ISO 12743:1998

Copper, lead and zinc sulfide concentrates - Sampling procedures for determination of metal and moisture content

Concentrés sulfurés de cuivre, de plomb et de zinc — Procédures d'échantillonnage pour la détermination de la teneur en métal et de l'humidité

Koncentrati sulfidov bakra, svinca in cinka - Postopki vzorčenja za določevanje kovine in vlage

General Information

• Status: Withdrawn
• Publication Date: 29-Apr-1998
• Withdrawal Date: 29-Apr-1998
• 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
• Start Date: 19-Jun-2006
• Completion Date: 13-Dec-2025
• Ref Project: SIST ISO 12743:2000 - Copper, lead and zinc sulfide concentrates -- Sampling procedures for determination of metal and moisture content

Relations

• Revised: ISO 12743:2006 - Copper, lead, zinc and nickel concentrates - Sampling procedures for determination of metal and moisture content
• Effective Date: 15-Apr-2008

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 12743
First edition
1998-05-01
Copper, lead and zinc sulfide
concentrates — Sampling procedures for
determination of metal and moisture
content
Concentrés sulfurés de cuivre, de plomb et de zinc — Procédures
d'échantillonnage pour la détermination de la teneur en métal et de
l'humidité
A
Reference number
Contents
Page
1 Scope . 1
2 Normative references . 1
3 Definitions . 1
4 Sampling theory . 3
5 Establishing a sampling scheme . 11
6 Mass of increment . 16
7 Methods of sampling of concentrate streams . 17
8 Mechanical sampling of concentrate streams . 22
9 Manual sampling of concentrate streams . 27
10 Stopped-belt reference sampling . 29
11 Sampling from grabs. 30
12 Sampling from trucks and railway wagons . 31
13 Sampling of concentrate in bags or drums . 32
14 Sampling of stockpiles . 35
15 Methods of comminution, mixing, division and drying . 35
16 Sample requirements . 46
17 Packing and marking of samples . 47
Annexes
A (informative) Sampling stage method of estimating sampling and total variance . 48
B (informative) Estimation of total variance — Barge unloading using a grab . 55
C (informative) Mechanical sample cutters . 59
D (informative) Checklist for mechanical sampling systems . 64
E (normative) Manual sampling devices . 66
F (informative) Apparatus for manual sampling of concentrates from stopped belts . 68
G (informative) Sampling of stockpiles . 69
H (normative) Increment division scoops for conducting manual increment division . 71
Bibliography . 72
©  ISO 1998
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by
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ii
©
ISO ISO 12743:1998(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide
federation of national standards bodies (ISO member bodies). The work
of 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 of electrotechnical
standardization.
Draft International Standards adopted by the technical committees are
circulated 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 ISO 12743 was prepared by Technical Committee
ISO/TC 183, Copper lead and zinc and concentrates.
Annexes E and H form an integral part of this International Standard.
Annexes A to D and F and G are for information only.
iii
©
INTERNATIONAL STANDARD  ISO ISO 12743:1998(E)
Copper, lead and zinc sulfide concentrates — Sampling
procedures for determination of metal and moisture content
1 Scope
This International Standard sets out the basic methods for sampling copper, lead and zinc
concentrates from moving streams and stationary lots, including stopped-belt sampling, to provide
samples for chemical analysis, physical testing and determination of moisture content in accordance
with the relevant International Standards. Where the concentrates are susceptible to significant
oxidation or decomposition, it is necessary to use a common sample for moisture determination and
chemical analysis to eliminate bias (see ISO 10251). In such cases, the common sample needs to be
sufficiently representative, i.e. unbiased and sufficiently precise, for chemical analysis and
determination of moisture content. Any large agglomerates (>10 mm) present in the primary sample
are crushed prior to further sample processing. Sampling of concentrates in slurry form is specifically
excluded from this International Standard.
Stopped-belt sampling is the reference method for collecting concentrate samples against which
mechanical and manual sampling procedures may be compared. Sampling from moving streams is
the preferred method. Both falling-stream and cross-belt samplers are described.
Sampling from stationary lots is used only where sampling from moving streams is not possible. The
procedures described in this International Standard for sampling from stationary lots only minimize
some of the systematic sampling errors.
2 Normative references
The following standards contain provisions which, through reference in this text, constitute provisions
of this International Standard. At the time of publication, the editions indicated were valid. All standards
are subject to revision, and parties to agreements based on this International Standard are
encouraged to investigate applying the most recent editions of standards indicated below. Members of
IEC and ISO maintain registers of currently valid International Standards.
1)
ISO 10251:— , Copper, lead and zinc sulfide concentrates - Determination of mass loss of bulk
material on drying.
ISO 12744:1997, Copper, lead and zinc sulfide concentrates - Experimental methods for checking the
precision of sampling.
1)
ISO 13292:— , Copper, lead and zinc sulfide concentrates - Experimental methods for checking the
bias of sampling.
3 Definitions
For the purposes of this International Standard, the following definitions apply.
3.1 representative sample: A quantity of concentrate representing a larger mass of concentrate with
both precision and bias within acceptable limits.
3.2 lot: A quantity of concentrate to be sampled.
___________
1)  To be published.
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ISO
3.3 lot sample: A quantity of concentrate representative of the lot.
3.4 sub-lot: Subdivided parts of a lot which are processed separately, each of them producing a
subsample which is analysed separately, e.g. for moisture determination.
3.5 subsample: A quantity of concentrate representative of the sub-lot.
3.6 sampling: A sequence of operations aimed at obtaining a sample representative of a lot. It
comprises a series of sampling stages, each stage usually comprising operations of selection and
preparation.
3.7 selection: The operation by which a smaller quantity of concentrate is taken from a larger
quantity of concentrate.
3.8 increment: A quantity of concentrate selected by a sampling device in one operation.
3.9 increment selection: A selection process that consists of extracting from the lot or from an
intermediate sample successive increments which can be combined to constitute a sample.
3.10 division: The operation of decreasing sample mass, without change of particle size, where a
representative part of the sample is retained.
3.11 constant-mass division: A method of division in which the retained portions from individual
increments or subsamples are of uniform mass.
3.12 proportional division: A method of division in which the retained portions from individual
increments or subsamples are a constant proportion of their original mass.
3.13 preparation: A non-selective operation without division such as sample transfer, drying,
comminution or homogenization.
3.14 sample processing: The whole sequence of selection and preparation operations which
transforms a stage i sample into a test sample.
3.15 comminution: The operation of reducing particle size by crushing, grinding or pulverization.
3.16 stage i sample: A sample obtained at the ith stage of the sampling scheme.
3.17 moisture sample: A representative quantity of concentrate from which test portions are taken
for moisture determination. Alternatively, the whole moisture sample may be dried to determine its
moisture content.
3.18 laboratory sample: A sample that is processed so that it can be sent to the laboratory and
used for further processing and selection of one or more test samples for analysis.
3.19 common sample: A representative quantity of concentrate which is dried to determine its
mass loss and subsequently used for further processing and selection of one or more test samples for
chemical analysis.
3.20 test sample: A representative quantity of concentrate obtained from a laboratory sample when
additional preparation, such as drying or hygroscopic moisture determination, is needed prior to the
selection of one or more test portions.
3.21 test portion: A representative quantity of concentrate taken from a moisture sample, a
laboratory sample or a test sample which is submitted for moisture determination or analysis in its
entirety.
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ISO
3.22 systematic sampling: The selection of increments in which the concentrate being sampled is
divided into equal strata and the first increment is taken at random within the first stratum, the interval
between subsequent increments being equal to the stratum size.
3.23 stratified random sampling: The selection of increments in which the concentrate being
sampled is divided into equal strata, each increment being taken at random within each stratum.
3.24 homogenization: A preparation operation that reduces the distribution heterogeneity of the
concentrate.
3.25 agglomerate: A cluster of particles that are held together by chemical or physical phenomena.
3.26 nominal top size: The aperture size of a test sieve that retains 5 % of the mass of concentrate.
3.27 moisture determination: The quantitative measurement of the mass loss of the moisture test
portion under the conditions of drying specified in ISO 10251.
3.28 chemical analysis: The quantitative determination of the required chemical constituents of the
analysis test portion.
3.29 error: In any quantitative measurement, the difference between the true value and the value
obtained for an individual measurement.
3.30 bias: The statistically significant difference between the mean of the test results and an
accepted reference value (see also ISO 13292).
3.31 precision: The closeness of agreement between independent test results obtained under
stipulated conditions (see also ISO 12744).
3.32  interleaved samples: Samples constituted by placing consecutive primary increments
alternately into two separate sample containers.
4 Sampling theory
4.1 General
The basic rule for a correct sampling method is that all possible increments from the concentrate
stream or stratum have the same probability of being selected and appearing in the sample. Any
deviation from this basic requirement can result in a bias. An incorrect sampling scheme cannot be
relied on to provide representative samples.
Sampling should preferably be carried out on a systematic basis, either on a mass basis (see 7.2) or
on a time basis (see 7.3), but only where it can be shown that no systematic error (or bias) could be
introduced due to any periodic variation in quality or quantity that may coincide with, or approximate
to, any multiples of the proposed sampling interval. In such cases, it is recommended that stratified
random sampling within fixed time or mass intervals be carried out (see 7.4).
The methods for sampling, including sample processing, depend on the final choice of the sampling
scheme and on the steps necessary to minimize possible systematic errors. The aim always is to
reduce the total variance to an acceptable level while at the same time eliminating any significant
biases, e.g. minimizing degradation of samples used for determination of size distribution.
Moisture samples shall be processed as soon as possible and test portions weighed immediately. If
this is not possible, samples shall be stored in impervious air-tight containers with a minimum of free
air space to minimize any change in moisture content, but should be prepared without delay.
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ISO
4.2 Total variance
The general aim of a sampling scheme is to provide one or several test portions, sufficiently
representative of a lot, for determination of the quality characteristics of the lot. The total variance of
the final result, denoted by s consists of the variance of sampling (including sample processing)
T
plus the variance of analysis (chemical analysis, moisture determination, determination of particle size
distribution, etc.) as follows:
2 2 2
ss=+s . . . (1)
T S A
where
is the sampling variance (including sample processing);
s
S
is the analytical variance.
s
A
In equation 1, the sampling variance includes the variances due to all sampling (and sample
processing) steps except selection of the test portion. The variance due to selection of the test portion
is included in the analytical variance, s , which is determined in accordance with ISO 12744,
A
because it is difficult to determine separately the "true" analytical variance.
Often replicate analyses of quality characteristics are carried out, reducing the total variance. In this
case, if r replicate analyses are made:
s
A
2 2
ss=+ . . .(2)
T S
r
The estimation or measurement of the total variance can be carried out in several ways, depending
on the purpose of the exercise. In many respects the different approaches are complementary.
[3],[4]
The first method, which was developed by Gy, , is to break up the sampling variance into its
components for each sampling stage (see annex A). The total variance is then given by:
s
A
22 2 2
s=+sss.+ + .+ + . . .(3)
TS S S
1-iu1
r
where
s is the sampling variance for stage 1, i.e. the primary sampling variance;
S
s is the sampling variance for stage i;
S
i
s is the sampling variance for stage u-1, the second last stage;
S
u -1
is the number of sampling stages, stage corresponding to selection of the test portion.
u u
This is referred to as the "sampling stage" method (see 4.3) and provides very detailed information on
the variance components, which is particularly useful for designing and assessing sampling schemes.
However, to obtain maximum benefit, it is necessary to collect data at each sampling stage.
The second method, called the "simplified" method (see 4.4), is to break up the total variance into
primary sampling, sample processing and analytical variances only as follows:
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ISO
s
A
2 2 2
ss=+s+ . . .(4)
T S P
r
where
s is the primary sampling variance;
S
s is the variance due to all subsequent sampling steps, i.e. sample processing, except
P
selection of the test portion;
s is the analytical variance, including selection of the test portion (at stage u in equation 3).
A
The primary sampling variance is identical to the sampling variance for stage 1 in equation 3, while
s is equal to the total sampling variance for the remaining sampling stages, except for selection of
P
the test portion which is included in the analytical variance. The relative magnitudes of the variance
components in equation 4 indicate where additional effort is required to reduce the total variance.
However, it is not possible to separate the variances of the separate sample processing stages. This
method is suitable for estimating the total variance for new sampling schemes based on the same
sample processing procedures, where the numbers of primary increments, sample processings and
analyses are varied.
Finally, the total variance s can be estimated experimentally by collecting interleaved duplicate
T
samples (see 4.5). This is called the "interleaved sample" method and gives valuable information on
the total variance actually achieved for a given sampling scheme with no extra effort, provided that
[5]
facilities are available for collecting duplicate samples (Merks ). It gives no information on variance
components, but the total variance can be compared with the analytical variance to ascertain whether
the sampling scheme used was optimized or not. It is therefore of limited use for designing sampling
schemes.
4.3 Sampling stage method of estimating sampling and total variance
The sampling variance for stage i is given by (see annex A):
s
b
i
s = . . .(5)
S
i
n
i
where
s is the variance between increments for stage i;
b
i
n is the number of increments for stage i.
i
The variance between increments for stage i, s , can be estimated using the following equation:
b
i
n
xx−
()
∑ j
ji=
2 2
s = −s . . .(6)
b PA
i
n − 1
i
where
x is the test result for increment j;
j
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ISO
x is the mean test result for all increments;
s is the variance of subsequent sample processing and analysis.
PA
The variance of subsequent sample processing and analysis of each increment, s , has been taken
PA
into account in equation 6 to obtain an unbiased estimate of s .
b
i
NOTE —  Care is needed in subtracting variances. The difference is significant only if the F ratio of the
variances being subtracted is statistically significant.
Remembering that the variance due to selection of the test portion is included in the analytical
variance , the total sampling variance is given by:
s
A
u −1
s
b
2 i
s = . . .(7)
S ∑
n
i
i =1
Combining equations 2 and 7 gives the total variance s as follows:
T
u−1 2
s
s
b
2 i A
s=+ . . .(8)
∑
T
n r
i
i=1
For a three-stage sampling scheme (including selection of the test portion), equation 8 reduces to:
2 2
ss
s
b b
12 A
=+ + . . .(9)
s
T
nn r
1 2
The best way of reducing the value of to an acceptable level is to reduce the largest terms in
s
T
equation 8 first. Clearly for a given sampling stage can be reduced by increasing the number
s
n
i
b
i
of increments n or reducing s by homogenizing the concentrate prior to sampling. The last term
i
b
i
can be reduced by reducing the particle size prior to selection of the test portion, or performing
replicate analyses. Selecting the optimum number of increments n for each sampling stage may
i
require several iterations to obtain the required total variance .
s
T
Example
Consider a four-stage sampling scheme for determining the metal content of a copper concentrate
containing 31,2 % Cu. Assume that the concentrate is being conveyed at 500 t/h on a conveyor belt,
that the lot size is 500 t, and that the following parameters have been determined using equation 6
where appropriate:
= 0,3 % Cu
s
b
= 0,2 % Cu
s
b
= 0,1 % Cu
s
b
s = 0,05 % Cu
A
NOTE —  Many measurements may be required to obtain good estimates of , , and s .
s s s
A
b b b
1 2 3
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ISO
Stage 1
Assume that the primary cutter takes increments of 12 kg mass at 2 min intervals. Thus:
n = 30
Primary sample mass = 360 kg
Equation 5 gives:
= (0,3) /30 = 0,003 0
s
S
Stage 2
The primary increments are collected in a hopper, and then fed to the secondary cutter at the rate of
360 kg/h. Secondary increments of 0,01 kg are taken at 30 s intervals. Thus:
= 120
n
Divided sample mass = 1,2 kg
= (0,2) /120  = 0,000 333
s
S
Stage 3
The 1,2 kg sample is transported to the sample processing laboratory and fed through a rotary
sample divider with a sample collection canister divided into 8 equal sectors rotating at 30 rev/min
-1
(0,5 s ). Sample division takes 2 min. Thus:
n = 60
Divided sample mass = 150 g
= (0,1) /60 = 0,000 167
s
S
Stage 4
Dry the sample and then pulverize to 150 μm. Select a 1 g test portion by taking 10 increments of
0,1 g with a spatula and conduct a single analysis. Thus:
s = 0,05 % Cu
A
Total variance
The total variance is given by:
2 2 2 2 2
=  + + +
s s sss
T S S S A
12 3
= 0,003 0 + 0,000 333 + 0,000 167 + 0,002 5
= 0,006
Hence:
s = 0,077 % Cu
T
In this example, the largest components of variance are due to primary sampling and analysis.
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ISO
Consequently, the total variance can be reduced by increasing the number of primary increments and
conducting replicate analyses.
An example of the application of the sampling stage method of estimating total variance to sampling
from grabs is given in annex B.
4.4 Simplified method of estimating sampling and total variance
While it is not possible to partition, i.e. separate, the variances of the individual sample processing
stages, the simplified method is suitable for estimating the total variance for new sampling schemes
based on the same sample processing procedures, where the numbers of primary increments,
sample processings and analyses are varied.
Using equation 5, the primary sampling variance is given by:
s
S
s
b
= . . . (10)
s
S
n
where
n is the number of primary increments;
is the primary variance between increments determined using equation 6.
s
b
The primary sampling variance can be reduced by increasing the number of primary increments n .
2 2
The sample processing variance and analytical variance are determined experimentally by
s s
P A
duplicate sample processing and determination of quality characteristics in accordance with
ISO 12744. The analytical variance can also be obtained by carrying out duplicate analyses on
s
A
test samples.
Multiple sample processings and analyses are often carried out to reduce the total variance. In this
case, combining equations 4 and 10 gives:
a) Where a single sample is constituted for the lot and r replicate analyses are carried out on the
test sample:
s
s
b
1 A
2 2
= + + . . . (11)
s s
T P
r
n
b) Where the lot is divided into k sub-lots, a subsample is constituted for each sub-lot, and
r replicate analyses are carried out on each resultant test sample:
2 2
s
s s
b
1 P A
= + + . . . (12)
s
T
k rk
n
c) Where sample processing and analysis is carried out on each increment taken from the lot and r
replicate analyses are carried out:
s
A
2 2
+ +
ss
b P
r
= . . . (13)
s
T
n
©
ISO
Example
Assume that 50 primary increments are taken from a zinc concentrate lot that has been divided into
two sub-lots. The resultant two subsamples are processed separately and analysed in duplicate.
Assume that the primary increment, sample processing and analytical standard deviations have been
determined experimentally as follows:
= 0,3 % Zn
s
b
s = 0,1 % Zn
P
s = 0,05 % Zn
A
Using equation 12, the total variance is given by:
2 2 2
= (0,3) /50 + (0,1) /2 + (0,05) /(2 x 2)
s
T
= 0,001 8 + 0,005 + 0,000 625
= 0,007 43
Hence:
s = 0,086 % Zn
T
In this example, the major component of variance is sample processing. This component could be
reduced by dividing the lot into a larger number of sub-lots, and constituting a subsample for each
sub-lot.
4.5 Interleaved sample method of measuring total variance
The total variance actually achieved for a given sampling operation can be estimated
s
T
experimentally by collecting interleaved duplicate samples as shown in figure 1. The odd and even
numbered increments from two adjacent lots are separately combined to give samples A and B for the
two lots (each sample essentially representing a lot twice the size). Samples A and B are then
separately submitted to sample processing and analysis.
This procedure is repeated until sampling has been completed. The total variance for a single lot is
then given by:
N
 
xx−
 
∑AB
ii
p  
i =1
= . . . (14)
s
 
T
N
 
 
 
 
where
x and x are the analyses for each pair of samples A and B ;
A B i i
i i
N is the number of pairs (in the range 10 to 20);
π/4 is a statistical factor relating range to variance for a pair of measurements.
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ISO
Because the same number of samples are generated for analysis, the total variance is obtained with
no extra effort, provided that facilities are available for collecting interleaved duplicate samples.
Example
The analyses of interleaved samples taken from 10 lots of copper concentrate are given in table 1.
Equation 14 gives:
= (π/4) (0,27/10)
s
T
= 0,000 573
Hence:
s = 0,024 % Cu
T
Table 1 — Analyses of interleaved samples taken from copper concentrate
Odd samples (A) Even samples (B) Absolute difference
Lot
% Cu (m/m) % Cu (m/m) % Cu (m/m)
1 30,37 30,34 0,03
2 30,47 30,46 0,01
3 29,99 30,01 0,02
4 29,97 29,98 0,01
5 30,12 30,18 0,06
6 30,02 30,05 0,03
7 30,32 30,35 0,03
8 30,18 30,17 0,01
9 30,31 30,27 0,04
10 30,28 30,25 0,03
Sum of absolute differences 0,27
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Figure 1 — Procedure for collecting interleaved duplicate samples
5 Establishing a sampling scheme
The procedure for establishing a sampling scheme is as follows:
a) Identify the quality characteristics to be measured and specify the mass of the lot or sub-lot and
the desired total variance . Typical values of s are given in table 2.
s
T
T
b) Ascertain the nominal top size of the concentrate.
c) Specify the cutter aperture or the dimensions of the manual sampling implement according to the
nominal top size of the concentrate.
d) Ascertain the analytical variance . Typical values of s are given in table 2.
s
A
A
e) Determine the variance between primary increments and the sample processing variance
s
b
2 2
if the simplified method is used (see 4.4), or the variance between increments for each
s s
P b
i
proposed stage if the sampling stage method is used (see 4.3). Table 3 gives typical values of
for the first sampling stage.
s
b
i
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ISO
f) If the simplified method is used, use equation 11, 12 or 13 to select the number of primary
increments, sample processings and replicate analyses so that the total variance does not
s
T
exceed the desired value specified in step a).
Alternatively, if the sampling stage method is used, use equation 8 to select the number of
increments n required at each sampling stage and the number of replicate analyses so that the
i
total variance does not exceed the value selected in step a).
s
T
g) Determine the sampling intervals at each stage, in tonnes for mass-basis systematic sampling
(see 7.2) and stratified random sampling within fixed mass intervals (see 7.4), or in minutes for
time-basis systematic sampling (see 7.3) and stratified random sampling within fixed time
intervals (see 7.4).
h) Take increments at the intervals determined in step g) for each stage during the whole period of
handling the lot.
i) Either combine the primary increments into lot samples or subsamples for analysis or analyse
each primary increment separately. Examples of suitable sampling schemes are given in figure 2,
but the scheme shown in figure 2a) is not suitable for preparing chemical analysis samples used
to analyse for volatile elements such as mercury.
The lot is often divided into sub-lots from which subsamples are prepared and analysed separately to
reduce the total variance, as outlined in 4.4. Subsamples may also be prepared to provide
progressive information on the quality of the lot or to reduce possible changes in the moisture content
of samples.
Table 2 — Typical target values of the required total and analytical standard
deviations for determination of metal and moisture content
Characteristic Parameter Content range/Standard deviation
Range < 30 % (m/m) 30-50 % (m/m)
Cu s 0,05 % 0,1 %
T
s 0,03 % 0,03 %
A
Range < 30 % (m/m) 30-50 % (m/m) > 50 % (m/m)
Pb, Zn s 0,1 % 0,2 % 0,3 %
T
s 0,07 % 0,07 % 0,15 %
A
Range < 500 g/t 500-1000 g/t > 1000 g/t
Ag s 10 g/t 2% of conc. 2% of conc.
T
s 7 g/t 15 g/t 20 g/t
A
Range < 5 g/t 5-15 g/t > 15 g/t
Au s 0,5 g/t 0,5 g/t 2 % of conc.
T
s 0,15 g/t 0,2 g/t 0,4 g/t
A
Range < 20 % (m/m)
Moisture s 0,3 %
T
s 0,07 %
A
NOTE —  s can be reduced if required by performing replicate analyses.
T
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ISO
Table 3 — Examples of standard deviations between primary increments
Constituent
Primary increment standard deviation ( )
s
b
i
Cu in copper concentrate 0,1-0,5 % Cu
Pb and Zn in lead and zinc concentrates 0,1-2,0 % Pb/Zn
Ag in copper, lead and zinc concentrates 1-5 g/t Ag
Au in copper, lead and zinc concentrates 0,5-2,0 g/t Au
Moisture in copper, lead and zinc concentrates 0,2-0,7 %
NOTE —  The standard deviation between primary increments for silver content is applicable to
Ag < 500 g/t only.
Figure 2(a) — Example of a sampling scheme in which a common sample is constituted for
the lot for moisture determination and subsequent chemical analysis
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ISO
NOTE —  Mixing, comminution and division steps have been omitted for simplicity. This scheme is not suitable
for concentrates that are susceptible to oxidation or decomposition.
Figure 2(b) — Example of a sampling scheme in which the lot is divided into sub-lots for
moisture determination and a separate lot sample is constituted for chemical analysis
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ISO
NOTE —  Mixing, comminution and division steps have been omitted for simplicity. This scheme
is suitable for concentrates that are susceptible to oxidation or decomposition.
Figure 2(c) — Example of a sampling scheme in which the lot is divided into sub-lots for
moisture determination, and the dried moisture subsamples are subsequently
combined into a single lot sample for chemical analysis
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ISO
6 Mass of increment
6.1 General
To avoid bias, it is essential that increments are extracted in such a manner that all possible
increments from the concentrate stream have the same probability of being selected and becoming
part of the final sample for analysis, irrespective of the size, mass or density of individual particles in
the stream. This determines the increment mass required to obtain an unbiased sample.
However, there is also a practical minimum increment mass that should always be exceeded to
minimize the effect of handling on the characteristics of the increment as it passes through the
sampling system. This is particularly important for moisture content, where moisture loss (or gain) is
to be minimized. The minimum mass needs to be specified for each concentrate type and each
sampling device.
6.2 Mass of increment for falling-stream samplers
To avoid bias, the mass of increment at any sampling stage taken by a mechanical or manual cutter-
type sampler from the concentrate stream at the discharge end of a moving conveyor is determined
by the minimum cutter aperture as specified in 8.3.2.1, the maximum cutter speed as specified in
8.3.3.2 and the flowrate of the concentrate stream as follows:
GA
m = . . . (15)
I
3,6 v
c
where
m is the mass of increment, in kilograms;
I
G is the flowrate of concentrate stream, in tonnes per hour;
A is the cutter aperture, in metres (see 8.3.2.1);
v is the cutter speed, in metres per second (see 8.3.3.2).
C
6.3 Mass of increment for cross-belt samplers
The mass of increment taken by a cross-belt cutter from a moving stream to avoid bias is determined
by the minimum cutter aperture as specified in 8.3.2.2 and the flowrate of the concentrate stream as
follows:
GA
m = . . . (16)
I
3,6
v
B
where
is the cutter aperture, in metres (see 8.3.2.2);
A
is the speed of concentrate stream, in metres per second.
v
B
6.4 Mass of increment for manual sampling
6.4.1 Primary increments
The minimum mass of primary increment taken by a manual sampling implement from a stationary lot
shall be 0,25 kg. However, if the nominal top size exceeds 16 mm due to the presence of
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ISO
agglomerates, the mass shall be increased in accordance with the following equation based on a
sampling implement of minimum dimensions 3d × 3d × 3d:
36−
m= 27 r d × 10 . . . (17)
Imin
where
m is the minimum mass of increment, in kilograms;
Imin
r is the bulk density of concentrate, in tonnes per cubic metre;
d is the nominal top size of the agglomerates, in millimetres.
6.4.2 Mass of secondary and subsequent increments
The minimum mass of secondary and subsequent increments taken by a manual sampling implement
shall be 10 g.
7 Methods of sampling from concentrate streams
7.1 General
Mechanical and manual sampling of concentrate streams may be carried out on either a mass-basis
or a time-basis. This needs to be decided before designing a sampling system and before sampling
commences.
7.2 Mass-basis systematic sampling
7.2.1 General
Mass-basis sampling involves the following steps:
a) Distributing the required number of primary increments on a uniform tonnage basis throughout
the lot to be sampled.
b) Taking increments of almost uniform mass from each tonnage interval.
NOTE —  Sample masses are considered almost uniform if the coefficient of variation (CV) of the masses is
20 % or less. If increments are not of almost uniform mass, constant-mass division is required so that the mass
of sample reporting to the lot sample or subsample is almost uniform.
7.2.2 Sampling interval
The interval between primary increments for mass-basis sampling shall be determined from the
following equation:
m
L
Dm < . . . (18)
n
where
Δm is the mass interval between primary increments, in tonnes;
m is the mass of lot, in tonnes;
L
n is the number of primary increments determined in accordance with clause 5.
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ISO
7.2.3 Sample cutter
The following cutters may be used for taking primary increments:
a) A falling-stream cutter whose cutting speed is constant during the course of handling the entire
lot.
b) A falling-stream cutter whose cutting speed is constant while cutting the stream but can be
regulated, primary increment by primary increment, corresponding to the flow rate of the
concentrate on the conveyor belt.
c) A cross-belt cutter.
7.2.4 Taking of primary increments
Each primary increment shall preferably be taken by a single traverse of the sampling device so that a
full cross-section of the concentrate stream is taken. However, in manual sampling cases where it is
not possible to obtain a complete cross-section in one operation, increments may be taken
systematically across the concentrate stream so that, when they are combined, they represent the full
cross-section of the stream (see 9.7).
The first primary increment shall be taken at a random mass less than the mass interval Δm
determined in 7.2.2. Thereafter, the required number of primary increments shall be taken at fixed
mass intervals of Δm, and this interval shall not be changed during the entire course of sampling the
lot.
NOTE —  The mass interval between primary increments calculated in 7.2.2 should be rounded down to the
nearest tonne to ensure that the number of primary increments taken will be larger than the minimum number
required.
If the planned number of primary increments has been taken and handling has not been completed,
additional primary increments shall be taken at the same mass interval until the handling operation is
completed.
7.2.5 Constitution of subsamples and lot samples
If the coefficient of variation of primary increment masses is 20 % or less, primary increments may be
combined into subsamples or a lot sample, either as-taken or after having been processed individually
to a particular stage. Subsamples shall preferably comprise equal numbers of consecutive primary
increments.
However, if the coefficient of variation of primary increment masses exceeds 20 %, either:
a) each primary increment shall be subjected separately to division (according to the rules of
division) and determination of its quality characteristics or
b) primary increments shall be subjected to constant-mass division prior to combining into
subsamples or a lot sample.
NOTE —  Primary increments and subsamples should not be combined into a single sample for the lot unless
the composite sample can be adequately mixed (see 15.3).
For determination of moisture content, it is recommended that a moisture subsample be constituted
for each sub-lot. This will not only reduce the total variance, but it will also minimize loss of moisture
and hence bias.
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ISO
7.2.6 Types of division
Two types of division are applicable to mass-basis sampling as follows:
a) Constant-mass division, which is a method of obtaining divided increments, subsamples or lot
samples having almost uniform mass regardless of the variation in the masses to be divided.
Cutter-type dividers having variable cutting frequencies can be used for this type of division (see
15.4.5).
b) Proportional division, which is a method of obtaining divided increments, subsamples or lot
samples having masses proportional to the varied masses to be divided. Rotary sample dividers
can be used for this type of division (see 15.4.4).
NOTE —  Cutter-type dividers may lead to moisture loss, so are not recommended for division of moisture
samples.
7.2.7 Division of increments
Where increments require division and subsamples or a lot sample are constituted from the divided
increments, division shall be carried out as follows (see table 4):
a) If the coefficient of variation of the increment masses is 20 % or less, either constant-mass or
proportional division shall be used.
b) If the coefficient of variation of the increment masses is greater than 20 %, division shall be
carried out on an increment-by-increment basis using constant-mass division.
7.2.8 Division of subsamples
Where subsamples are divided and a lot sample is constituted from the divided subsamples, division
shall be carried out as follows (see table 4):
a) If the coefficient of variation of the subsample masses is 20 % or less, and the subsamples
consist of an equal number of increments, either constant-mass or proportional division shall be
used.
b) If the coefficient of variation of the subsample masses is greater than 20 %, and the subsamples
consist of an equal number of increments, constant-mass division shall be used.
c) If the subsamples consist of different numbers of increments, proportional division shall be used.
7.2.9 Division of lot samples
When a lot sample is divided, either constant-mass or proportional division shall be used.
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ISO
Table 4 - Rules for division of increments, subsamples and lot samples for
mass-basis and time-basis sampling
Sampling conditions Type of division
Sample for
Sampling Increments CV Constant Proportional
division
method per (%) mass
subsample
< 20 Yes Yes
Mass-basis -
Increment > 20 Yes No
Time-basis - - No Yes
Mass-basis
< 20 Yes Yes
Equal
> 20 Yes No
Subsample
Unequal - No Yes
Time-basis Equal or - No Yes
unequal
Lot sample Mass-basis - - Yes Yes
Time-basis
7.3 Time-basis systematic sampling
7.3.1 General
Time-basis sampling involves the following steps.
a) Distributing the required number of primary increments on a uniform time basis throughout the lot
to be sampled.
b) For each time interval, taking increments of mass proportional to the concentrate flow rate at the
time of taking the increment.
7.3.2 Sampling interval
The interval between primary increments for time-basis sampling shall be determined from the
following equation:
3 600 m
L
Dt<
. . . (19)
Gn
max 1
where
Δt is the time interval between primary increments, in seconds;
G is the maximum flow rate, in tonnes per hour.
max
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ISO
7.3.3 Sample cutter
The following cutters may be used for taking primary increments:
a) A falling-stream cutter whose cutting speed is constant during the course of handling the entire
lot.
b) A cross-belt cutter.
7.3.4 Taking of primary increments
Each primary increment shall preferably be taken by a single traverse of the sampling device so that a
full cross-section of the concentrate stream is taken. However, in manual sampling cases where it is
not possible to obtain a complete cross-section in one operation, increments may be taken
systematically across the concentrate stream so that, when they are combined, they represent the full
cross-section of the stream over time (see 9.7).
The first primary increment shall be taken at a random time less than the time interval Δt determined
in 7.3.2. Thereafter, the required number of primary increments shall be taken at fixed time intervals
of Δt, and this interval shall not be changed during the entire course of sampling the lot.
NOTE —  The time interval between primary increments calculated in 7.3.2 should be rounded down to the
nearest minute to ensure that the number of primary increments taken will be larger than the minimum number
required.
If the planned number of primary increments has been taken and handling has not been completed,
additional primary increments shall be taken at the same time interval until the handling operation is
completed.
7.3.5 Constitution of subsamples and lot samples
Subsamples or lot samples may be constituted in either of the following ways:
a) primary increments as-taken shall be combined into subsamples or a lot sample irrespective of
the variation of masses of primary increments or
b) primary increments shall be divided by proportional division; subsamples or lot samples shall
then be constituted by combining divided increments.
Where subsamples are analysed to determine the quality characteristics for the lot, the mass of the
sub-lot from which the subsample was taken shall be determined to obtain the weighted average of
the quality characteristic for the lot.
NOTE —  Primary increments and subsamples should not be combined into a single sample for the lot unless
the composite sample can be adequately mixed (see 15.3).
For determination of moisture content, it is recommended that a moisture subsample be constituted
for each sub-lot. This will not only reduce the total variance, but it will also minimize loss of moisture
and hence bias.
7.3.6 Types of division
Both constant-mass and proportional division are applicable to time-basis sampling (see 7.2.6).
7.3.7 Division of increments and subsamples
Increments and subsamples shall be divi
...

SLOVENSKI STANDARD
01-junij-2000
.RQFHQWUDWLVXOILGRYEDNUDVYLQFDLQFLQND3RVWRSNLY]RUþHQMD]DGRORþHYDQMH
NRYLQHLQYODJH
Copper, lead and zinc sulfide concentrates -- Sampling procedures for determination of
metal and moisture content
Concentrés sulfurés de cuivre, de plomb et de zinc -- Procédures d'échantillonnage pour
la détermination de la teneur en métal et de l'humidité
Ta slovenski standard je istoveten z: ISO 12743:1998
ICS:
73.060.99 Druge rude Other metalliferous minerals
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

INTERNATIONAL ISO
STANDARD 12743
First edition
1998-05-01
Copper, lead and zinc sulfide
concentrates — Sampling procedures for
determination of metal and moisture
content
Concentrés sulfurés de cuivre, de plomb et de zinc — Procédures
d'échantillonnage pour la détermination de la teneur en métal et de
l'humidité
A
Reference number
Contents
Page
1 Scope . 1
2 Normative references . 1
3 Definitions . 1
4 Sampling theory . 3
5 Establishing a sampling scheme . 11
6 Mass of increment . 16
7 Methods of sampling of concentrate streams . 17
8 Mechanical sampling of concentrate streams . 22
9 Manual sampling of concentrate streams . 27
10 Stopped-belt reference sampling . 29
11 Sampling from grabs. 30
12 Sampling from trucks and railway wagons . 31
13 Sampling of concentrate in bags or drums . 32
14 Sampling of stockpiles . 35
15 Methods of comminution, mixing, division and drying . 35
16 Sample requirements . 46
17 Packing and marking of samples . 47
Annexes
A (informative) Sampling stage method of estimating sampling and total variance . 48
B (informative) Estimation of total variance — Barge unloading using a grab . 55
C (informative) Mechanical sample cutters . 59
D (informative) Checklist for mechanical sampling systems . 64
E (normative) Manual sampling devices . 66
F (informative) Apparatus for manual sampling of concentrates from stopped belts . 68
G (informative) Sampling of stockpiles . 69
H (normative) Increment division scoops for conducting manual increment division . 71
Bibliography . 72
©  ISO 1998
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by
any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from the
publisher.
International Organization for Standardization
Case postale 56 • CH-1211 Genève 20 • Switzerland
Internet [e-mail]
X.400 c=ch; a=400net; p=iso; o=isocs; s=central
Printed in Switzerland
ii
©
ISO ISO 12743:1998(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide
federation of national standards bodies (ISO member bodies). The work
of 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 of electrotechnical
standardization.
Draft International Standards adopted by the technical committees are
circulated 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 ISO 12743 was prepared by Technical Committee
ISO/TC 183, Copper lead and zinc and concentrates.
Annexes E and H form an integral part of this International Standard.
Annexes A to D and F and G are for information only.
iii
©
INTERNATIONAL STANDARD  ISO ISO 12743:1998(E)
Copper, lead and zinc sulfide concentrates — Sampling
procedures for determination of metal and moisture content
1 Scope
This International Standard sets out the basic methods for sampling copper, lead and zinc
concentrates from moving streams and stationary lots, including stopped-belt sampling, to provide
samples for chemical analysis, physical testing and determination of moisture content in accordance
with the relevant International Standards. Where the concentrates are susceptible to significant
oxidation or decomposition, it is necessary to use a common sample for moisture determination and
chemical analysis to eliminate bias (see ISO 10251). In such cases, the common sample needs to be
sufficiently representative, i.e. unbiased and sufficiently precise, for chemical analysis and
determination of moisture content. Any large agglomerates (>10 mm) present in the primary sample
are crushed prior to further sample processing. Sampling of concentrates in slurry form is specifically
excluded from this International Standard.
Stopped-belt sampling is the reference method for collecting concentrate samples against which
mechanical and manual sampling procedures may be compared. Sampling from moving streams is
the preferred method. Both falling-stream and cross-belt samplers are described.
Sampling from stationary lots is used only where sampling from moving streams is not possible. The
procedures described in this International Standard for sampling from stationary lots only minimize
some of the systematic sampling errors.
2 Normative references
The following standards contain provisions which, through reference in this text, constitute provisions
of this International Standard. At the time of publication, the editions indicated were valid. All standards
are subject to revision, and parties to agreements based on this International Standard are
encouraged to investigate applying the most recent editions of standards indicated below. Members of
IEC and ISO maintain registers of currently valid International Standards.
1)
ISO 10251:— , Copper, lead and zinc sulfide concentrates - Determination of mass loss of bulk
material on drying.
ISO 12744:1997, Copper, lead and zinc sulfide concentrates - Experimental methods for checking the
precision of sampling.
1)
ISO 13292:— , Copper, lead and zinc sulfide concentrates - Experimental methods for checking the
bias of sampling.
3 Definitions
For the purposes of this International Standard, the following definitions apply.
3.1 representative sample: A quantity of concentrate representing a larger mass of concentrate with
both precision and bias within acceptable limits.
3.2 lot: A quantity of concentrate to be sampled.
___________
1)  To be published.
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ISO
3.3 lot sample: A quantity of concentrate representative of the lot.
3.4 sub-lot: Subdivided parts of a lot which are processed separately, each of them producing a
subsample which is analysed separately, e.g. for moisture determination.
3.5 subsample: A quantity of concentrate representative of the sub-lot.
3.6 sampling: A sequence of operations aimed at obtaining a sample representative of a lot. It
comprises a series of sampling stages, each stage usually comprising operations of selection and
preparation.
3.7 selection: The operation by which a smaller quantity of concentrate is taken from a larger
quantity of concentrate.
3.8 increment: A quantity of concentrate selected by a sampling device in one operation.
3.9 increment selection: A selection process that consists of extracting from the lot or from an
intermediate sample successive increments which can be combined to constitute a sample.
3.10 division: The operation of decreasing sample mass, without change of particle size, where a
representative part of the sample is retained.
3.11 constant-mass division: A method of division in which the retained portions from individual
increments or subsamples are of uniform mass.
3.12 proportional division: A method of division in which the retained portions from individual
increments or subsamples are a constant proportion of their original mass.
3.13 preparation: A non-selective operation without division such as sample transfer, drying,
comminution or homogenization.
3.14 sample processing: The whole sequence of selection and preparation operations which
transforms a stage i sample into a test sample.
3.15 comminution: The operation of reducing particle size by crushing, grinding or pulverization.
3.16 stage i sample: A sample obtained at the ith stage of the sampling scheme.
3.17 moisture sample: A representative quantity of concentrate from which test portions are taken
for moisture determination. Alternatively, the whole moisture sample may be dried to determine its
moisture content.
3.18 laboratory sample: A sample that is processed so that it can be sent to the laboratory and
used for further processing and selection of one or more test samples for analysis.
3.19 common sample: A representative quantity of concentrate which is dried to determine its
mass loss and subsequently used for further processing and selection of one or more test samples for
chemical analysis.
3.20 test sample: A representative quantity of concentrate obtained from a laboratory sample when
additional preparation, such as drying or hygroscopic moisture determination, is needed prior to the
selection of one or more test portions.
3.21 test portion: A representative quantity of concentrate taken from a moisture sample, a
laboratory sample or a test sample which is submitted for moisture determination or analysis in its
entirety.
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ISO
3.22 systematic sampling: The selection of increments in which the concentrate being sampled is
divided into equal strata and the first increment is taken at random within the first stratum, the interval
between subsequent increments being equal to the stratum size.
3.23 stratified random sampling: The selection of increments in which the concentrate being
sampled is divided into equal strata, each increment being taken at random within each stratum.
3.24 homogenization: A preparation operation that reduces the distribution heterogeneity of the
concentrate.
3.25 agglomerate: A cluster of particles that are held together by chemical or physical phenomena.
3.26 nominal top size: The aperture size of a test sieve that retains 5 % of the mass of concentrate.
3.27 moisture determination: The quantitative measurement of the mass loss of the moisture test
portion under the conditions of drying specified in ISO 10251.
3.28 chemical analysis: The quantitative determination of the required chemical constituents of the
analysis test portion.
3.29 error: In any quantitative measurement, the difference between the true value and the value
obtained for an individual measurement.
3.30 bias: The statistically significant difference between the mean of the test results and an
accepted reference value (see also ISO 13292).
3.31 precision: The closeness of agreement between independent test results obtained under
stipulated conditions (see also ISO 12744).
3.32  interleaved samples: Samples constituted by placing consecutive primary increments
alternately into two separate sample containers.
4 Sampling theory
4.1 General
The basic rule for a correct sampling method is that all possible increments from the concentrate
stream or stratum have the same probability of being selected and appearing in the sample. Any
deviation from this basic requirement can result in a bias. An incorrect sampling scheme cannot be
relied on to provide representative samples.
Sampling should preferably be carried out on a systematic basis, either on a mass basis (see 7.2) or
on a time basis (see 7.3), but only where it can be shown that no systematic error (or bias) could be
introduced due to any periodic variation in quality or quantity that may coincide with, or approximate
to, any multiples of the proposed sampling interval. In such cases, it is recommended that stratified
random sampling within fixed time or mass intervals be carried out (see 7.4).
The methods for sampling, including sample processing, depend on the final choice of the sampling
scheme and on the steps necessary to minimize possible systematic errors. The aim always is to
reduce the total variance to an acceptable level while at the same time eliminating any significant
biases, e.g. minimizing degradation of samples used for determination of size distribution.
Moisture samples shall be processed as soon as possible and test portions weighed immediately. If
this is not possible, samples shall be stored in impervious air-tight containers with a minimum of free
air space to minimize any change in moisture content, but should be prepared without delay.
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ISO
4.2 Total variance
The general aim of a sampling scheme is to provide one or several test portions, sufficiently
representative of a lot, for determination of the quality characteristics of the lot. The total variance of
the final result, denoted by s consists of the variance of sampling (including sample processing)
T
plus the variance of analysis (chemical analysis, moisture determination, determination of particle size
distribution, etc.) as follows:
2 2 2
ss=+s . . . (1)
T S A
where
is the sampling variance (including sample processing);
s
S
is the analytical variance.
s
A
In equation 1, the sampling variance includes the variances due to all sampling (and sample
processing) steps except selection of the test portion. The variance due to selection of the test portion
is included in the analytical variance, s , which is determined in accordance with ISO 12744,
A
because it is difficult to determine separately the "true" analytical variance.
Often replicate analyses of quality characteristics are carried out, reducing the total variance. In this
case, if r replicate analyses are made:
s
A
2 2
ss=+ . . .(2)
T S
r
The estimation or measurement of the total variance can be carried out in several ways, depending
on the purpose of the exercise. In many respects the different approaches are complementary.
[3],[4]
The first method, which was developed by Gy, , is to break up the sampling variance into its
components for each sampling stage (see annex A). The total variance is then given by:
s
A
22 2 2
s=+sss.+ + .+ + . . .(3)
TS S S
1-iu1
r
where
s is the sampling variance for stage 1, i.e. the primary sampling variance;
S
s is the sampling variance for stage i;
S
i
s is the sampling variance for stage u-1, the second last stage;
S
u -1
is the number of sampling stages, stage corresponding to selection of the test portion.
u u
This is referred to as the "sampling stage" method (see 4.3) and provides very detailed information on
the variance components, which is particularly useful for designing and assessing sampling schemes.
However, to obtain maximum benefit, it is necessary to collect data at each sampling stage.
The second method, called the "simplified" method (see 4.4), is to break up the total variance into
primary sampling, sample processing and analytical variances only as follows:
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ISO
s
A
2 2 2
ss=+s+ . . .(4)
T S P
r
where
s is the primary sampling variance;
S
s is the variance due to all subsequent sampling steps, i.e. sample processing, except
P
selection of the test portion;
s is the analytical variance, including selection of the test portion (at stage u in equation 3).
A
The primary sampling variance is identical to the sampling variance for stage 1 in equation 3, while
s is equal to the total sampling variance for the remaining sampling stages, except for selection of
P
the test portion which is included in the analytical variance. The relative magnitudes of the variance
components in equation 4 indicate where additional effort is required to reduce the total variance.
However, it is not possible to separate the variances of the separate sample processing stages. This
method is suitable for estimating the total variance for new sampling schemes based on the same
sample processing procedures, where the numbers of primary increments, sample processings and
analyses are varied.
Finally, the total variance s can be estimated experimentally by collecting interleaved duplicate
T
samples (see 4.5). This is called the "interleaved sample" method and gives valuable information on
the total variance actually achieved for a given sampling scheme with no extra effort, provided that
[5]
facilities are available for collecting duplicate samples (Merks ). It gives no information on variance
components, but the total variance can be compared with the analytical variance to ascertain whether
the sampling scheme used was optimized or not. It is therefore of limited use for designing sampling
schemes.
4.3 Sampling stage method of estimating sampling and total variance
The sampling variance for stage i is given by (see annex A):
s
b
i
s = . . .(5)
S
i
n
i
where
s is the variance between increments for stage i;
b
i
n is the number of increments for stage i.
i
The variance between increments for stage i, s , can be estimated using the following equation:
b
i
n
xx−
()
∑ j
ji=
2 2
s = −s . . .(6)
b PA
i
n − 1
i
where
x is the test result for increment j;
j
©
ISO
x is the mean test result for all increments;
s is the variance of subsequent sample processing and analysis.
PA
The variance of subsequent sample processing and analysis of each increment, s , has been taken
PA
into account in equation 6 to obtain an unbiased estimate of s .
b
i
NOTE —  Care is needed in subtracting variances. The difference is significant only if the F ratio of the
variances being subtracted is statistically significant.
Remembering that the variance due to selection of the test portion is included in the analytical
variance , the total sampling variance is given by:
s
A
u −1
s
b
2 i
s = . . .(7)
S ∑
n
i
i =1
Combining equations 2 and 7 gives the total variance s as follows:
T
u−1 2
s
s
b
2 i A
s=+ . . .(8)
∑
T
n r
i
i=1
For a three-stage sampling scheme (including selection of the test portion), equation 8 reduces to:
2 2
ss
s
b b
12 A
=+ + . . .(9)
s
T
nn r
1 2
The best way of reducing the value of to an acceptable level is to reduce the largest terms in
s
T
equation 8 first. Clearly for a given sampling stage can be reduced by increasing the number
s
n
i
b
i
of increments n or reducing s by homogenizing the concentrate prior to sampling. The last term
i
b
i
can be reduced by reducing the particle size prior to selection of the test portion, or performing
replicate analyses. Selecting the optimum number of increments n for each sampling stage may
i
require several iterations to obtain the required total variance .
s
T
Example
Consider a four-stage sampling scheme for determining the metal content of a copper concentrate
containing 31,2 % Cu. Assume that the concentrate is being conveyed at 500 t/h on a conveyor belt,
that the lot size is 500 t, and that the following parameters have been determined using equation 6
where appropriate:
= 0,3 % Cu
s
b
= 0,2 % Cu
s
b
= 0,1 % Cu
s
b
s = 0,05 % Cu
A
NOTE —  Many measurements may be required to obtain good estimates of , , and s .
s s s
A
b b b
1 2 3
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ISO
Stage 1
Assume that the primary cutter takes increments of 12 kg mass at 2 min intervals. Thus:
n = 30
Primary sample mass = 360 kg
Equation 5 gives:
= (0,3) /30 = 0,003 0
s
S
Stage 2
The primary increments are collected in a hopper, and then fed to the secondary cutter at the rate of
360 kg/h. Secondary increments of 0,01 kg are taken at 30 s intervals. Thus:
= 120
n
Divided sample mass = 1,2 kg
= (0,2) /120  = 0,000 333
s
S
Stage 3
The 1,2 kg sample is transported to the sample processing laboratory and fed through a rotary
sample divider with a sample collection canister divided into 8 equal sectors rotating at 30 rev/min
-1
(0,5 s ). Sample division takes 2 min. Thus:
n = 60
Divided sample mass = 150 g
= (0,1) /60 = 0,000 167
s
S
Stage 4
Dry the sample and then pulverize to 150 μm. Select a 1 g test portion by taking 10 increments of
0,1 g with a spatula and conduct a single analysis. Thus:
s = 0,05 % Cu
A
Total variance
The total variance is given by:
2 2 2 2 2
=  + + +
s s sss
T S S S A
12 3
= 0,003 0 + 0,000 333 + 0,000 167 + 0,002 5
= 0,006
Hence:
s = 0,077 % Cu
T
In this example, the largest components of variance are due to primary sampling and analysis.
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Consequently, the total variance can be reduced by increasing the number of primary increments and
conducting replicate analyses.
An example of the application of the sampling stage method of estimating total variance to sampling
from grabs is given in annex B.
4.4 Simplified method of estimating sampling and total variance
While it is not possible to partition, i.e. separate, the variances of the individual sample processing
stages, the simplified method is suitable for estimating the total variance for new sampling schemes
based on the same sample processing procedures, where the numbers of primary increments,
sample processings and analyses are varied.
Using equation 5, the primary sampling variance is given by:
s
S
s
b
= . . . (10)
s
S
n
where
n is the number of primary increments;
is the primary variance between increments determined using equation 6.
s
b
The primary sampling variance can be reduced by increasing the number of primary increments n .
2 2
The sample processing variance and analytical variance are determined experimentally by
s s
P A
duplicate sample processing and determination of quality characteristics in accordance with
ISO 12744. The analytical variance can also be obtained by carrying out duplicate analyses on
s
A
test samples.
Multiple sample processings and analyses are often carried out to reduce the total variance. In this
case, combining equations 4 and 10 gives:
a) Where a single sample is constituted for the lot and r replicate analyses are carried out on the
test sample:
s
s
b
1 A
2 2
= + + . . . (11)
s s
T P
r
n
b) Where the lot is divided into k sub-lots, a subsample is constituted for each sub-lot, and
r replicate analyses are carried out on each resultant test sample:
2 2
s
s s
b
1 P A
= + + . . . (12)
s
T
k rk
n
c) Where sample processing and analysis is carried out on each increment taken from the lot and r
replicate analyses are carried out:
s
A
2 2
+ +
ss
b P
r
= . . . (13)
s
T
n
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Example
Assume that 50 primary increments are taken from a zinc concentrate lot that has been divided into
two sub-lots. The resultant two subsamples are processed separately and analysed in duplicate.
Assume that the primary increment, sample processing and analytical standard deviations have been
determined experimentally as follows:
= 0,3 % Zn
s
b
s = 0,1 % Zn
P
s = 0,05 % Zn
A
Using equation 12, the total variance is given by:
2 2 2
= (0,3) /50 + (0,1) /2 + (0,05) /(2 x 2)
s
T
= 0,001 8 + 0,005 + 0,000 625
= 0,007 43
Hence:
s = 0,086 % Zn
T
In this example, the major component of variance is sample processing. This component could be
reduced by dividing the lot into a larger number of sub-lots, and constituting a subsample for each
sub-lot.
4.5 Interleaved sample method of measuring total variance
The total variance actually achieved for a given sampling operation can be estimated
s
T
experimentally by collecting interleaved duplicate samples as shown in figure 1. The odd and even
numbered increments from two adjacent lots are separately combined to give samples A and B for the
two lots (each sample essentially representing a lot twice the size). Samples A and B are then
separately submitted to sample processing and analysis.
This procedure is repeated until sampling has been completed. The total variance for a single lot is
then given by:
N
 
xx−
 
∑AB
ii
p  
i =1
= . . . (14)
s
 
T
N
 
 
 
 
where
x and x are the analyses for each pair of samples A and B ;
A B i i
i i
N is the number of pairs (in the range 10 to 20);
π/4 is a statistical factor relating range to variance for a pair of measurements.
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Because the same number of samples are generated for analysis, the total variance is obtained with
no extra effort, provided that facilities are available for collecting interleaved duplicate samples.
Example
The analyses of interleaved samples taken from 10 lots of copper concentrate are given in table 1.
Equation 14 gives:
= (π/4) (0,27/10)
s
T
= 0,000 573
Hence:
s = 0,024 % Cu
T
Table 1 — Analyses of interleaved samples taken from copper concentrate
Odd samples (A) Even samples (B) Absolute difference
Lot
% Cu (m/m) % Cu (m/m) % Cu (m/m)
1 30,37 30,34 0,03
2 30,47 30,46 0,01
3 29,99 30,01 0,02
4 29,97 29,98 0,01
5 30,12 30,18 0,06
6 30,02 30,05 0,03
7 30,32 30,35 0,03
8 30,18 30,17 0,01
9 30,31 30,27 0,04
10 30,28 30,25 0,03
Sum of absolute differences 0,27
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Figure 1 — Procedure for collecting interleaved duplicate samples
5 Establishing a sampling scheme
The procedure for establishing a sampling scheme is as follows:
a) Identify the quality characteristics to be measured and specify the mass of the lot or sub-lot and
the desired total variance . Typical values of s are given in table 2.
s
T
T
b) Ascertain the nominal top size of the concentrate.
c) Specify the cutter aperture or the dimensions of the manual sampling implement according to the
nominal top size of the concentrate.
d) Ascertain the analytical variance . Typical values of s are given in table 2.
s
A
A
e) Determine the variance between primary increments and the sample processing variance
s
b
2 2
if the simplified method is used (see 4.4), or the variance between increments for each
s s
P b
i
proposed stage if the sampling stage method is used (see 4.3). Table 3 gives typical values of
for the first sampling stage.
s
b
i
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f) If the simplified method is used, use equation 11, 12 or 13 to select the number of primary
increments, sample processings and replicate analyses so that the total variance does not
s
T
exceed the desired value specified in step a).
Alternatively, if the sampling stage method is used, use equation 8 to select the number of
increments n required at each sampling stage and the number of replicate analyses so that the
i
total variance does not exceed the value selected in step a).
s
T
g) Determine the sampling intervals at each stage, in tonnes for mass-basis systematic sampling
(see 7.2) and stratified random sampling within fixed mass intervals (see 7.4), or in minutes for
time-basis systematic sampling (see 7.3) and stratified random sampling within fixed time
intervals (see 7.4).
h) Take increments at the intervals determined in step g) for each stage during the whole period of
handling the lot.
i) Either combine the primary increments into lot samples or subsamples for analysis or analyse
each primary increment separately. Examples of suitable sampling schemes are given in figure 2,
but the scheme shown in figure 2a) is not suitable for preparing chemical analysis samples used
to analyse for volatile elements such as mercury.
The lot is often divided into sub-lots from which subsamples are prepared and analysed separately to
reduce the total variance, as outlined in 4.4. Subsamples may also be prepared to provide
progressive information on the quality of the lot or to reduce possible changes in the moisture content
of samples.
Table 2 — Typical target values of the required total and analytical standard
deviations for determination of metal and moisture content
Characteristic Parameter Content range/Standard deviation
Range < 30 % (m/m) 30-50 % (m/m)
Cu s 0,05 % 0,1 %
T
s 0,03 % 0,03 %
A
Range < 30 % (m/m) 30-50 % (m/m) > 50 % (m/m)
Pb, Zn s 0,1 % 0,2 % 0,3 %
T
s 0,07 % 0,07 % 0,15 %
A
Range < 500 g/t 500-1000 g/t > 1000 g/t
Ag s 10 g/t 2% of conc. 2% of conc.
T
s 7 g/t 15 g/t 20 g/t
A
Range < 5 g/t 5-15 g/t > 15 g/t
Au s 0,5 g/t 0,5 g/t 2 % of conc.
T
s 0,15 g/t 0,2 g/t 0,4 g/t
A
Range < 20 % (m/m)
Moisture s 0,3 %
T
s 0,07 %
A
NOTE —  s can be reduced if required by performing replicate analyses.
T
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Table 3 — Examples of standard deviations between primary increments
Constituent
Primary increment standard deviation ( )
s
b
i
Cu in copper concentrate 0,1-0,5 % Cu
Pb and Zn in lead and zinc concentrates 0,1-2,0 % Pb/Zn
Ag in copper, lead and zinc concentrates 1-5 g/t Ag
Au in copper, lead and zinc concentrates 0,5-2,0 g/t Au
Moisture in copper, lead and zinc concentrates 0,2-0,7 %
NOTE —  The standard deviation between primary increments for silver content is applicable to
Ag < 500 g/t only.
Figure 2(a) — Example of a sampling scheme in which a common sample is constituted for
the lot for moisture determination and subsequent chemical analysis
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NOTE —  Mixing, comminution and division steps have been omitted for simplicity. This scheme is not suitable
for concentrates that are susceptible to oxidation or decomposition.
Figure 2(b) — Example of a sampling scheme in which the lot is divided into sub-lots for
moisture determination and a separate lot sample is constituted for chemical analysis
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NOTE —  Mixing, comminution and division steps have been omitted for simplicity. This scheme
is suitable for concentrates that are susceptible to oxidation or decomposition.
Figure 2(c) — Example of a sampling scheme in which the lot is divided into sub-lots for
moisture determination, and the dried moisture subsamples are subsequently
combined into a single lot sample for chemical analysis
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6 Mass of increment
6.1 General
To avoid bias, it is essential that increments are extracted in such a manner that all possible
increments from the concentrate stream have the same probability of being selected and becoming
part of the final sample for analysis, irrespective of the size, mass or density of individual particles in
the stream. This determines the increment mass required to obtain an unbiased sample.
However, there is also a practical minimum increment mass that should always be exceeded to
minimize the effect of handling on the characteristics of the increment as it passes through the
sampling system. This is particularly important for moisture content, where moisture loss (or gain) is
to be minimized. The minimum mass needs to be specified for each concentrate type and each
sampling device.
6.2 Mass of increment for falling-stream samplers
To avoid bias, the mass of increment at any sampling stage taken by a mechanical or manual cutter-
type sampler from the concentrate stream at the discharge end of a moving conveyor is determined
by the minimum cutter aperture as specified in 8.3.2.1, the maximum cutter speed as specified in
8.3.3.2 and the flowrate of the concentrate stream as follows:
GA
m = . . . (15)
I
3,6 v
c
where
m is the mass of increment, in kilograms;
I
G is the flowrate of concentrate stream, in tonnes per hour;
A is the cutter aperture, in metres (see 8.3.2.1);
v is the cutter speed, in metres per second (see 8.3.3.2).
C
6.3 Mass of increment for cross-belt samplers
The mass of increment taken by a cross-belt cutter from a moving stream to avoid bias is determined
by the minimum cutter aperture as specified in 8.3.2.2 and the flowrate of the concentrate stream as
follows:
GA
m = . . . (16)
I
3,6
v
B
where
is the cutter aperture, in metres (see 8.3.2.2);
A
is the speed of concentrate stream, in metres per second.
v
B
6.4 Mass of increment for manual sampling
6.4.1 Primary increments
The minimum mass of primary increment taken by a manual sampling implement from a stationary lot
shall be 0,25 kg. However, if the nominal top size exceeds 16 mm due to the presence of
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agglomerates, the mass shall be increased in accordance with the following equation based on a
sampling implement of minimum dimensions 3d × 3d × 3d:
36−
m= 27 r d × 10 . . . (17)
Imin
where
m is the minimum mass of increment, in kilograms;
Imin
r is the bulk density of concentrate, in tonnes per cubic metre;
d is the nominal top size of the agglomerates, in millimetres.
6.4.2 Mass of secondary and subsequent increments
The minimum mass of secondary and subsequent increments taken by a manual sampling implement
shall be 10 g.
7 Methods of sampling from concentrate streams
7.1 General
Mechanical and manual sampling of concentrate streams may be carried out on either a mass-basis
or a time-basis. This needs to be decided before designing a sampling system and before sampling
commences.
7.2 Mass-basis systematic sampling
7.2.1 General
Mass-basis sampling involves the following steps:
a) Distributing the required number of primary increments on a uniform tonnage basis throughout
the lot to be sampled.
b) Taking increments of almost uniform mass from each tonnage interval.
NOTE —  Sample masses are considered almost uniform if the coefficient of variation (CV) of the masses is
20 % or less. If increments are not of almost uniform mass, constant-mass division is required so that the mass
of sample reporting to the lot sample or subsample is almost uniform.
7.2.2 Sampling interval
The interval between primary increments for mass-basis sampling shall be determined from the
following equation:
m
L
Dm < . . . (18)
n
where
Δm is the mass interval between primary increments, in tonnes;
m is the mass of lot, in tonnes;
L
n is the number of primary increments determined in accordance with clause 5.
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7.2.3 Sample cutter
The following cutters may be used for taking primary increments:
a) A falling-stream cutter whose cutting speed is constant during the course of handling the entire
lot.
b) A falling-stream cutter whose cutting speed is constant while cutting the stream but can be
regulated, primary increment by primary increment, corresponding to the flow rate of the
concentrate on the conveyor belt.
c) A cross-belt cutter.
7.2.4 Taking of primary increments
Each primary increment shall preferably be taken by a single traverse of the sampling device so that a
full cross-section of the concentrate stream is taken. However, in manual sampling cases where it is
not possible to obtain a complete cross-section in one operation, increments may be taken
systematically across the concentrate stream so that, when they are combined, they represent the full
cross-section of the stream (see 9.7).
The first primary increment shall be taken at a random mass less than the mass interval Δm
determined in 7.2.2. Thereafter, the required number of primary increments shall be taken at fixed
mass intervals of Δm, and this interval shall not be changed during the entire course of sampling the
lot.
NOTE —  The mass interval between primary increments calculated in 7.2.2 should be rounded down to the
nearest tonne to ensure that the number of primary increments taken will be larger than the minimum number
required.
If the planned number of primary increments has been taken and handling has not been completed,
additional primary increments shall be taken at the same mass interval until the handling operation is
completed.
7.2.5 Constitution of subsamples and lot samples
If the coefficient of variation of primary increment masses is 20 % or less, primary increments may be
combined into subsamples or a lot sample, either as-taken or after having been processed individually
to a particular stage. Subsamples shall preferably comprise equal numbers of consecutive primary
increments.
However, if the coefficient of variation of primary increment masses exceeds 20 %, either:
a) each primary increment shall be subjected separately to division (according to the rules of
division) and determination of its quality characteristics or
b) primary increments shall be subjected to constant-mass division prior to combining into
subsamples or a lot sample.
NOTE —  Primary increments and subsamples should not be combined into a single sample for the lot unless
the composite sample can be adequately mixed (see 15.3).
For determination of moisture content, it is recommended that a moisture subsample be constituted
for each sub-lot. This will not only reduce the total variance, but it will also minimize loss of moisture
and hence bias.
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7.2.6 Types of division
Two types of division are applicable to mass-basis sampling as follows:
a) Constant-mass division, which is a method of obtaining divided increments, subsamples or lot
samples having almost uniform mass regardless of the variation in the masses to be divided.
Cutter-type dividers having variable cutting frequencies can be used for this type of division (see
15.4.5).
b) Proportional division, which is a method of obtaining divided increments, subsamples or lot
samples having masses proportional to the varied masses to be divided. Rotary sample dividers
can be used for this type of division (see 15.4.4).
NOTE —  Cutter-type dividers may lead to moisture loss, so are not recommended for division of moisture
samples.
7.2.7 Division of increments
Where increments require division and subsamples or a lot sample are constituted from the divided
increments, division shall be carried out as follows (see table 4):
a) If the coefficient of variation of the increment masses is 20 % or less, either constant-mass or
proportional division shall be used.
b) If the coefficient of variation of the increment masses is greater than 20 %, division shall be
carried out on an increment-by-increment basis using constant-mass division.
7.2.8 Division of subsamples
Where subsamples are divided and a lot sample is constituted from the divided subsamples, division
shall be carried out as follows (see table 4):
a) If the coefficient of variation of the subsample masses is 20 % or less, and the subsamples
consist of an equal number of increments, either constant-mass or proportional division shall be
used.
b) If the coefficient of variation of the subsample masses is greater than 20 %, and the subsamples
consist of an equal number of increments, constant-mass division shall be used.
c) If the subsamples consist of different numbers of increments, proportional division shall be used.
7.2.9 Division of lot samples
When a lot sample is divided, either constant-mass or proportional division shall be used.
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Table 4 - Rules for division of increments, subsamples and lot samples for
mass-basis and time-basis sampling
Sampling conditions Type of division
Sample for
Sampling Increments CV Constant Proportional
division
method per (%) mass
subsample
< 20 Yes Yes
Mass-basis -
Increment > 20 Yes No
Time-basis - - No Yes
Mass-basis
< 20 Yes Yes
Equal
> 20 Yes No
Subsample
Unequal - No Yes
Time-basis Equal or - No Yes
unequal
Lot sample Mass-basis - - Yes Yes
Time-basis
7.3 Time-basis systematic sampling
7.3.1 General
Time-basis sampling involves the following steps.
a) Distributing the required number of primary increments on a uniform time basis throughout the lot
to be sampled.
b) For each time interval, taking increments of mass proportional to the concentrate flow rate at the
time of taking the increment.
7.3.2 Sampling interval
The interval between primary increments for time-basis sampling shall be determined from the
following equation:
3 600 m
L
Dt<
. . . (19)
Gn
max 1
where
Δt is the time interval between primary increments, in seconds;
G is the maximum flow rate, in tonnes per hour.
max
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7.3.3 Sample cutter
The following cutters may be used for taking primary increments:
a) A falling-stream cutter whose cutting speed is constant during the course of handling the entire
lot.
b) A cross-belt cutter.
7.3.4 Taking of primary increments
Each primary increment shall preferably be taken by a single traverse of the sampling device so that a
full cross-section of the concentrate stream is taken. However, in manual sampling cases where it is
not possible to obtain a complete cross-section in one operation, increments may be taken
systematically across the concentrate stream so that, when they are combined, they represent the full
cross-section of the stream over time (see 9.7).
The first primary increment shall be taken at a random time less than the time interval Δt determined
in 7.3.2. Thereafter, the required number of primary increments shall be taken at fixed time intervals
of Δt, and this interval shall not be changed during the entire course of sampling the lot.
NOTE —  The time interval between primary increments calculated in 7.3.2 should be rounded down to the
nearest minute to ensure that the number of primary increments taken will be larger than the minimum number
required.
If the planned number of primary increments has been taken and
...