ISO 12744:1997

Copper, lead and zinc sulfide concentrates — Experimental methods for checking the precision of sampling

Concentrés sulfurés de cuivre, de plomb et de zinc — Méthodes expérimentales de contrôle de la fidélité de l'échantillonnage

Koncentrati sulfidov bakra, svinca in cinka - Eksperimentalne metode za preverjanje natančnosti vzorčenja

General Information

• Status: Withdrawn
• Publication Date: 30-Apr-1997
• Withdrawal Date: 30-Apr-1997
• ICS: 73.060.99 - Other metalliferous minerals
• Technical Committee: ISO/TC 183 - Copper, lead, zinc and nickel ores and concentrates
• Drafting Committee: ISO/TC 183/WG 9 - Sampling of copper, lead and zinc concentrates
• Current Stage: 9599 - Withdrawal of International Standard
• Completion Date: 19-Apr-2006
• Ref Project: SIST ISO 12744:2000 - Copper, lead and zinc sulfide concentrates -- Experimental methods for checking the precision of sampling

Relations

• Revised: ISO 12744:2006 - Copper, lead, zinc and nickel concentrates — Experimental methods for checking the precision of sampling
• Effective Date: 15-Apr-2008

Standards Content (Sample)

INTERNATIONAL IS0
STANDARD 12744
First edition
1997-05-01
Copper, lead and zinc sulfide
concentrates - Experimental methods for
checking the precision of sampling
Concent& sulfur& de cuivre, de plomb et de zinc - M&hodes
exp&imentales de con trdle de la fidklit6 de /‘khan tillonnage
Reference number
IS0 12744:-l 997(E)

---------------------- Page: 1 ----------------------
IS0 12744:1997(EI)
Page
Contents
...........................................................................................
Scope
..................................................................
Normative reference.
.....................................................................
General conditions.
Definition of symbols. .
Method of experiment. .
..................................................
Evaluation of experimental data
Assessment of results and action .
Recording of data . .
Annexes
9
A Recording of sampling data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 12
B Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0 IS0 1997
All rights reserved. Unless otherwise specified, no part of this publication may be repro-
duced or utilized in any form or by any means, electronic or mechanical, including photo-
copying and microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case postale 56 l CH-1211 Geneve 20 l Switzerland
Internet [e-mail]
x.400 c=ch; a=400net; p=iso; o=isocs; s=centraI
Printed in Switzerland
ii

---------------------- Page: 2 ----------------------
@ IS0 IS0 12744:1997(E)
Foreword
IS0 (the International Organization for Standardization) is a worldwide fed-
eration of national standards bodies IS0 member bodies). The work of
preparing International Standards is normally carried out through IS0
technical committees. Each membe body interested in a subject for
which a technical committee has beer established has the right to be rep-
resented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. IS0 col-
laborates closely with the International Electrotechnical Commission (IEC)
on all matters of electrotechnical standardization.
Draft International Standards adopted by the technical committees are cir-
culated to the member bodies for voting. Publication as an International
Standard requires approval by at least 75 % of the member bodies casting
a vote.
International Standard IS0 12744 was prepared by Technical Committee
ISOfTC 183, Copper, lead and zinc ores and concentrates.
Annexes A and B of this International Standard are for information only.

---------------------- Page: 3 ----------------------
This page intentionally left blank

---------------------- Page: 4 ----------------------
IS0 12744:1997(E)
INTERNATIONAL STANDARD @ IS0
Copper, lead and zinc sulfide concentrates - Experimental
methods for checking the precision of sampling
of concentrate in order to reach a reliable conclusion.
1 Scope
The lot size shall be chosen to ensure this require-
ment is met.
This International Standard specifies methods for
checking the precision of primary sampling, sample
processing, chemical analysis, physical testing and de-
termination of moisture content of copper, lead and
3.3 Number of increments and number of
zinc sulfide concentrates being carried out in ac-
samples
cordance with the methods specified in IS0 12743,
expressed in terms of standard deviations.
The minimum number of increments for checking
precision should preferably be twice the number de-
termined in accordance with IS0 12743. Hence, if the
number of increments required for routine sampling is
2 Normative reference
IZ and one lot sample is constituted, the minimum
number of increments should be 2n, and two inter-
The following standard contains provisions which,
leaved samples shall be constituted.
through reference in this text, constitute provisions of
this International Standard. At the time of publication,
Alternatively, if the precision is being checked as part
‘ the edition indicated was valid. All standards are sub-
of routine sampling, n increments may be taken and
ject to revision, and parties to agreements based on
two interleaved samples constituted, each comprising
this International Standard are encouraged to investi-
n/2 increments. The sampling precision thus obtained
gate the possibility of applying the most recent edi-
tions of the standards indicated below. Members of
must be divided by fi to obtain the sampling pre-
IEC and IS0 maintain registers of currently valid Inter-
cision for lot samples comprising n increments.
national Standards.
IS0 12743:- 1), Copper, lead and zinc sulfide concen-
trates - Sampling procedures for determination of
3.4 Sample processing and analysis
metal and moisture con tent.
Sample processing shall be carried out in accordance
with IS0 12743. The analysis of samples shall be
carried out according to the methods specified in the
3 General conditions
relevant International Standards.
3.1 General
The determination of precision of primary sampling is
3.5 Frequency of precision checks
based on collecting pairs of interleaved samples from
each lot. If sample processing and measurement are
It is recommended that, even after a precision check
also carried out in duplicate, it is possible to determine
has been conducted, further checks be carried out at
the precision of sample processing and analysis.
regular intervals. Precision checks should also be car-
ried out when there is a change in equipment.
3.2 Number of lots
Because of the large amount of work involved in
checking precision, it is recommended that checks be
It is recommended that pairs of interleaved samples
carried out as a part of routine sampling and analysis.
be collected from more than 20 lots of the same type
1) To be published.

---------------------- Page: 5 ----------------------
IS0 12744:1997(E)
4 Definition of symbols
Number of increments
Absolute difference between duplicates for interleaved samples A and B
Mean absolute difference between duplicates for interleaved samples A and B for k lots
Absolute difference between means for divided interleaved samples AI and A*, and B-, and B2
Mean absolute difference between means for divided interleaved samples A-, and AZ, and B-, and B2, for k lots
Absolute difference between means for interleaved sample A and interleaved sample B
Mean absolute difference between means for interleaved sample A and interleaved sample B for k lots
Estimated value of standard deviation, 0
Estimated variance from RI
Estimated variance from R2
Estimated variance from Es
Estimated standard deviation of analysis
Estimated standard deviation of sample processing
Estimated standard deviation of primary sampling
Estimated standard deviation of primary sampling and sample processing
Estimated total standard deviation of primary sampling, sample processing and analysis
First duplicate result for interleaved sample, where I” = 1 and 2 and indicates interleaved sample A or B
Second duplicate result for interleaved sample, where i = 1 and 2 and indicates interleaved sample A or B
First duplicate result for interleaved sample, where i = 1 and 2 and indicates interleaved sample A or 9, and
j = 1 or 2 and indicates laboratory samples AI or AZ, and B1 or B2
Second duplicate result for sample, where i = 1 and 2 and indicates interleaved sample A or 9, and j = 1 or 2
and indicates laboratory samples AI or AZ, and 9, or 92
Mean value of duplicate results
Mean of mean of duplicate results
Mean of 2 values, and grand mean for sample processing method 3
example of a sampling plan for producing pairs of in-
5 Method of experiment
terleaved samples A and B is shown in figure I.
5.2 Sample processing and analysis
5.1 Interleaved samples
The pairs of interleaved samples A and B taken in ac-
Each alternate primary increment shall be diverted so cordance with 5.1 shall be divided separately and sub-
that pairs of interleaved samples A and B are formed.
jetted to either method 1, method 2 or method 3
The number of divided increments per primary incre-
sample processing and analysis as described in 5.2.1,
ment should be the same as for routine sampling. An
5.2.2 or 5.2.3.
2

---------------------- Page: 6 ----------------------
IS0 12744:1997(E)
c ,
Primary
increment
Primary
increment
Primary
increment
Primary
increment
Primary
ti fL
Lot -
Primary
increment
interleaved
f
sample B
--I I
Primary
increment
t
Primary
increment
Primary
increment
4
,
Primary
increment
Primary
increment
- Example of a plan for interleaved duplicate sampling
Figure 1
52.1 Sample processing method 1 (see figure 2) for sample A,, and x2l
and x22 for sample B. The six
determinations shall be run in random order by the
The two interleaved samples A and B shall be divided
same analyst on the same day using the same ana-
separately to prepare four laboratory samples, A-,, A,,
lytical equipment.
and B,, B2. These laboratory samples shall each be
analysed in duplicate, and the duplicates designated NOTE 2 By using method 2, the estimated precisions of
primary sampling, sample processing and analysis can be
xl l l and xl l2 for sample A,, xlzl and xl22 for sample
obtained separately. However, the estimated values will be
for sample B, and x22l and x222 for
A,, x21 1 and x212
less precise than those obtained using method 1.
sample B,. The eight determinations shall be run in
random order by the same analyst on the same day
using the same analytical equipment. An example is
5.2.3 Sample processing method 3 (see figure 4)
given in annex A.
From each of the two interleaved samples A and B,
NOTE 1 By using method 1, the estimated precisions of
primary sampling, sample processing and analysis can be one laboratory sample shall be prepared. The two la-
obtained separately.
boratory samples A and B shall be analysed in dupli-
cate and the measurements obtained shall be desi-
gnated xl1 and xl2
for sample A and x2l and x22 for
52.2 Sample processing method 2 (see figure 3)
sample B. The four determinations shall be run in ran-
dom order by the same analyst on the same day using
Sample A shall be divided to prepare two laboratory
the same analytical equipment.
samples, A, and A,. From sample B, only one labora-
tory sample shall be prepared. The laboratory samples
NOTE 3 By using method 3, only the estimated precision
shall each be analysed in duplicate, and the duplicates
of analysis and the combined precision of primary sampling
designated xl l l and xl l2 for sample A,, xl2l and xl22 and sample processing are obtained.
3

---------------------- Page: 7 ----------------------
IS0 12744:1997(E)
Lot
I
I
B (Interleaved samples)
A
n
(Laboratory samples)
BI B2
AI A2
I
x212 x221 X 222 (Analyses)
x 111 x122 x 211
Figure 2 - Flowsheet for sample processing method 1
A B (Interleaved samples)
n I
(Laboratory samples)
B
AI A2
X 22 (Analyses)
Flowsheet for sample processing method 2
Figure 3 -
B (Interleaved samples)
(Laboratory samples)
X 22 (Analyses)
Figure 4 - Flowsheet for sample processing method 3

---------------------- Page: 8 ----------------------
@ IS0
(El
e) Calculate the variances ST, S; and sg from
6 Evaluation of experimental data
means of ranges RI, R2 and Es:
6.1 General
--
S2 . D .
(11)
n (q*
The method for evaluation of experimental data shall 1-4
be as specified below, depending on the method of
sample processing selected.
--
S2
. . . (12)
n: (R*)*
2-4
S2 . . .
(13)
n: (713)*
3=4
6.2 Sample processing method 1
The estimated standard deviations of primary sam-
where n/4 is a statistical factor relating range to
pling, sample processing and analysis shall be calcu-
variance for a pair of measurements.
lated in accordance with the following procedure.
a) Calculate the mean and range for each pair of
f) Conduct F-tests on the variances ST, ~22 and S: to
duplicates:
determine whether their differences are statisti-
tally significant using the following procedure:
xij = $x”‘+ x4 . . .
(1)
calculate the variance ratios s~/s: and s:/s$
1)
. 0 ”
(2)
4=I%jr%j*~
compare these ratios with the 95 % con-
2)
where
fidence F-ratios given in table 1 for the num-
i = 1 and 2 representing interleaved samples
ber of degrees of freedom applicable to each
A and B respectively;
variance estimate;
j = 1 and 2 representing laboratory samples
3) if the calculated variance ratio exceeds the
A, and A2 or B1 and B2.
F-ratio, partition the two variances into vari-
ance components as their difference is stat-
b) Calculate the mean of the mean and range for
istically significant.
each pair of duplicates:
If the calculated variance ratio does not exceed
. . .
Xi (3)
the F-ratio, the variances S$ and/or S: cannot be
meaningfully partitioned
into variance compo-
. . . (4)
nents and more data need to be collected.
Calculate the mean and range for each pair of
d
interleave d sa mples, A and B:
g) Assuming the F-tests conducted in f) indicate that
the differences between the variances ST, S$ and
“+X,fXp)
x . . .
(5)
sz are significant, calculate the estimated values
- -
of the variance of analysis (s$, sample processing
3= Xl-- x2 . . .
(6)
R I
(s$ and primary sampling (s: ) as follows:
1
Calculate the grand mean and the means of
d)
S2 S2
. . . (14)
A= 1
ranges R,, R2 and R,:
-
-1 f
1 2
=s; ---s
S2
. . . . . . (15)
(7)
P
c 2 1
x=ii x
1
2 2 12
&=--CR, . . . . . . (16)
(8)
% = 3 - zs*
4k
R2=9R2 . . .
(9)
2k
Calculate the total variance of primary sampling,
h)
1 sample processing and analysis (s$ as follows:
R3’-CR3 . . .
(10)
k
S2
=s; +s;+s; . . I
(17)
where k is the number of lots. T 1
5

---------------------- Page: 9 ----------------------
IS0 12744:1997(E)
F-ratios at the 95 % confidence level for comparison of two variances
Table 1 -
0 Calculate the estimated values of the total stan- I 1
- I , - - L
K3= x . n .
- 4x*, + +*I (23)
dard deviation (ST) and the standard deviations of
2
primary sampling (ss ), sample processing (sp) and
1
analysis (sA).
d) Calculate the grand mean and the means of
ranges RI, R, and R,:
compare the Values Of ST, ss , sp and SA thus ob-
I)
-
tained with the desired standard deviations.
rl =
. . .
C24
c
x=c x
1
RI=- RI . . I
i25)
c
6.3 Sample processing method 2
3k
1
R2=-zR2 . . .
(26)
The estimated standard deviations of primary sam-
k
pling, sample processing and analysis shall be calcu-
1
lated in accordance with the following procedure.
R3=-xR3 . . .
(27)
k
where k is the number of lots.
a) Calculate the mean and range for each pair of
duplicates:
e) Calculate the variances s:, S: and S: from the
1
(x121 +"l**)f
?
means of ranges RI, R2 and R3:
. . .
(18)
s: =-
. . .
(28)
B (q*
RI= 1 XIII - x112 II Xl21 -X122 ’
2 n:---2
--
. . . . . .
(19) (29)
...

SLOVENSKI STANDARD
SIST ISO 12744:2000
01-junij-2000
.RQFHQWUDWLVXOILGRYEDNUDVYLQFDLQFLQND(NVSHULPHQWDOQHPHWRGH]D
SUHYHUMDQMHQDWDQþQRVWLY]RUþHQMD
Copper, lead and zinc sulfide concentrates -- Experimental methods for checking the
precision of sampling
Concentrés sulfurés de cuivre, de plomb et de zinc -- Méthodes expérimentales de
contrôle de la fidélité de l'échantillonnage
Ta slovenski standard je istoveten z: ISO 12744:1997
ICS:
73.060.99 Druge rude Other metalliferous minerals
SIST ISO 12744:2000 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------

SIST ISO 12744:2000

---------------------- Page: 2 ----------------------

SIST ISO 12744:2000
INTERNATIONAL IS0
STANDARD 12744
First edition
1997-05-01
Copper, lead and zinc sulfide
concentrates - Experimental methods for
checking the precision of sampling
Concent& sulfur& de cuivre, de plomb et de zinc - M&hodes
exp&imentales de con trdle de la fidklit6 de /‘khan tillonnage
Reference number
IS0 12744:-l 997(E)

---------------------- Page: 3 ----------------------

SIST ISO 12744:2000
IS0 12744:1997(EI)
Page
Contents
...........................................................................................
Scope
..................................................................
Normative reference.
.....................................................................
General conditions.
Definition of symbols. .
Method of experiment. .
..................................................
Evaluation of experimental data
Assessment of results and action .
Recording of data . .
Annexes
9
A Recording of sampling data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 12
B Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0 IS0 1997
All rights reserved. Unless otherwise specified, no part of this publication may be repro-
duced or utilized in any form or by any means, electronic or mechanical, including photo-
copying and microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case postale 56 l CH-1211 Geneve 20 l Switzerland
Internet [e-mail]
x.400 c=ch; a=400net; p=iso; o=isocs; s=centraI
Printed in Switzerland
ii

---------------------- Page: 4 ----------------------

SIST ISO 12744:2000
@ IS0 IS0 12744:1997(E)
Foreword
IS0 (the International Organization for Standardization) is a worldwide fed-
eration of national standards bodies IS0 member bodies). The work of
preparing International Standards is normally carried out through IS0
technical committees. Each membe body interested in a subject for
which a technical committee has beer established has the right to be rep-
resented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. IS0 col-
laborates closely with the International Electrotechnical Commission (IEC)
on all matters of electrotechnical standardization.
Draft International Standards adopted by the technical committees are cir-
culated to the member bodies for voting. Publication as an International
Standard requires approval by at least 75 % of the member bodies casting
a vote.
International Standard IS0 12744 was prepared by Technical Committee
ISOfTC 183, Copper, lead and zinc ores and concentrates.
Annexes A and B of this International Standard are for information only.

---------------------- Page: 5 ----------------------

SIST ISO 12744:2000
This page intentionally left blank

---------------------- Page: 6 ----------------------

SIST ISO 12744:2000
IS0 12744:1997(E)
INTERNATIONAL STANDARD @ IS0
Copper, lead and zinc sulfide concentrates - Experimental
methods for checking the precision of sampling
of concentrate in order to reach a reliable conclusion.
1 Scope
The lot size shall be chosen to ensure this require-
ment is met.
This International Standard specifies methods for
checking the precision of primary sampling, sample
processing, chemical analysis, physical testing and de-
termination of moisture content of copper, lead and
3.3 Number of increments and number of
zinc sulfide concentrates being carried out in ac-
samples
cordance with the methods specified in IS0 12743,
expressed in terms of standard deviations.
The minimum number of increments for checking
precision should preferably be twice the number de-
termined in accordance with IS0 12743. Hence, if the
number of increments required for routine sampling is
2 Normative reference
IZ and one lot sample is constituted, the minimum
number of increments should be 2n, and two inter-
The following standard contains provisions which,
leaved samples shall be constituted.
through reference in this text, constitute provisions of
this International Standard. At the time of publication,
Alternatively, if the precision is being checked as part
‘ the edition indicated was valid. All standards are sub-
of routine sampling, n increments may be taken and
ject to revision, and parties to agreements based on
two interleaved samples constituted, each comprising
this International Standard are encouraged to investi-
n/2 increments. The sampling precision thus obtained
gate the possibility of applying the most recent edi-
tions of the standards indicated below. Members of
must be divided by fi to obtain the sampling pre-
IEC and IS0 maintain registers of currently valid Inter-
cision for lot samples comprising n increments.
national Standards.
IS0 12743:- 1), Copper, lead and zinc sulfide concen-
trates - Sampling procedures for determination of
3.4 Sample processing and analysis
metal and moisture con tent.
Sample processing shall be carried out in accordance
with IS0 12743. The analysis of samples shall be
carried out according to the methods specified in the
3 General conditions
relevant International Standards.
3.1 General
The determination of precision of primary sampling is
3.5 Frequency of precision checks
based on collecting pairs of interleaved samples from
each lot. If sample processing and measurement are
It is recommended that, even after a precision check
also carried out in duplicate, it is possible to determine
has been conducted, further checks be carried out at
the precision of sample processing and analysis.
regular intervals. Precision checks should also be car-
ried out when there is a change in equipment.
3.2 Number of lots
Because of the large amount of work involved in
checking precision, it is recommended that checks be
It is recommended that pairs of interleaved samples
carried out as a part of routine sampling and analysis.
be collected from more than 20 lots of the same type
1) To be published.

---------------------- Page: 7 ----------------------

SIST ISO 12744:2000
IS0 12744:1997(E)
4 Definition of symbols
Number of increments
Absolute difference between duplicates for interleaved samples A and B
Mean absolute difference between duplicates for interleaved samples A and B for k lots
Absolute difference between means for divided interleaved samples AI and A*, and B-, and B2
Mean absolute difference between means for divided interleaved samples A-, and AZ, and B-, and B2, for k lots
Absolute difference between means for interleaved sample A and interleaved sample B
Mean absolute difference between means for interleaved sample A and interleaved sample B for k lots
Estimated value of standard deviation, 0
Estimated variance from RI
Estimated variance from R2
Estimated variance from Es
Estimated standard deviation of analysis
Estimated standard deviation of sample processing
Estimated standard deviation of primary sampling
Estimated standard deviation of primary sampling and sample processing
Estimated total standard deviation of primary sampling, sample processing and analysis
First duplicate result for interleaved sample, where I” = 1 and 2 and indicates interleaved sample A or B
Second duplicate result for interleaved sample, where i = 1 and 2 and indicates interleaved sample A or B
First duplicate result for interleaved sample, where i = 1 and 2 and indicates interleaved sample A or 9, and
j = 1 or 2 and indicates laboratory samples AI or AZ, and B1 or B2
Second duplicate result for sample, where i = 1 and 2 and indicates interleaved sample A or 9, and j = 1 or 2
and indicates laboratory samples AI or AZ, and 9, or 92
Mean value of duplicate results
Mean of mean of duplicate results
Mean of 2 values, and grand mean for sample processing method 3
example of a sampling plan for producing pairs of in-
5 Method of experiment
terleaved samples A and B is shown in figure I.
5.2 Sample processing and analysis
5.1 Interleaved samples
The pairs of interleaved samples A and B taken in ac-
Each alternate primary increment shall be diverted so cordance with 5.1 shall be divided separately and sub-
that pairs of interleaved samples A and B are formed.
jetted to either method 1, method 2 or method 3
The number of divided increments per primary incre-
sample processing and analysis as described in 5.2.1,
ment should be the same as for routine sampling. An
5.2.2 or 5.2.3.
2

---------------------- Page: 8 ----------------------

SIST ISO 12744:2000
IS0 12744:1997(E)
c ,
Primary
increment
Primary
increment
Primary
increment
Primary
increment
Primary
ti fL
Lot -
Primary
increment
interleaved
f
sample B
--I I
Primary
increment
t
Primary
increment
Primary
increment
4
,
Primary
increment
Primary
increment
- Example of a plan for interleaved duplicate sampling
Figure 1
52.1 Sample processing method 1 (see figure 2) for sample A,, and x2l
and x22 for sample B. The six
determinations shall be run in random order by the
The two interleaved samples A and B shall be divided
same analyst on the same day using the same ana-
separately to prepare four laboratory samples, A-,, A,,
lytical equipment.
and B,, B2. These laboratory samples shall each be
analysed in duplicate, and the duplicates designated NOTE 2 By using method 2, the estimated precisions of
primary sampling, sample processing and analysis can be
xl l l and xl l2 for sample A,, xlzl and xl22 for sample
obtained separately. However, the estimated values will be
for sample B, and x22l and x222 for
A,, x21 1 and x212
less precise than those obtained using method 1.
sample B,. The eight determinations shall be run in
random order by the same analyst on the same day
using the same analytical equipment. An example is
5.2.3 Sample processing method 3 (see figure 4)
given in annex A.
From each of the two interleaved samples A and B,
NOTE 1 By using method 1, the estimated precisions of
primary sampling, sample processing and analysis can be one laboratory sample shall be prepared. The two la-
obtained separately.
boratory samples A and B shall be analysed in dupli-
cate and the measurements obtained shall be desi-
gnated xl1 and xl2
for sample A and x2l and x22 for
52.2 Sample processing method 2 (see figure 3)
sample B. The four determinations shall be run in ran-
dom order by the same analyst on the same day using
Sample A shall be divided to prepare two laboratory
the same analytical equipment.
samples, A, and A,. From sample B, only one labora-
tory sample shall be prepared. The laboratory samples
NOTE 3 By using method 3, only the estimated precision
shall each be analysed in duplicate, and the duplicates
of analysis and the combined precision of primary sampling
designated xl l l and xl l2 for sample A,, xl2l and xl22 and sample processing are obtained.
3

---------------------- Page: 9 ----------------------

SIST ISO 12744:2000
IS0 12744:1997(E)
Lot
I
I
B (Interleaved samples)
A
n
(Laboratory samples)
BI B2
AI A2
I
x212 x221 X 222 (Analyses)
x 111 x122 x 211
Figure 2 - Flowsheet for sample processing method 1
A B (Interleaved samples)
n I
(Laboratory samples)
B
AI A2
X 22 (Analyses)
Flowsheet for sample processing method 2
Figure 3 -
B (Interleaved samples)
(Laboratory samples)
X 22 (Analyses)
Figure 4 - Flowsheet for sample processing method 3

---------------------- Page: 10 ----------------------

SIST ISO 12744:2000
@ IS0
(El
e) Calculate the variances ST, S; and sg from
6 Evaluation of experimental data
means of ranges RI, R2 and Es:
6.1 General
--
S2 . D .
(11)
n (q*
The method for evaluation of experimental data shall 1-4
be as specified below, depending on the method of
sample processing selected.
--
S2
. . . (12)
n: (R*)*
2-4
S2 . . .
(13)
n: (713)*
3=4
6.2 Sample processing method 1
The estimated standard deviations of primary sam-
where n/4 is a statistical factor relating range to
pling, sample processing and analysis shall be calcu-
variance for a pair of measurements.
lated in accordance with the following procedure.
a) Calculate the mean and range for each pair of
f) Conduct F-tests on the variances ST, ~22 and S: to
duplicates:
determine whether their differences are statisti-
tally significant using the following procedure:
xij = $x”‘+ x4 . . .
(1)
calculate the variance ratios s~/s: and s:/s$
1)
. 0 ”
(2)
4=I%jr%j*~
compare these ratios with the 95 % con-
2)
where
fidence F-ratios given in table 1 for the num-
i = 1 and 2 representing interleaved samples
ber of degrees of freedom applicable to each
A and B respectively;
variance estimate;
j = 1 and 2 representing laboratory samples
3) if the calculated variance ratio exceeds the
A, and A2 or B1 and B2.
F-ratio, partition the two variances into vari-
ance components as their difference is stat-
b) Calculate the mean of the mean and range for
istically significant.
each pair of duplicates:
If the calculated variance ratio does not exceed
. . .
Xi (3)
the F-ratio, the variances S$ and/or S: cannot be
meaningfully partitioned
into variance compo-
. . . (4)
nents and more data need to be collected.
Calculate the mean and range for each pair of
d
interleave d sa mples, A and B:
g) Assuming the F-tests conducted in f) indicate that
the differences between the variances ST, S$ and
“+X,fXp)
x . . .
(5)
sz are significant, calculate the estimated values
- -
of the variance of analysis (s$, sample processing
3= Xl-- x2 . . .
(6)
R I
(s$ and primary sampling (s: ) as follows:
1
Calculate the grand mean and the means of
d)
S2 S2
. . . (14)
A= 1
ranges R,, R2 and R,:
-
-1 f
1 2
=s; ---s
S2
. . . . . . (15)
(7)
P
c 2 1
x=ii x
1
2 2 12
&=--CR, . . . . . . (16)
(8)
% = 3 - zs*
4k
R2=9R2 . . .
(9)
2k
Calculate the total variance of primary sampling,
h)
1 sample processing and analysis (s$ as follows:
R3’-CR3 . . .
(10)
k
S2
=s; +s;+s; . . I
(17)
where k is the number of lots. T 1
5

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SIST ISO 12744:2000
IS0 12744:1997(E)
F-ratios at the 95 % confidence level for comparison of two variances
Table 1 -
0 Calculate the estimated values of the total stan- I 1
- I , - - L
K3= x . n .
- 4x*, + +*I (23)
dard deviation (ST) and the standard deviations of
2
primary sampling (ss ), sample processing (sp) and
1
analysis (sA).
d) Calculate the grand mean and the means of
ran
...