2 yp3 A y11 — — Day — — — — 5.3 Graphical representation of the data 5.3.1 General All data can be evaluated by graphical representation just to get an overview o f the data population distribution I f there are laboratories which have obviously erroneous values for several levels, eliminating those laboratories as an outlier may be considered i f deemed necessary 5.3.2 Data plot Draw a graph for each o f the levels by plotting the data as follows a) For each of the laboratories in Table , plot Day to (= yi1), Day to (= yi2) and Day (= yi3) using di fferent symbols b) Indicate the average m x for each level An example of the graph for the original results is shown in Figure Y 0,015 0,014 0,013 yi1 0,012 0,011 yi2 0,010 0,009 yi3 0,008 mx 0,007 0,006 10 11 12 13 14 15 16 17 18 19 20 21 X Key X laboratory no Y contents % (mass fraction) Figure — Original results © ISO 2016 – All rights reserved ISO/TR 21074:2016(E) Statistical evaluation Figure Perform Cochran’s test and Grubbs’ test following the procedure shown below to detected the outliers f Figure T he genera l flow cha r t o f the s tati s tica l eva luation i s shown i n and dele te them T he flow char t d iagram o the te s ts i s shown i n I nput results ) Lis t o f raw data ) Plot of raw data Co chran' s test Grub bs ' test Remove the o utliers C alculate the precisio ns fo r Tab le List o f s tatistical values in Tab le Prepare the equation o f precision data in Table Validate the statistical values Vr < VRw < VR" (where V= variance) C VR, AI M CVR, M AXC VR, truenes s D etermine the precision of smo othed values in Tab le D etermine the sco p e Figure — Flow for determining the precision © ISO 2016 – All rights reserved ISO/TR 074: 01 6(E) Grub bs ' test START Co chran' s test START O ne o utlying o b servatio n fo r G- value M AX (o r G- value M I N) NO Are o utliers NO pres ent? Are outliers p res ent? YE S YE S D elete o utliers Two o utlier o bs ervatio ns for the D elete o utliers two larges t and two smallest Print o ut the outlier lab numb ers O ne o utlier o bs ervatio n for with a ub le asteris k ** NO G-value M I N (o r G- value MAX) Are outliers p resent? NO D elete outliers Are outliers p res ent? YE S YE S D elete o utliers NO Remaining data is ≥ D elete o utliers % o f o riginal YES Print out the o utlier lab numb ers with a ub le as terisk ** STO P STO P Figure — Flow diagram of the Cochran’s tes t and Grubbs ’ test 6.1 Cochran’s test See ISO 5725-2:1994, 7.3.3 T he pu rp o s e o f the C o ch ran’s te s t i s to eva luate the i nterlab orator y rep e atabi l ity va ri ance For th at pu r p o s e, the i ntra l ab orator y rep e atabi l ity varia nce i s c a lc u l ate d and comp a re d with tho s e o f o ther laboratories For each level , perform the following calculations on each test data set The test data sets are (A, B) and [(A+B)/2, C] a) Obtain the standard deviation: j S ij = y ij − y ij 2 b) Calculate the C-value: C= S max p ∑ S i2 i =1 © ISO 2016 – All rights reserved ISO/TR 074: 01 6(E) where i i s the identi fier for a cer tai n lab; j i s the identi fier for a cer tai n level; p is the number of laboratories of level j (note that the number, p , changes if outliers are dele te d) ; S max is the highest standard deviation in the set of level j c) Compare the calculated value with the value for n = in the critical values table (see ISO 5725-2:1994, Table 4) d) If the calculated value is larger than % critical value, assume it is an outlier and delete the corresponding data Then, repeat steps a) to c) for the remaining data e) Finish the test either when no outliers are detected or the remaining data are equal to or not less than 90 % of the original data NOTE A piece of statistical data greater than % or % of the critical value is called an “outlier” and “s traggler ”, re s p e c tivel y 6.2 Grubbs’ test 6.2 General See ISO 5725-2:1994, 7.3.4 T he pu r p o s e o f the Gr ub b s ’ te s t i s to eva luate the b e twe en-lab orator y s i s tenc y For that pu rp o s e, the cel l average for e ach lab orator y i s ob ta i ne d and eva luate d i n term s o f the devi ation average Using (A+B+C)/3 as the test data, perform the following calculations for each level j NO TE T he s ymb ol s u s e d i n th i s cl au s e a re the s a me a s tho s e i n a) Obtain the average value x i = y ij b) Arrange the average values x i x i (i = , NOTE , p the overa l l 6.1 of A-B-C = y ij in ascending order ) The number, p , changes if outliers are removed d) Obtain the unbiased variance for x i x= from p ∑ p i =1 xi S = p ∑ p − i =1 ( = y ij : xi − x) © ISO 2016 – All rights reserved ISO/TR 074: 01 6(E) 6.2 Grubbs’ test for one outlier observation See ISO 5725-2:1994, 7.3.4.1 a) Calculate the following G-values and compare them with the appropriate value in the table of critical values (see ISO 5725-2:1994, Table 5) If the calculated value is larger than % critical value, assume it is an outlier 1) Test of the maximum value: 2) Test of the minimum value: b) G G p = ( x p − x) 1= (x − x1 ) S S I f i n a) ab ove the ma xi mu m va lue (m i n i mu m va lue) i s an outl ier, remove it and apply the Grubb’s test to the minimum value (maximum value) c) Finish the test when no outliers are detected in steps a) and/or b) When no outliers are detected, conduct a further test for two outlier observations (6.2.2) 6.2 Grubbs’ test for two outlier observations See ISO 5725-2:1994, 7.3.4.2 If in the above Grubbs’ test [a) to c)] neither the maximum value nor the minimum value is an outlier, calculate the following G-values and compare them with the appropriate value in the table of critical values (see ISO 5725-2:1994, Table 5) If the calculated value is , assume it is an outlier a) Test of the two largest observations: = −1 02 b) Test of the two smallest observations: = 12 02 where sm aller G S G S p = ∑ i S p (x =1 p −1 , p = x p −1 , p S 1,2 ( = p ∑ (x −2 − x p −1 i p −2 =3 p x =1 p = i x 1, −2 = S ,p , S S − x) i ∑ i p i ) −2 ∑ i ,p =1 x i − x1 )2 , p ∑ i =3 x i © ISO 2016 – All rights reserved ISO/TR 21074:2016(E) 6.3 Treatment of outlier observations a) I f a result is found to be an outlier in one o f the tests, the entire laboratory data set o f the appropriate level containing this result is discarded before starting the precision calculation described in 6.4 b) I f results from a laboratory are found to be outliers at several levels, consider removing the whole results from this laboratory c) Eliminating only a single data (A or B or C as labelled in 6.1) for a specific level o f a specific laboratory is not done, since it influences the statistical calculations In addition to the method stipulated in the guidelines, there is a method in which the Grubbs’ test is carried out on the data a fter the elimination o f outliers by the Cochran’s test It is desirable that the statistician or convener makes the final judgement a fter conducting both tests, i f necessary, to identi fy outliers 6.4 Calculation of precision 6.4.1 Carry out the calculation o f precision data by following the steps described in which are based on ISO 5725-3 6.4.2 to 6.4.8, In this procedure, pay attention to the following points a) If the estimated value of variance becomes negative during the calculation, it is assumed to be zero A negative estimated variance is due to a small degree of freedom Therefore, it is desirable that the number o f participating laboratories should be as many as possible It is desirable that the factors causing the negative variance be analysed first in order to ascertain that nothing unusual exists b) The number of decimal places of the calculated precision data are the number required for the results of the related precision test plus one Figures are not rounded during the calculations 6.4.2 Mean value: y i(1 ) = y i(2) = y= 6.4.3 p ( yi1 + yi ) ( yi + yi + yi ) ∑ yi ( ) i Range: w i(1 ) = yi − yi 6.4.4 Total sum of squares: SST = ∑∑ i w i( ) = y i(1 ) − yi j ( y ij − y ) = SS + SS + SSe © ISO 2016 – All rights reserved ISO/TR 21074:2016(E) where SS = ∑ ( y i ( ) − y) i SS = SSe = ∑ wi 2 ( ) i ∑ wi ( ) i Divide SS0, SS1 and SSe, respectively, by the appropriate degree of freedom (SS0 = p-1, SS1 = p, SSe = p) to obtain mean squares MS0, MS1 and MSe NOTE With the SS0 formula given in ISO 5725-3:1994, C.1 , the value of MS0 can become negative as a result o f improper rounding when computer processing is per formed incorrectly There fore, it is not used in these guidelines Unbiased estimated values ofσ 20 , σ 21 and σ r2 : 6.4.5 ( ) s(20 ) = s(21 ) = 3 MS − 12 MS − MS + 12 ( ) MSe MSe s r2 = MSe NOTE Any estimated values that become negative during the calculation are assumed to be zero Repeatability variance: 6.4.6 s r2 = MSe Intermediate variance: 6.4.7 s 6.4.8 I(1 ) = s r + s(21 ) Reproducibility variance: s R2 = s r2 + s(21 ) + s(20 ) 6.5 Representation of the results of the statistical evaluations The results of statistical calculations are shown in Table 2, which contains the eleven items described in 6.5.2 to 6.5.12 6.5.1 © ISO 2016 – All rights reserved ISO/TR 074: 01 6(E) General mean Designation: m 6.5 Definition: 6.5 y Repeatability Designation: σ ( r) Definition: s r 6.5 Within-laboratory reproducibility Designation: σ R w ( Definition: 6.5 s I( ) ) Reproducibility Designation: σ ( R) Definition: s R 6.5 Repeatability limit Designation: r Definition: 6.5 r = 2, × σ ( r ) Within-laboratory reproducibility limit Designation: R w Definition: R w = × σ R w , 6.5 ( ) Reproducibility limit Designation: R Definition: 6.5 R = 2, × σ ( R ) Coe fficient o f variation Designation: CV R ( ) Definition: CV R = ( 6.5 ) σ ( R) m × 100 Aimed coe fficient o f variation Designation: AIMCV R This is obtained from regression Formula (1), which is derived from the mean line shown in Figure 5: CVR = − m+ (1) ( lo g 10 ) 0, 46 lo g lo g , 477 © ISO 2016 – All rights reserved ISO/TR 074: 01 6(E) M aximum co e fficient o f variatio n 6.5 1 Designation: MAXCV R This is obtained from regression Formula (2), which is derived from the mean+1s.d line shown in Figure 5: m > 001 % CVR = − m+ (2) ( ) lo g , 0, 46 lo g lo g 3, 46 70 £ 001 % CVR = 35 71 ( constant ) m , , NOTE Regression Formulae (1) and (2) limit (R) and unit (µg/g) in Figure NOTE Regression Formula (1), which is the regression formula for the value of R Figure NOTE Regression Formula (2), which is the regression formula for the value of R plus the value of the Figure a re b a s e d o n the e xp er i menta l d ata N o te th at the rep ro duc ib i l ity a re e xp re s s e d a s rep ro duc ib i l ity a nd % , re s p e c ti vel y, i n th i s c u ment , i s repre s ente d b y “me a n” i n s ta nd a rd devi ation σ, i s rep re s ente d b y “me a n +1 σ ” i n Trueness Concerning trueness, the following method is used 6.5 I f many level s are j udge d to have a s igni fic a nt bia s i n truene s s , it i s advi s able to che ck i f there are a ny problems with test method and procedure (or values of the reference materials) (a) For each level, calculate the difference between the reference material value, μ , and the measured mean value: ∧ δ = y−µ ∧ (b) Calculate the values of δ − Aσ R and laboratories): A = 96 n r 2− + r pn ( ) , r = σR σ ∧ ∧ δ + Aσ R (n = 3, number of measurements, p = number of r (c) If is included in the range δ − Aσ R ≤ δ ∧ ≤ δ + Aσ R , j udge that the me a s u ri ng me tho d h as no bia s O ther wi s e, j udge th at the me tho d s bi a s , and enter an as teri s k (*) i n the T RU l i ne For sample reported in Table 2, ∧ range δ − Aσ R ≤ δ material value, μ ∧ ≤ δ + Aσ R y = 0,105 9, μ = 0,10, Aσ R = 0,000 98 and is not included in the Hence, it c an b e j udge d that there i s a p o s iti ve bia s For the re ference , however, it i s advi s able to s ider the u ncer tai nty given to it © ISO 2016 – All rights reserved 11 ISO/TR 21074:2016(E) Table — Results of the statistical analysis Sample Cochran’s test C1 C2 Grubbs’s test G No discarded Mean % σ(r) % σ(Rw) % σ(R) % r % Rw % R % CV(R) % AIMCV(R) % MAXCV(R) % TRU Correct 20** Correct 0,009 798 0,000 381 0,000 603 0,000 801 0,001 067 0,001 688 0,002 243 8,175 138 7,340 303 16,132 955 20** Correct Correct 0,037 863 0,000 540 0,000 848 0,001 062 0,001 512 0,002 374 0,002 974 2,804 849 4,594 443 10,097 941 NOTE C1 dataset : (A, B), C2 dataset : [(A+B)/2,C] 12 Correct Correct Correct 0,105 900 0,001 739 0,002 305 0,002 650 0,004 869 0,006 454 0,007 420 2,502 361 3,216 720 7,069 899 Correct Correct Correct 0,213 900 0,003 588 0,005 693 0,007 307 0,010 046 0,015 940 0,020 460 3,416 082 2,521 106 5,541 038 Correct ** 20** 20** Correct 0,516 368 0,006 237 0,006 436 0,009 412 0,017 464 0,018 021 0,026 354 1,822 731 1,857 507 4,082 540 Correct 0,747 278 0,006 318 0,006 318 0,014 725 0,017 690 0,017 690 0,041 230 1,970 485 1,634 155 3,591 644 * © ISO 2016 – All rights reserved ISO/TR 21074:2016(E) a b Y % b R + σR f f + R σR e e e b e j j e j e j e k k k k j e e j e g f j p h 0,1 jj f c p t v p m u ,0 r u u r r r va r y s a a a e a e e s b l b s s e t b b d n g e y s n g b t b l d n n r al h yo g p l ac l g y j y e v a yy d c s r g h r m a u m a c r p g t u va n yy y yg ae j t s b fp c c h s r e o z yy g g e bn g c y j y eh c e v j e j e j v j e -σ R R j c e -2 R σR j c c j y vy c n r p n b s c b b l n b b y c y c ,00 b j m v z m a uv e c m j r m l au j vf e f n gl e e j g h j c g bb t y n n g n b b n n n c l l b t ,0 0 ,00 ,0 0,01 0,1 10 % X Key a mean+1 s.d b mean - “R” converted from CVR=21-log C(%) X element content, C Y reproducibility, R Figure — Graphical representation of the statistical calculation results 6.6 Functions linking the level and the precision parameters 6.6.1 Use the method shown in ISO 5725-2:1994, 7.5 to obtain a regression formula Since there are no definite rules for the use o f a straight line or logarithm in the regression formula, the working group may make its own judgement As long as there is some factor o f change that can technically be explained, a jagged line (= a line with di fferent slopes) may be used However, to the extent possible, using a straight line is recommended When assessing the functions linking the level and the precision parameters follow the steps described in 6.6.2 to 6.6.6 6.6.2 Draw the values of r, Rw and R for each level 6.6.3 Indicate the regression lines for r, Rw and R 6.6.4 Edit the mathematical expression and correlation coe fficient o f the regression formula It is not appropriate to use a regression formula when the correlation coe fficient is less than 0,65 In this case, use the permissible tolerance α: 6.6.5 © ISO 2016 – All rights reserved 13 ISO/TR 21074:2016(E) α = 2, × where β n n ∑β i i =1 r i s the s tati s tic a l va lue s o f σ ( ) , σ ( Rw) and σ ( R ) for each level T he worki ng group may de cide that , ti me s the h ighe s t va lue o f the s tati s tic a l p ara me ter under concern i s a s ta nt va lue, i f ne ce s s ar y 6.6.6 If the correlation lines of limits (r, Rw) or (R, Rw) intersect, an additional test is carried out, or if the results are adopted, the regression line of Rw f with the note that Rw = r or Rw = R Figure shows an example of the graphical representation of the precision data alo ne is rep res ented b eyo nd the p o int o inters ectio n, Y 1,000 R(%) 0,100 Rw(%) r(%) R(%) 0,010 Rw(%) r(%) 0,001 0,000 0,001 0,010 0,100 1,000 10,000 X lgR = 0,7147lgx-1,339 lgRw = 0,6232lgx-1,576 lgr = 0,7287lgx-1,602 R = 0,972 R = 0,962 R = 0,979 Key X precision % (mass fraction) Y contents % (mass fraction) Figure — Graphical representation of the precision data 14 © ISO 2016 – All rights reserved ISO/TR 21074:2016(E) Determining smoothed precision and scope O n the b as i s o f an overa l l j udgement on the c a lc u lation re s u lts precision of the smoothed value and scope I n th i s pro ce dure, p ay attention to the fol lowi ng shown i n Clause 6, determine the p oi nts (a) The scope is within the range of the precision test (b) The scope is decided with consideration to CV(R when it is lower than AIMCV(R AIMCV(R) and MAXCV(R CV(R) is between ) I t i s advi s able to u ncond itiona l ly adop t ) and rej e c t it when it i s h igher than MAXCV(R) If CV(R) ) T he worki ng group m ay de term i ne what to , givi ng s ideration to the e conomy o f the e xp eri ment, a lthough it dep end s more or le s s on the ci rc u m s tance s After determining the scope, obtain the smoothed values r, Rw, R, CV(R), AIMCV(R) and MAXCV(R) for the f f f f and edit them in a table having a format similar to that shown in Table s p e ci fie d level s ( or e xample, i nclud i ng m i n and ma x content or s cop e) rom the regre s s ion ormu lae Table — Results for the repeatability and reproducibility limits Content mass fraction % 0,01 0,05 0,10 0,50 1,00 Repeatability limit r mass fraction % 0,001 0,003 0,005 0,015 0,025 © ISO 2016 – All rights reserved Reproducibility limits Rw R mass fraction % 0,002 0,004 0,006 0,017 0,027 mass fraction % 0,002 0,005 0,009 0,028 0,046 CV(R) AIMCV(R) MAXCV(R) 6,1 3,8 3,2 2,0 1,6 7,3 4,2 3,3 1,9 1,5 16,0 9,2 7,2 4,1 3,2 15 ISO/TR 21074:2016(E) Bibliography [1] [2] ISO 5725 (all parts), Accuracy (trueness and precision) of measurement methods and results ISO 5725-2:1994, Accuracy (trueness and precision) of measurement methods and results — Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method [3] ISO 5725-3:1994, Accuracy (trueness and precision) ofmeasurement methods and results — Part 3: Intermediate measures of the precision of a standard measurement method [4] ISO 9647:1989, Steel and iron — Determination of vanadium content — Flame atomic absorption 16 © ISO 2016 – All rights reserved spectrometric method