ISO 11794:2010

Copper, lead, zinc and nickel concentrates - Sampling of slurries

ISO 11794:2010 sets out the basic methods for sampling particulate material that is mixed with a liquid, usually water, to form a slurry. In industry and in the mining and mineral processing literature, slurry is also referred to as pulp, but this term is not used in ISO 11794:2010. At very high ratios of fine particulate solids to liquids where material assumes a soft plastic form, the mixture is correctly termed as a paste. Sampling of pastes is not covered in ISO 11794:2010. The procedures described in ISO 11794:2010 apply to sampling of particulate materials that are transported in moving streams as slurries, but not pressurized slurries. These streams may fall freely or be confined in pipes, launders, flumes, sluices, spirals or similar channels. Sampling of slurries in stationary situations, such as a settled or even a well-stirred slurry in a holding vessel or dam, is not recommended and is not covered in ISO 11794:2010. ISO 11794:2010 describes procedures that are designed to provide samples representative of the slurry solids and particle-size distribution of the slurry under examination. After draining the slurry sample of fluid and measuring the fluid volume, damp samples of the contained particulate material in the slurry are available for drying (if required) and measurement of one or more characteristics in an unbiased manner and with a known degree of precision. The characteristics are measured by chemical analysis, physical testing or both. The sampling methods described are applicable to slurries that require inspection to verify compliance with product specifications, determination of the value of a characteristic as a basis for settlement between trading partners or estimation of a set of average characteristics and variances that describes a system or procedure.

Concentrés de cuivre, de plomb, de zinc et de nickel — Échantillonnage des schlamms

General Information

• Status: Withdrawn
• Publication Date: 20-Sep-2010
• Withdrawal Date: 20-Sep-2010
• 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: 08-Jun-2017
• Completion Date: 13-Dec-2025

Relations

• Revised: ISO 11794:2017 - Copper, lead, zinc and nickel concentrates - Sampling of slurries
• Effective Date: 16-Apr-2016

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 11794
First edition
2010-10-01
Copper, lead, zinc and nickel
concentrates — Sampling of slurries
Concentrés de cuivre, de plomb, de zinc et de nickel — Échantillonnage
des schlamms
Reference number
©
ISO 2010
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©  ISO 2010
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ii © ISO 2010 – All rights reserved

Contents Page
Foreword .v
1 Scope.1
2 Normative references.1
3 Terms and definitions .2
4 Principles of sampling slurries .2
4.1 General .2
4.2 Sampling errors .3
4.2.1 General .3
4.2.2 Preparation error, PE .4
4.2.3 Delimitation and extraction errors, DE and EE .4
4.2.4 Weighting error, WE .6
4.2.5 Periodic quality-fluctuation error, QE .6
4.3 Sampling and total variance.6
4.3.1 Sampling variance.6
4.3.2 Total variance .6
4.3.3 Sampling-stage method of estimating sampling and total variance .8
4.3.4 Simplified method of estimating sampling and total variance .9
4.3.5 Interleaved sample method of measuring total variance.10
5 Establishing a sampling scheme.11
6 Minimization of bias and unbiased increment mass .16
6.1 Minimization of bias .16
6.2 Volume of increment for falling-stream samplers to avoid bias .17
7 Number of increments .17
7.1 General .17
7.2 Simplified method .18
8 Minimum mass of solids contained in lot and sub-lot samples.18
8.1 Minimum mass of solids in lot samples.18
8.2 Minimum mass of solids in sub-lot samples.18
8.3 Minimum mass of solids in lot and sub-lot samples after size reduction.18
9 Time-basis sampling.19
9.1 General .19
9.2 Sampling interval.19
9.3 Cutters .19
9.4 Taking of increments .19
9.5 Constitution of lot or sub-lot samples .20
9.6 Division of increments and sub-lot samples.20
9.7 Division of lot samples .20
9.8 Number of cuts for division.20
10 Stratified random sampling within fixed time intervals.20
11 Mechanical sampling from moving streams.21
11.1 General .21
11.2 Design of the sampling system .21
11.2.1 Safety of operators.21
11.2.2 Location of sample cutters.21
11.2.3 Provision for duplicate sampling.21
11.2.4 System for checking the precision and bias .21
11.2.5 Avoiding bias .22
11.3 Slurry sample cutters .22
11.3.1 General.22
11.3.2 Falling-stream cutters .23
11.3.3 Cutter velocities.23
11.4 Mass of solids in increments.23
11.5 Number of primary increments .23
11.6 Routine checking.23
12 Manual sampling from moving streams.24
12.1 General.24
12.2 Choosing the sampling location .24
12.3 Sampling implements.25
12.4 Mass of solids in increments.25
12.5 Number of primary increments .25
12.6 Sampling procedures .25
13 Sampling of stationary slurries.26
14 Sample preparation .26
14.1 General.26
14.2 Sample division.26
14.3 Sample grinding.26
14.4 Chemical analysis samples .26
14.5 Physical test samples .27
15 Packing and marking of samples.27
Annex A (normative) Sampling-stage method for estimating sampling and total variance .28
Annex B (informative) Examples of correct slurry sampling devices .34
Annex C (informative) Examples of incorrect slurry sampling devices .37
Annex D (normative) Manual sampling implements.41
Bibliography .42

iv © ISO 2010 – All rights reserved

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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. 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.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 11794 was prepared by Technical Committee ISO/TC 183, Copper, lead, zinc and nickel ores and
concentrates.
INTERNATIONAL STANDARD ISO 11794:2010(E)

Copper, lead, zinc and nickel concentrates — Sampling
of slurries
WARNING — This International Standard may involve hazardous materials, operations and equipment.
It is the responsibility of the user of this International Standard to establish appropriate health and
safety practices and determine the applicability of regulatory limitations prior to use.
1 Scope
This International Standard sets out the basic methods for sampling particulate material that is mixed with a
liquid, usually water, to form a slurry. In industry and in the mining and mineral processing literature, slurry is
also referred to as pulp, but this term is not used in this International Standard. At very high ratios of fine
particulate solids to liquids where material assumes a soft plastic form, the mixture is correctly termed as a
paste. Sampling of pastes is not covered in this International Standard.
The procedures described in this International Standard apply to sampling of particulate materials that are
transported in moving streams as slurries, but not pressurized slurries. These streams may fall freely or be
confined in pipes, launders, flumes, sluices, spirals or similar channels. Sampling of slurries in stationary
situations, such as a settled or even a well-stirred slurry in a holding vessel or dam, is not recommended and
is not covered in this International Standard.
This International Standard describes procedures that are designed to provide samples representative of the
slurry solids and particle-size distribution of the slurry under examination. After draining the slurry sample of
fluid and measuring the fluid volume, damp samples of the contained particulate material in the slurry are
available for drying (if required) and measurement of one or more characteristics in an unbiased manner and
with a known degree of precision. The characteristics are measured by chemical analysis, physical testing or
both.
The sampling methods described are applicable to slurries that require inspection to verify compliance with
product specifications, determination of the value of a characteristic as a basis for settlement between trading
partners or estimation of a set of average characteristics and variances that describes a system or procedure.
Provided that flow rates are not too high, the reference method against which other sampling procedures are
compared is one where the entire stream is diverted into a vessel for a specified time or volume interval. This
method corresponds to the stopped-belt method described in ISO 12743.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 12743, Copper, lead, zinc and nickel concentrates — Sampling procedures for determination of metal and
moisture content
ISO 12744, Copper, lead, zinc and nickel concentrates — Experimental methods for checking the precision of
sampling
ISO 13292, Copper, lead, zinc and nickel concentrates — Experimental methods for checking the bias of
sampling
ISO 20212, Copper, lead, zinc and nickel sulfides — Sampling procedures for ores and smelter residues
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 12743, ISO 12744, ISO 13292 and
ISO 20212 apply.
4 Principles of sampling slurries
4.1 General
In this International Standard, a slurry is defined as “any fluid mixture of a solid of nominal top size < 1 mm
that is mixed with water, which is frequently used as a convenient form to handle solids in bulk”. Slurry flows
are found in many mineral processing plants, with the water and entrained solids mixture being transported
through the plant circuits by means of pumps and pipelines and under gravity in sluices, flumes and launders.
In a number of operations, ore is transported to the mill in slurry form, and in others concentrates are
transported long distances in slurry pipelines. Tailings from wet plants are also discharged as slurries through
pipelines to the tailings dam. In many of these operations, collection of increments at selected sample points
is required for evaluation of the particulate material in the slurry.
A lot sample is constituted from a set of unbiased primary increments from a lot. The sample container is
weighed immediately after collection and combination of increments to avoid water loss by evaporation or
spillage. Weighing is necessary to determine the percentage of solids by mass in the slurry sample. The
sample may then be filtered, dried and weighed. Alternatively, the sample may be sealed in plastic bags after
filtering for transport and drying at a later stage. The liquid removed during filtration should be retained if it
needs to be analysed.
Test samples are prepared from samples after filtering and drying. Test portions may then be taken from the
test sample and analysed using an appropriate and properly calibrated analytical method or test procedure
under prescribed conditions.
The objective of the measurement chain is to determine the characteristic of interest in an unbiased manner
with an acceptable and affordable degree of precision. The general sampling theory, which is based on the
additive property of variances, can be used to determine how the variances of sampling, sample preparation
and chemical analysis or physical testing propagate and hence determine the total variance for the
measurement chain. This sampling theory can also be used to optimize manual sampling methods and
mechanical sampling systems.
If a sampling scheme is to provide representative samples, all parts of the slurry in the lot must have an equal
opportunity of being selected and appearing in the sample for testing. Hence, slurries are to be sampled in
such a manner that all possible primary increments in the set into which the slurry can be divided have the
same probability of being selected. Any deviation from this basic requirement can result in bias. A sampling
scheme having incorrect selection techniques, i.e. with non-uniform selection probabilities, cannot be relied
upon to provide representative samples.
Sampling of slurries should preferably be carried out by systematic sampling on a time basis (see Clause 9). If
the slurry flow rate and the solids concentration vary with time, the slurry volume and the mass of dry solids
for each increment will vary accordingly. It needs to be shown that no systematic error (bias) is introduced by
periodic variation in quality or quantity, where the proposed sampling interval is approximately equal to a
multiple of the period of variation in quantity or quality. Otherwise, stratified random sampling should be used
(see Clause 10).
2 © ISO 2010 – All rights reserved

Best practice for sampling slurries is to cut freely falling streams mechanically (see Clause 11), with a
complete cross-section of the stream being taken during the traverse of the cutter. Access to freely falling
streams can sometimes be engineered at the end of pipes or, alternatively, a full-stream sample by-line can
be added to a pipe that diverts the slurry into a holding tank, or weirs can be incorporated in launders, sluices
and flumes. If samples are not collected in this manner, non-uniform concentration of solids in the slurry due
to segregation and stratification of the solids may lead to bias in the sample that is collected. Slurry flow in
pipes can be homogeneous with very fine particles, such as clays, dispersed uniformly in turbulent suspension
along the length and across the diameter of the pipe. However, more commonly, the slurry in a pipe will have
significant particle concentration gradients across the pipe and there may be particle concentration
fluctuations along the length of the pipe. These common conditions are called heterogeneous flow. Examples
of such flow are full-pipe flow of a heterogeneous suspension, or partial-pipe flow of a fine particle suspension
above a slower moving or even stationary bed of coarser particles in the slurry.
For heterogeneous flow, bias is likely to occur where a tapping is made into the slurry pipe to locate either a
flush-fitting sample take-off pipe or a sample tube projecting into the slurry stream for extraction of samples.
The bias is caused by non-uniform radial concentration profiles in the pipe and the different trajectories
followed by particles of different masses due to their inertia, resulting in larger or denser particles being
preferentially rejected from, or included in, the sample.
In slurry channels such as launders, heterogeneous flow is almost always present, and this non-uniformity in
particle concentration is usually preserved in the discharge over a weir or step. However, sampling at a weir or
step allows complete access to the full width and breadth of the stream, thereby enabling all parts of the slurry
stream to be collected with equal probability.
Sampling of slurries in stationary situations, such as a settled or even a well-stirred slurry in a tank, holding
vessel or dam, is not recommended, because it is virtually impossible to ensure that all parts of the slurry in
the lot have an equal opportunity of being selected and appearing in the lot sample for testing. Instead,
sampling should be carried out from moving streams, as the tank, vessel or dam is filled or emptied.
4.2 Sampling errors
4.2.1 General
The processes of sampling, sample preparation and measurement are experimental procedures, and each
procedure has its own uncertainty appearing as variations in the final results. Where the average of these
variations is close to zero, they are called random errors. More serious variations contributing to the
uncertainty of results are systematic errors, which have averages biased away from zero. There are also
human errors that introduce variations due to departures from prescribed procedures for which statistical
analysis procedures are not applicable.
The characteristics of the solids component of a slurry can be determined by extracting samples from the
slurry stream, preparing test samples and measuring the required quality characteristics. The total sampling
error TSE can be expressed as the sum of a number of independent components (Gy, 1992; Pitard, 1993).
Such a simple additive combination would not be possible if the components were correlated. The sampling
error, expressed as a sum of its components, is given by Equation (1):
TSE=+QE QE+QE+WED+ EE+ E+PE (1)
12 3
where
QE is the short-range quality-fluctuation error associated with short-range variations in quality of the
solids component of the slurry;
QE is the long-range quality-fluctuation error associated with long-range variations in quality of the
solids component of the slurry;
QE is the periodic quality-fluctuation error associated with periodic variations in quality of the solids
component of the slurry;
WE is the weighting error associated with variations in the slurry flow rate;
DE is the increment delimitation error introduced by incorrect increment delimitation;
EE is the increment extraction error introduced by incorrect increment extraction from the slurry;
PE is the preparation error (also known as accessory error) introduced by departures (usually
unintentional) from correct practices, e.g. during constitution of the lot sample, draining and filtering
away the water, and transportation and drying of the sample
The short-range quality-fluctuation error consists of two components, as shown by Equation (2):
QE=+FE GE (2)
where
FE is the fundamental error due to variation in quality between particles;
GE is the segregation and grouping error.
The fundamental error results from the composition heterogeneity of the lot, i.e. the heterogeneity that is
inherent to the composition of each particle making up the solids component of the lot. The greater the
differences in the compositions of particles, the greater the composition heterogeneity and the higher the
fundamental error variance. The fundamental error can never be completely eliminated. It is an inherent error
resulting from the variation in composition of the particles in the slurry being sampled.
The segregation and grouping error results from the distribution heterogeneity of the sampled material (Pitard,
1993). The distribution heterogeneity of a lot is the heterogeneity arising from the manner in which particles
are distributed in the slurry. It can be reduced by taking a greater number of smaller increments, but it can
never be completely eliminated.
A number of the components of the total sampling error, namely DE, EE and PE, can be minimized, or
reduced to an acceptable level, by correct design of the sampling procedure.
4.2.2 Preparation error, PE
In this context, the preparation error includes errors associated with non-selective sample-preparation
operations that should not change mass, such as sample transfer, draining and filtering, drying, crushing,
grinding or mixing. It does not include errors associated with sample division. Preparation errors, also known
as accessory errors, include sample contamination, loss of sample material, alteration of the chemical or
physical composition of the sample, operator mistakes, fraud or sabotage. These errors can be made
negligible by correct design of the sampling system and by staff training. For example, cross-stream slurry
cutters should have caps to prevent entry of splashes when the cutter is in the parked position, and care
needs to be taken during filtering to avoid loss of fines that are still suspended in the water to be discarded.
4.2.3 Delimitation and extraction errors, DE and EE
Delimitation and extraction errors arise from incorrect sample cutter design and operation. The increment
delimitation error, DE, results from an incorrect shape of the volume delimiting the slurry increment, and this
can be due to both design and operation faults. Because of the incorrect shape of the slurry increment volume,
sampling with non-uniform selection probabilities results. The average of DE is often non-zero, which makes it
a source of sampling bias. The delimitation error can be made negligible if all parts of the stream cross-section
are diverted by the sample cutter for the same length of time.

4 © ISO 2010 – All rights reserved

Sampling from moving slurry streams usually involves methods that fall into three broad operational
categories as follows (Pitard, 1993).
a) Taking the whole stream for part of the time with a cross-stream cutter as shown in Figure 1 a) (after
Pitard, 1993), usually where the slurry falls from a pipe or over a weir or step. Cuts 1 and 2 show correct
sampling with the cutter diverting all parts of the stream for the same length of time. Cuts 3 to 5 show
incorrect sampling where the cutter diverts different parts of the stream for different lengths of time.
b) Taking part of the stream all of the time as shown in Figure 1 b) (after Pitard, 1993) with an on-stream
point sampler or probe within a pipe or channel, which is always incorrect.
c) Taking part of the stream part of the time as shown in Figure 1 c) (after Pitard, 1993), also with an
on-stream point sampler or probe within a pipe or channel, which is always incorrect.

a) Taking all of the stream for part of the time

b) Taking all of the stream for all of the time (always incorrect)

c) Taking all of the stream for part of the time (always incorrect)
Key
a
Correct.
b
Incorrect.
Figure 1 — Plan view of volumes diverted by a slurry cutter
The increment extraction error, EE, results from incorrect extraction of the slurry increment. The extraction is
said to be correct if, and only if, all particles in the slurry that have their centre of gravity inside the boundaries
of the correctly delimited increment are extracted. The average of EE is often non-zero, which makes it a
source of sampling bias. The extraction error can be made negligible by ensuring that the slurry increment is
completely extracted from the stream without any particulate material being lost from the cutter in splashes or
slops. The depth and capacity of the cutter must be sufficient to avoid slurry reflux from the cutter aperture,
resulting in loss of part of the extracted slurry increment.
4.2.4 Weighting error, WE
The weighting error is an error component arising from the selection model underlying Equation (1). In the
model, the time-dependent flow rate of the solids in the slurry stream is a weighting function applied to the
corresponding time-dependent quality characteristic over time, which gives the weighted average quality
characteristic of the solids component of the lot. The weighting error results from the application of incorrect
weights to the quality characteristics. The best solution to reducing the weighting error is to stabilize the flow
rate. As a general rule, the weighting error is negligible for variations in flow rate up to 10 %, and acceptable
for variations in flow rate up to 20 %.
4.2.5 Periodic quality-fluctuation error, QE
Periodic quality-fluctuation errors result from periodic variations in quality generated by some equipment used
for slurry processing and transportation, e.g. grinding and screening circuits, splitters and pumps. In such
cases, stratified random sampling should be carried out as discussed in Clause 10. The alternative is to
reduce the source of periodic variations in quality significantly, which may require plant redesign.
4.3 Sampling and total variance
4.3.1 Sampling variance
Assume that the weighting error (WE), increment delimitation error (DE), increment extraction error (EE) and
preparation error (PE) described in 4.2 have been eliminated or reduced to insignificant values by careful
design and sampling practice. In addition, assume that periodic variations in quality have been eliminated and
that the flow rate has been regulated. The sampling error in Equation (1) then reduces to the form:
TSE=+QE QE (3)
Hence, the sampling variance s is given by:
()
S
22 2
ss=+s (4)
SQE1 QE2
The short-range quality-fluctuation variance, s , arises from the different internal composition of increments
QE1
taken at the shortest possible interval apart. This is a local or random variance due to the particulate nature of
the solids in the slurry.
The long-range quality-fluctuation variance, s , arises from the continuous trends in quality that occur
QE2
while sampling a slurry and is usually space- and time-dependent. This component is often the combination of
a number of trends generated by diverse causes.
4.3.2 Total variance
Assuming that sources of bias have either been eliminated or minimized, the next objective of a sampling
scheme is to provide one or more test portions, sufficiently representative of a lot, for determination of the
quality characteristics of the lot with good precision, i.e. low variance. The total variance of the final result,
denoted by s , consists of the variance of sampling (including sample processing) plus the variance of
T
analysis (chemical analysis, determination of particle-size distribution, etc.) as follows:
6 © ISO 2010 – All rights reserved

22 2
s =+ss (5)
TS A
where
s is the sampling variance (including sample processing);
S
s is the analytical variance.
A
In Equation (5), 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, because it is difficult to determine
A
separately the “true” analytical variance.
Often, replicate analyses of quality characteristics are carried out, which reduces the total variance. In this
case, if “r” replicate analyses are made:
s
A
ss=+ (6)
TS
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.
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
22 2 2
A
ss=+ .+s +s + (7)
TS S S
11iu−
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
u is the number of sampling stages, stage u corresponding to selection of the test portion.
This is referred to as the “sampling-stage” method (see 4.3.3) and provides very detailed information on the
variance components that 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 4.3.4), is to break up the total variance into primary
sampling, sample processing and analytical variances only as follows:
s
22 2
A
ss=+s+ (8)
TS 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 selection of the
P
test portion;
s is the analytical variance, including selection of the test portion [at stage u in Equation (7)].
A
The primary sampling variance is identical to the sampling variance for stage 1 in Equation (7), while s is
P
equal to the total sampling variance for the remaining sampling stages, except for selection of the test portion
which is included in the analytical variance. The relative magnitudes of the variance components in
Equation (8) 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 samples
T
(see 4.3.5). 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 facilities are available
for collecting duplicate samples (Merks, 1986). 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 is
optimized or not. It is therefore of limited use for designing sampling schemes, but it can be used to monitor
whether a sampling scheme is in control.
4.3.3 Sampling-stage method of estimating sampling and total variance
The sampling variance for stage i (see Annex A) is given by:
s
b
i
s = (9)
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
j=1
s=− s (10)
bPA
i
n −1
i
where
x is the test result for increment j;
j
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 into
PA
account in Equation (10) to obtain an unbiased estimate of s .
b
i
NOTE Care is needed in subtracting variances. The difference is significant only when the F ratio of the variances
being subtracted is statistically significant.
8 © ISO 2010 – All rights reserved

Remembering that the variance due to selection of the test portion is included in the analytical variance, s ,
A
the total sampling variance is given by:
u−1
s
b
i
s = (11)
S ∑
n
i
i=1
Combining Equations (6) and (11) gives the total variance s as follows:
T
u−1
s
s
b
i A
s=+ (12)
T ∑
nr
i
i=1
For a three-stage sampling scheme (including selection of the test portion), Equation (12) reduces to:
ss
bb s
12 A
s=+ + (13)
T
nn r
The best way of reducing the value of s to an acceptable level is to reduce the largest terms in Equation (12)
T
first. Clearly, s /n for a given sampling stage can be reduced by increasing the number of increments n or
b i i
i
reducing s by homogenizing the slurry prior to sampling. The last term can be reduced by reducing the
b
i
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 require several iterations to obtain the required total
i
variance s .
T
4.3.4 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 (11), the primary sampling variance s is given by:
S
s
b
s = (14)
S
n
where
n is the number of primary increments;
s is the variance between primary increments determined using Equation (10).
b
The primary sampling variance can be reduced by increasing the number of primary increments, n .
2 2
The sampling processing variance s and analytical variance s are determined experimentally by duplicate
P A
sample processing and determination of quality characteristics in accordance with ISO 12744. The analytical
variance s can also be obtained by carrying out duplicate analyses on test samples.
A
Multiple sample processings and analyses are often carried out to reduce the total variance. In this case,
combining Equations (8) and (14) gives the following:
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
ss=+ + (15)
TP
nr
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:
s
s s
b
1 PA
s=+ + (16)
T
nk rk
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
ss++
bP
r
s = (17)
T
n
4.3.5 Interleaved sample method of measuring total variance
The total variance s achieved for a given sampling operation can be estimated experimentally by collecting
T
interleaved duplicate samples as shown in Figure 2. If the number of primary increments for routine sampling
is n , then 2n primary increments are taken from each lot and the odd- and even-numbered increments are
1 1
separately combined to give samples A and B for the lot. 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
π⎢⎥
i=1
s = (18)
T⎢⎥
4 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.
The total variance is obtained with a minimum of extra effort, provided faculties are available for collecting
interleaved duplicate samples.
10 © ISO 2010 – All rights reserved

Figure 2 — Example of a plan for interleaved duplicate sampling
5 Establishing a sampling scheme
Most sampling operations are routine and are carried out to determine the average quality characteristics of a
lot as well as variations in quality characteristics between sub-lots and lots for monitoring and controlling
quality. In establishing a sampling scheme for routine sampling so that the required precision for a lot can be
obtained, it is necessary to carry out the following sequence of steps. This sequence includes experimental
procedures, such as step f) below, that are non-routine and carried out infrequently, e.g. determining the
variance between increments, particularly if a significant change has occurred to the slurry source or to the
sampling equipment. The procedure is as follows.
a) Define the purpose for which the samples are being taken. Sampling for commercial transactions is
usually the main purpose of sampling standards. However, the procedures described in this International
Standard are equally applicable to monitoring plant performance, process control and metallurgical
accounting.
b) Define the lot by specifying the duration of slurry flow, e.g. one day of operation.
c) Identify the quality characteristics to be measured and specify the overall precision (combined precision
of sampling, sample preparation and measurement) required for each quality characteristic.
d) Ascertain the nominal top size and particle density of the solids in the slurry for determining the minimum
mass of solids in the
...