Tiêu chuẩn iso tr 21074 2016

© 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[.]

A pplication ofISO 5725 for the

Ap lication de la n rme ISO 5 25 p ur la déte mination de la

ré éta ilité et la r productibilité de s e ssais de précision ré lisés en

tra a x de n rmalisation p ur l’a alyse chimique de l’acier

COPYRIGHT PROTECTED DOCUMENT

© ISO 2016, P blshed in Sw itz rlan

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written permis ion Permis ion c n be r eq esed fr om either ISO at the ad r es below or ISO’s member bod y in the c u ty of

F r eword i v

1 Sc ope 1

2 Nor mati ve r eferenc es 1

3 Terms an definitions 1

4 Precision test 1

4.1 Structur e of the precision tes 1

4.2 Homog eneity of samples 2

4.3 Numbe of la oratories an n mbe of levels 2

5 Representatio of the e x per imental r esults 2

5.1 General 2

5.2 Ta le of r esult an n mbe of de imal plac s 2

5.3 Graphical r epr esentation of the data 3

5.3.1 General 3

5.3.2 Data plot 3

6 Statistical evaluatio 4

6.1 Cochran ’s tes 5

6.2 Grub s’ tes 6

6.2.1 General 6

6.2.2 Grub s’ tes for one ou ie o se v tion 7

6.2.3 Grub s’ tes for two outle o se v tions 7

6.3 Tr eatment of ou ie o se v tions 8

6.4 Calculation of pr ecision 8

6.5 Representation of the r esult of the statistical ev luations 9

6.6 Fu ctions lnking the level an the pr ecision p r amete s 1

7 Deter mining smoothed precisio and sc ope 15

Biblog raphy 16

ISO (he Int ernational Org nization for Stan ardization) is a worldwide fede ation of national s an ards

b dies (ISO membe b dies) The work of pr paring Int ernational Stan ards is normal y car ied out

through ISO t ech ical committ ees Each membe b dy int er st ed in a subje t for w hich a t ech ical

committ ee has be n es a lshed has the right t o be r pr sent ed on that committ ee Int ernational

org nizations, g ove nmental an non-g ove nmental, in laison with ISO, also take p rt in the work

ISO cola orat es closely with the Int ernational Ele trot ech ical C mmis ion (IEC) on al matt ers of

ele trot ech ical s an ardization

The proc d r s used t o develo this document an those int en ed for it furthe maint enanc ar

desc ibed in the ISO/IEC Dir ctives, Part 1 In p rticular the dife ent a pro al c it eria ne ded for the

dife ent ty es of ISO document should be not ed This document was draft ed in ac ordanc with the

edit orial rules of the ISO/IEC Dir ctives, Part 2 ( e www.iso.org dir ctives)

A tt ention is drawn t o the p s ibi ity that some of the element of this document ma be the subje t of

p t ent right ISO shal not be held r sponsible for identifying any or al such p t ent right Detai s of

any p t ent right identif ied d ring the develo ment of the document wi be in the Introduction an / r

on the ISO ls of p t ent de larations r c ived ( e www.iso.org p t ent )

Any trade name used in this document is information given for the convenienc of use s an does not

cons itut e an en orsement

For an ex lanation on the meaning of ISO spe ific t erms an ex r s ions r lated to conformity as es ment,

as wel as information a out ISO’s adhe enc to the Wor ld Trade Org nization (WTO) principles in the

Te h ical Bar ie s to Trade (TBT) se the folowing URL: www.iso.org iso/for word.html

The committ ee r sponsible for this document is ISO/TC 1 , Ste l, Subcommitt ee SC 1, Meth ds o

dete min tio o chemic al c omp s itio

A pplication ofISO 5725 for the determination of

ofsteel

This document desc ibes how t o det ermine the r peata i ty an r prod cibi ty of pr cision t es s

pe formed within s an ardization work using the chemical analy sis method Spe ificaly, this document

ex lains the proc d r for calculating pr cision, using pr cision t es data of ISO 5 2 -3:1 94, Ta le D.2

for the pr cision t es in ISO 9 47 :1 8 as an ex mple

The proc d r of the int ernational t es for det ermining pr cision is desc ibed in ISO 5 2 - 2 an

ISO 5 2 -3

2 Normati ve referenc es

The e ar no normative r fe enc s in this document

3 Terms and definitions

No t erms an def initions ar lst ed in this document

ISO an IEC maintain t erminolo ical data ases for use in s andardization at the folowing ad r s es:

— IECEle tro edia: a aia le at ht p:/ www.ele tro edia.org

— ISO Onlne brow sing plat orm:a ai a le at ht p:/ www.iso.org o p

4 Precision test

4.1 Structure of the precision test

The s ructur of the pr cision t es normal y used within s an ardization work using chemical analy sis

is a 3-fact or, s a g er d-nest ed s ructur , as shown in Figur 1

a) Both A an B (Da 1) ar o tained u de r peata i ity w he ein epen ent t es r sult ar o tained

with the same method on identical it ems in the same la orat ory b the same o e at or using the

same eq ipment within short int erv ls of time

b) C (Da 2) is o tained u de time-dife ent int ermediat e pr cision con itions, ex cept for the time

fact or The measur ment is pe formed b the same o e at or an , in ad ition, the measur ment at

a given level ar pe formed using the same sample an eq ipment throughout

4.2 Homog eneity ofsamples

F or a pr cision t es it is imp rtant t o use homog eneous samples The efor , it is ne es ary t o control the

homog eneity of the samples sele t ed for each pr cision t es , if the samples ar not c rtif ied r fe enc

mat erials, befor s arting a t es in orde t o be sur that the het erog eneity level of the sample can be

inclu ed in the ex e t ed pr cision v alues

4.3 Number of labor atories and number of levels

In principle, the n mbe of la orat ories that particip t e in an int ernational co pe ative t es is de ided

on theb sis of the r q ir d pr cision As this a pro ch is oft en diff icult t o implement, the practical rule

ty icaly folowed is the sele tion of 8 t o 1 (or mor )la orat oriesse ISO 5 2 -1:1 94, 6.3.4, pr fe a ly

in 5 cou tries The n mbe of levels depen s on the rang e an sco e of the method t o be t est ed A

minimum of two levels b de ade with the scheme (for ex mple, 1 1 ) is r q ir d, an in the case of

l mit ed a plcation rang es, thr e or mor levels b de ade (for ex mple, 1– 2– – 0) can be sele t ed

NOTE F l y-nested e periments ofer higher relia ility of repe ta ility than sta g red-nested e periments

However, it wil not improve the relia ility of reprod cibility signif icantly From the stan point of improving

relia ility, it is efective t o inc e se the n mb r of participating la orat ories

5 Representation ofthe ex perimental r esults

5.1 General

Firs , on the b sis of pr cision t es r sult , pr par the folowing ta les an gra hs

5.2 Table of r esults and number of decimal plac es

Pr p r a ls of pr cision data

In the l s of data, the n mbe of de imal plac s is the n mbe r q ir d in the ex e iment plus one

ac ording t o the convenor’ s r q ir ment

Ta le 1 show s an ex mple of a ls of data

The data o tained b la orat ory i ar in icat ed b y

i( j = 1, 2, 3)

The symb l p r pr sent the n mbe of la orat ories p rticip ting in the ex e iment (It should be

not ed that the n mbe chang es if outl e s ar delet ed )

Table 1 — Original results

Al data can be ev luat ed b gra hical r pr sentation jus t o g et an o e view of the data p pulation

dis ribution If the e ar la orat ories w hich ha e o viously e roneous v lues for seve al levels,

el minating those la orat ories as an outle ma be conside ed if de med ne es ary

5.3.2 Data plot

Draw a gra h for each of the levels b plot ing the data as fol ow s

a) F r each of the la orat ories in Ta le 1, plot Da 1 t o 1 (= yi1), Da 1 t o 2 (= yi2) an Da 2 (= yi3)

using dife ent symb ls

b) In icat e the a e ag e mx for each level

An ex mple of the gra h for the original r sult is shown in Figur 2

Key

X la oratory no

Y contents % (mas fraction)

Figure 2 — Original results

6 Statistical evaluation

The g ene al flow chart of the s atis ical ev luation is shown in Figur 3

Pe form Cochran t es an Grub s’ t es folowing the proc d r shown below t o det ect ed the outle s

an delet e them The flow chart dia ram of the t es s is shown in Figur 4

In ut r esults

Remove the outlier

Calculate the pre isions for

Table 2

Table 2 Lis of satistic l values in

pre ision data in Table 2 Prepare the eq ation of

Valdate the statistic l values

Vr < VR w < V R" (where V =varianc )

CVR, A IMCVR, MA X CVR, tuenes

Determine the pre ision of

smo thed values in Table 3

Determine the sc pe

1) Lis of raw data

2) Plot of raw data

Figure 3— Flow for determining the precisio

A re otler s pr ent?

Delete otlier s

A re o tlier s pr esnt?

Delete o tleYES N

Y ES

N

Gru bs' tet STA RT

One o tlyin o s vatio for

G-v alue MA X (or G-v alue MIN)

A re otler s pr ent?

Y ES

N

One o tle o s v atio for

G-v alue MIN (or G-value MA X)

Tw o o tle os vatio s for the

two larg est ad tw o smale t

The purp se of the Cochran t es is t o ev luat e the int erla orat ory r peata i ity v rianc F r that

purp se, the intrala orat ory r peata i ty v rianc is calculat ed an comp r d with those of othe

is the highes s an ard deviation in the set of level j.

c) C mp r the calculat ed v lue with the v lue for n = 2 in the c itical v lues ta le

( e ISO 5 2 - 2:1 94, Ta le 4 )

d) If the calculat ed v lue is larg er than 1 % c itical v lue, as ume it is an outle an delet e the

cor esp n ing data Then, r peat st eps a) t o c) for the r maining data

e) Finish the t es eithe w hen no outle s ar det ect ed or the r maining data ar eq al t o or not les

than 9 % of theoriginal data

NOTE A piece of statistical data gre t er than 1 % or 5 % of the c itical value is caled an “outlier” an

“ tra gler” , respectively

6.2 Grubbs’ test

6.2.1 General

S e ISO 5 2 - 2:1 94, 7.3.4

The purpose of the Grub s’ t es is t o ev luat e the betwe n-la orat ory consist ency F or that purp se,

the c l a e ag e for each la orat ory is o tained an ev luat ed in t erms of the deviation from the o e al

a e ag e

Using (A+B+ )/ as the t es data, pe form the folowing calculations for each level j

NOTE T e symb ls used in this clause are the same as those in 6.1

a) Obtain the a e ag e v lue x y

ii

= of A-B-C

b) Ar ang e the a e ag e v lues x y

ii

= in asc n ing orde

NOT T e n mb r,p, chang es if outlier are removed

d) Obtain the u biased v rianc for x y

ii

1

2

1

6.2.2 Grubbs’ test for one o tle obser vatio

S e ISO 5 2 - 2:1 94, 7.3.4.1

a) Calculat e the fol owing G-v lues and comp r them with the a pro riat e v lue in the ta le of

c itical v lues ( e ISO 5 2 - 2:1 94, Ta le 5) If the calculat ed v lue is larg er than 1 % c itical

v lue, as ume it is an outle

1) Tes of the ma imum v lue: G x x S

b) If in a) a o e the ma imum v lue (minimum v lue) is an outle , r mo e it an a ply the Grub ’ s

t es t o the minimum v lue (ma imum v lue)

c) Finish the t es w hen no outle s ar det ect ed in st eps a) an / r b) When no outle s ar det ect ed,

con uct a furthe t es for two outle o se v tions (6.2.2)

6.2.3 Grubbs’ test for two o tl e o ser vatio s

S e ISO 5 2 - 2:1 94, 7.3.4.2

If in the a o e Grub s’ t es [a) t o c)] neithe the ma imum v lue nor the minimum v lue is an outle ,

calculat e the folowing G-v lues an comp r them with the a pro riat e v lue in the ta le of c itical

v lues ( e ISO 5 2 - 2:1 94, Ta le 5) If the calculat ed v lue is s male , as ume it is an outle

a) Tes of the two larg es o se v tions: G S S

=

−12

02

,

b) Tes of the two smales o se v tions: G= S S

122

02

12

1

2

1

2,

12

31

2,

=

−

=

∑

6.3 T reatment of outl er observations

a) If a r sult is fou d t o be an outle in one of the t es s, the entir la orat ory data set of the a pro riat e

level containing this r sult is discarded befor s arting the pr cision calculation desc ibed in 6.4

b) If r sult from a la orat ory ar foun t o be outle s at seve al levels, conside r mo ing the w hole

r sult from thisla orat ory

c) El minating only a single data (A or B or C as la eled in 6.1) for a spe ific level of a spe if ic

la orat ory is not done, sinc it influenc s the s atis ical calculations

In ad ition t o the method s ipulat ed in the guidel nes, the e is a method in w hich the Grub s’ t es is

car ied out on the data aft er the elmination of outl e s b the C chran ’ s t es It is desira le that the

s atis ician or convene makes the f inal ju g ement aft er con ucting b th t es s, if ne es ary, t o identify

outle s

6.4 Calculation of precision

6.4.1 C r y out the calculation of pr ecision data b folowing the s eps desc ibed in 6.4.2 to 6.4.8,

which are b sed on ISO 57 5-3

In this proc d r , pa att ention t o the folowing point

a) If the es imat ed v lue of v rianc be omes neg tive d ring the calculation, it is as umed t o be z ro

A neg tive es imat ed v rianc is d e t o a smal degr e of fr edom The efor , it is desira le that he

n mbe of particip ting la orat ories should be as many as p s ible It is desira le that the fact ors

causing the neg tive v rianc be analysed f irs in orde t o asc rtain that nothing u usual exis s

b) The n mbe of de imal plac s of the calculat ed pr cision data ar the n mbe r q ir d for the

r sult of the r lat ed pr cision t es plus one Figur s ar not roun ed d ring the calculations

3

22

( )

Divide SS0, SS1an S e, r spe tively, b the a pro riat e degr e of fr edom (SS0 = p-1, SS1 = p, S e = p)

t o o tain mean sq ar s MS0, MS1an MSe

NOTE With the SS 0 formula given in ISO 572 -3:1 94, C.1, the value of MS 0 can b come ne ative as a result

of improper rou ding when comp ter proces ing is performed incor ectly Therefore, it is not used in these

guidelines

6.4.5 Unbiased estimated v lues ofσ

(0)2

,σ

(1)2

r2

111

NOTE An estimated values that b come ne ative d ring the calculation are as umed t o b zero

6.4.6 Repeata i ity v rianc :

02

6.5 Representation of the results ofthe statistical evaluations

6.5.1 T e r esults of s atis ical calculations ar e shown in Ta le 2, which contains the eleven items

desc ibed in 6.5.2 to 6.5.1

( )

σ

6.5.10 A imed coeficient of v riation

Designation: AIMCV(R)

This is o tained from r gr s ion F ormula (1), w hich is de ived from the mean l ne shown in Figur 5:

6.5.11 Ma imum coeficient of v riation.

Designation: MAX V(R)

This is o tained from r gr s ion F ormula (2), w hich is de ived from the mean+ s.d l ne shown in

NOTE 1 R egres ion Formula (1) an (2) are b sed on the e perimental data Not e that the reprod cibility

limit ( R)an u it µg g)in Figure 5are e pres ed as reprod cibility an %, respectively, in this document

NOTE 2 R egres ion F ormula (1),which is the re res ion formula for the value of R, is represent ed by “ me n” in

Figure 5

NOTE 3 R egres ion Formula (2), which is the re res ion formula for the value of R plus the value of the

stan ard deviation σ , is represented by “ me n + σ” in Figure 5

6.5.12 Truenes

Conc rning truenes , the folowing method is used

If many levels ar ju g ed t o ha e a significant bias in truenes , it is advisa le t o che k if the e ar any

pro lems with t es method an proc d r (or v lues of the r fe enc mat erials)

(a) F r each level, calculat e the dife enc betwe n the r fe enc mat erial v lue, μ, an the measur d

rR

r

=σ

, ju g e that the measuring method has no bias

Othe wise, ju g e that the method has bias, an ent er an ast erisk ( ) in the TRU lne

Henc , it can be ju g ed that the e is a p sitive bias F or the r fe enc

mat erial v lue, μ, however, it is advisa le t o conside the unc rtainty given t o it