ISO 13909-7:2016

Hard coal and coke - Mechanical sampling - Part 7: Methods for determining the precision of sampling, sample preparation and testing

In ISO 13909-7:2016, formulae are developed which link the variables that contribute to overall sampling precision. Methods are described for estimating overall precision and for deriving values for primary increment variance which can be used to modify the sampling scheme to change the precision. Methods for checking the variance of sample preparation and testing are also described.

Houille et coke — Échantillonnage mécanique — Partie 7: Méthodes pour la détermination de la fidélité de l'échantillonnage, de la préparation de l'échantillon et de l'essai

General Information

• Status: Published
• Publication Date: 22-Jun-2016
• ICS: 73.040 - Coals
• ICS: 75.160.10 - Solid fuels
• Technical Committee: ISO/TC 27/SC 4 - Sampling
• Drafting Committee: ISO/TC 27/SC 4 - Sampling
• Current Stage: 9599 - Withdrawal of International Standard
• Start Date: 22-Jul-2025
• Completion Date: 13-Dec-2025

Relations

• Revised: ISO 13909-7:2025 - Coal and coke - Mechanical sampling - Part 7: Methods for determining the precision of sampling, sample preparation and testing
• Effective Date: 27-May-2023
• Revises: ISO 13909-7:2001 - Hard coal and coke - Mechanical sampling - Part 7: Methods for determining the precision of sampling, sample preparation and testing
• Effective Date: 04-May-2013

Overview

ISO 13909-7:2016 - Hard coal and coke - Mechanical sampling - Part 7 - specifies methods for determining the precision of mechanical sampling, sample preparation and testing for hard coal and coke. The standard develops formulae that link the variables contributing to overall sampling precision and describes practical procedures to estimate precision, derive primary increment variance, and check the variance introduced during sample preparation and laboratory testing.

Key topics

• Precision concept and index: Defines precision as an index related to the sample estimate of population standard deviation (commonly expressed as two times the sample standard deviation).
• Formulae relating precision factors: Mathematical relationships linking primary increment variance, number and mass of increments, and preparation/testing variances to overall sampling precision.
• Estimation of primary increment variance:
  • Direct determination from individual primary increments
  • Indirect determination using precision estimates
• Methods for estimating precision:
  • Replicate sampling and duplicate sampling approaches
  • Duplicate sampling during routine operations and alternatives when capacity is limited
  • Precision adjustment procedures to modify sampling schemes
• Calculation procedures:
  • How to compute precision for replicate and normal sampling schemes
• Checking sample preparation and testing:
  • Procedures for on-line and off-line preparation
  • Target variance criteria and staged checking methods (including obtaining parallel samples with riffles or mechanical dividers)
• Informative methods: Annex A (variogram method) and Annex B (Grubbs’ estimators) provide additional techniques for variance determination.

Applications and users

ISO 13909-7:2016 is intended for organizations and professionals involved in coal and coke sampling and quality assurance:

• Sampling engineers and designers - to design or modify sampling schemes to meet required precision.
• Quality control managers and laboratory analysts - to evaluate and verify precision of sample preparation and testing.
• Operations and production teams - to implement duplicate or replicate sampling for routine checks.
• Regulatory bodies, auditors and traders - to assess the reliability of reported fuel quality data.

Practical uses include estimating expected variability of results, determining the number/mass of increments needed, setting target variances for preparation and analysis, and diagnosing where precision losses occur (sampling vs. preparation vs. testing).

Related standards

ISO 13909-7 is part of the ISO 13909 series on mechanical sampling of hard coal and coke. Relevant companion parts include:

• ISO 13909-1 to ISO 13909-6 and ISO 13909-8 (general introduction, sampling from moving streams and stationary lots, preparation of test samples, and methods for testing for bias).

Keywords: ISO 13909-7:2016, mechanical sampling, hard coal and coke, sampling precision, primary increment variance, duplicate sampling, replicate sampling, sample preparation variance, testing variance.

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 13909-7
Second edition
2016-07-01
Hard coal and coke — Mechanical
sampling —
Part 7:
Methods for determining the
precision of sampling, sample
preparation and testing
Houille et coke — Échantillonnage mécanique —
Partie 7: Méthodes pour la détermination de la fidélité de
l’échantillonnage, de la préparation de l’échantillon et de l’essai
Reference number
©
ISO 2016
© ISO 2016, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. [phone]
Fax [phone]
[e-mail]
www.iso.org
ii © ISO 2016 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 General . 1
5 Formulae relating to factors affecting precision . 2
5.1 General . 2
5.2 Sampling . 3
6 Estimation of primary increment variance . 4
6.1 Direct determination of individual primary increments . 4
6.2 Determination using the estimate of precision. 5
7 Methods for estimating precision . 5
7.1 General . 5
7.2 Duplicate sampling with twice the number of increments. 5
7.3 Duplicate sampling during routine sampling . 8
7.4 Alternatives to duplicate sampling . 9
7.5 Precision adjustment procedure . 9
8 Calculation of precision .10
8.1 Replicate sampling .10
8.2 Normal sampling scheme .11
9 Methods of checking sample preparation and testing errors .12
9.1 General .12
9.2 Target value for variance of sample preparation and analysis .12
9.2.1 General.12
9.2.2 Off-line preparation . .13
9.2.3 On-line preparation .13
9.3 Checking procedure as a whole .13
9.4 Checking stages separately .14
9.4.1 General.14
9.4.2 Procedure 1 .15
9.4.3 Procedure 2 .18
9.4.4 Interpretation of results .21
9.5 Procedure for obtaining two samples at each stage .22
9.5.1 With a riffle .22
9.5.2 With a mechanical sample divider .22
9.6 Example .22
Annex A (informative) Variogram method for determining variance .26
Annex B (informative) Grubbs’ estimators method for determining sampling precision .34
Bibliography .43
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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO’s adherence to the WTO principles in the Technical
Barriers to Trade (TBT), see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 27, Solid mineral fuels, Subcommittee SC 4,
Sampling.
This second edition cancels and replaces the first edition (ISO 13909-7:2001), which has been technically
revised.
ISO 13909 consists of the following parts, under the general title Hard coal and coke — Mechanical
sampling:
— Part 1: General introduction
— Part 2: Coal — Sampling from moving streams
— Part 3: Coal — Sampling from stationary lots
— Part 4: Coal — Preparation of test samples
— Part 5: Coke — Sampling from moving streams
— Part 6: Coke — Preparation of test samples
— Part 7: Methods for determining the precision of sampling, sample preparation and testing
— Part 8: Methods of testing for bias
iv © ISO 2016 – All rights reserved

Introduction
Two different situations are considered when a measure of precision is required. In the first, an estimate
is made of the precision that can be expected from an existing sampling scheme and, if this is different
from that desired, adjustments are made to correct it. In the second, the precision that is achieved on a
particular lot is estimated from the experimental results actually obtained using a specifically designed
sampling scheme.
The formulae developed in this part of ISO 13909 are based on the assumption that the quality of the
fuel varies in a random manner throughout the mass being sampled and that the observations will
follow a normal distribution. Neither of these assumptions is strictly correct. Although the assumption
that observations will follow a normal distribution is not strictly correct for some fuel parameters, this
deviation from assumed conditions will not materially affect the validity of the formulae developed for
precision checking since the statistics used are not very sensitive to non-normality. Strictly speaking,
however, confidence limits will not always be symmetrically distributed about the mean. For most
practical uses of precision, however, the errors are not significant.
NOTE In the text, the term “fuel” is used where both coal and coke would be applicable in the context and
either “coal” or “coke” where that term is exclusively applicable.
INTERNATIONAL STANDARD ISO 13909-7:2016(E)
Hard coal and coke — Mechanical sampling —
Part 7:
Methods for determining the precision of sampling, sample
preparation and testing
1 Scope
In this part of ISO 13909, formulae are developed which link the variables that contribute to overall
sampling precision. Methods are described for estimating overall precision and for deriving values for
primary increment variance which can be used to modify the sampling scheme to change the precision.
Methods for checking the variance of sample preparation and testing are also described.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 13909-1, Hard coal and coke — Mechanical sampling — Part 1: General introduction
ISO 13909-2, Hard coal and coke — Mechanical sampling — Part 2: Coal — Sampling from moving streams
ISO 13909-3, Hard coal and coke — Mechanical sampling — Part 3: Coal — Sampling from stationary lots
ISO 13909-4, Hard coal and coke — Mechanical sampling — Part 4: Coal — Preparation of test samples
ISO 13909-5, Hard coal and coke — Mechanical sampling — Part 5: Coke — Sampling from moving streams
ISO 13909-6, Hard coal and coke — Mechanical sampling — Part 6: Coke — Preparation of test samples
ISO 13909-8, Hard coal and coke — Mechanical sampling — Part 8: Methods of testing for bias
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 13909-1 apply.
4 General
When designing a sampling scheme in order to meet a required precision of results, formulae are
necessary that link certain fuel and sampling characteristics to that precision. The main factors to be
considered are the variability of primary increments, preparation and testing errors, the number of
increments and samples taken to represent the lot, and the mass of the samples. These formulae are
derived in Clause 5. Methods for estimating the parameters used in those formulae are given in Clause 6.
Once a sampling system has been designed and installed, the precision which is being achieved on
a routine basis should be checked. An estimate of the precision can be obtained from the primary
increment variance, V , the numbers of increments, n, and sub-lots, m, (see Clause 5) and the preparation
I
and testing variance, V . The preparation component of V is made up of on-line sample processing
PT PT
and off-line sample preparation.
Sampling variance is a function of product variability, so the same number of increments, sub-lots, and
preparation and testing errors will yield different precision with fuels that exhibit different product
variability.
Depending on the extent to which serial correlation exists and which method of estimating primary
increment variance is used, such an estimate could represent a considerable overestimate of the
numerical value of the precision (i.e. indicate that it is worse than is really the case). In addition, in
order for the results to be meaningful, large numbers of increments (in duplicate) would need to be
prepared and analysed for the estimation of V and V .
I PT
Quality variations obtained in the form of primary increment variances on existing systems are not
absolute and therefore designers should exercise caution when using such results in a different
situation. The estimated value of the primary increment variance, V , should be derived experimentally
I
for each fuel and at each sampling location.
Whenever a sampling scheme is used for determining increment variance, the operating conditions
should be as similar as possible to the conditions known, or anticipated, to prevail during the sampling
for which the increment variance is needed, whether it be carried out by the same or by a different
sampling system.
An estimate of the precision actually achieved can be obtained by taking the sample in a number of
parts and comparing the results obtained from these parts. There are several methods of doing this,
depending on
a) the purpose of the test, and
b) the practical limitations imposed by the available sampling procedures and equipment.
Where a sampling system is in existence, the purpose of the test is to check that the scheme is in fact
achieving the desired precision (see Clause 7). If it is not, it may need to be modified and rechecked until
it meets the precision required. In order to do this, a special check scheme should be devised which may
be different from the regular scheme but which measures the precision of the regular scheme.
For regular sampling schemes, the most rigorous approach is that of duplicate sampling of sub-lots.
In many existing mechanical sampling systems, however, the capacity of individual components and
the interval between increments in the regular scheme is insufficient to allow the taking of extra
increments. In such cases, duplicate samples can be constituted from the normal number of increments
and the result adjusted for the smaller number of increments in each sample (see 7.3).
The need may arise to sample a particular lot and to know the precision of the result obtained
(see Clause 8). Once again, a special check scheme needs to be devised, but in this case, it is the precision
achieved by that scheme on that lot which is required. For the measurement of the precision achieved
for a particular lot, replicate sampling is the best method.
Methods for detailed checking of preparation and testing errors are given in Clause 9. The results may
also be used to provide data for the formulae used in Clause 5.
5 Formulae relating to factors affecting precision
5.1 General
Precision is a measure of the closeness of agreement between the results obtained by repeating a
measurement procedure several times under specified conditions and is a characteristic of the method
used. The smaller the random errors of a method, the more precise the method is. A commonly accepted
index of precision is two times the sample estimate of the population standard deviation and this index
of precision is used throughout this part of ISO 13909.
2 © ISO 2016 – All rights reserved

If a large number of replicate samples, j, are taken from a sub-lot of fuel and are prepared and analysed
separately, the estimated precision, P, of a single observation is given by Formula (1):
Ps22 V (1)
SPT
where
s is the sample estimate of the population standard deviation;
V is the total variance.
SPT
The total variance, V , in Formula (1) is a function of the primary increment variance, the number of
SPT
increments, and the errors associated with sample preparation and testing.
NOTE The components of primary increment variance are the variance of sample extraction and the
variance contributed by product variability. The variance contributed by product variability is generally, but not
always, the largest source of variance in sampling.
For a single sample, this relationship is expressed by Formula (2):
V
I
V =+V (2)
SPT PT
n
where
V is the primary increment variance;
l
V is the preparation and testing variance;
PT
n is the number of primary increments in the sample.
5.2 Sampling
Where the test result is the arithmetic mean of a number of samples, resulting from dividing the lot into
a series of sub-lots and taking a sample from each, Formula (2) becomes:
V V
IPT
V =+ (3)
SPT
mn m
where
m is the number of sample results used to obtain the mean.
Since a sample is equivalent to one member of a set of replicate samples, by combining Formulae (1) and
(3), it can be shown that:
V V
IPT
P =+2 (4)
mn m
Formula (4) gives an estimate of the precision that can be expected to be achieved when a given
sampling scheme is used for testing a given fuel, the variability of which is known or can somehow
be estimated. In addition, Formula (4) enables the designer of the sampling scheme to determine, for
the desired precision and with fuel of known or estimated variability, the combination of numbers of
increments and samples, respectively, which will be most favourable considering the relative merits
of the sampling equipment and the laboratory facilities in question. For the latter purpose, however,
==
it is more convenient to use either or both Formulae (5) and (6), both of which have been derived by
rearranging Formula (4).
4V
I
n = (5)
mP −4V
PT
4 Vn+ V
()
IPT
m = (6)
nP
NOTE Results obtained from solid mineral fuels flowing in a stream will frequently display serial
correlation, i.e. immediately adjoining fuel tends to be of similar composition, while fuel further apart tends to
be of dissimilar composition. When this is so, the estimates of precision of the result of a single sample based on
primary increment variance and the variance of preparation and testing would indicate precision that is worse,
i.e. numerically higher, than the precision actually achieved. The effect of serial correlation can be taken into
account using the variographic method of determining variance given in informative Annex A.
6 Estimation of primary increment variance
6.1 Direct determination of individual primary increments
The direct estimation of primary increment variance can be accomplished with a duplicate sampling
scheme comprised of several hierarchical levels which allows both the overall variance and the variance
of preparation and testing to be estimated. The estimated variance of primary increments can then be
obtained by subtraction of the variance of preparation and testing from the estimated overall variance.
A number of primary increments is taken systematically and either divided into two parts or prepared
so that duplicate samples are taken at the first division stage. Each part is prepared and tested for
the quality characteristic of interest, using the same methods that are expected to be used in routine
operations. The mean of the two results and the difference between the two results are calculated for
each pair.
It is recommended that at least 30 increments be taken, spread if possible over an entire lot or even
over several lots of the same type of fuel.
The procedure is as follows.
a) Calculate the preparation and testing variance, V .
PT
d
∑
V = (7)
PT
2n
p
where
d is the difference between pair members;
n is the number of pairs.
p
b) Calculate the primary increment variance, V .
l
x − x
()
∑ ∑
n
V
p
PT
V = − (8)
I
n −1
()
p
where
x is the mean of the two measurements for each increment.
4 © ISO 2016 – All rights reserved

An alternative method for estimating primary increment variance, V is as follows:
l,
D
V
∑
PT
V =− (9)
I
22h
where
D is the difference between the means of successive pairs;
h is the number of successive pairs.
This method avoids the overestimation of sampling variance when there is serial correlation (see Note
in 5.2) but can only be used if the primary-increment sampling interval at which the increments are
taken is more than or approximately equal to the primary-increment sampling interval used when the
scheme is implemented in routine sampling operations.
The most rigorous treatment of serial correlation is to use the variographic method given in Annex A.
This takes into account both serial correlation and sampling interval effects, thereby avoiding
overestimation of sampling variance and number of primary increments due to these factors.
6.2 Determination using the estimate of precision
The primary increment variance can be calculated from the estimate of precision obtained either using
the method of duplicate sampling given in 7.2 or replicate sampling given in Clause 8 according to
Formula (10) which is derived by rearranging the terms of Formula (4).
mnP
V =−nV (10)
IPT
This value can then be used to adjust the sampling scheme if necessary.
7 Methods for estimating precision
7.1 General
For all the methods given in this Clause, the following symbols and definitions apply:
— n is the number of increments in a sub-lot for the regular scheme;
— m is the number of sub-lots in a lot for the regular scheme;
— P is the desired precision for the regular scheme;
— P is the worst (highest absolute value) precision to be permitted.
W
In all cases, the same methods of sample preparation shall be used as for the regular scheme.
7.2 Duplicate sampling with twice the number of increments
Twice the normal number of increments (2n ) are taken from each sub-lot and combined as duplicate
samples (see Figure 1), each containing n increments. This process is repeated, if necessary, over
several lots of the same fuel, until at least 10 pairs of duplicate samples have been taken.
A parameter of the fuel is chosen to be analysed, e.g. ash content (dry basis) for coal, or Micum 40 index
for coke. The standard deviation within duplicate samples for the test parameter is then calculated
using Formula (11):
d
∑
s= (11)
2n
p
where
d is the difference between duplicates;
n is the number of pairs of duplicates being examined.
p
An example of results for coal ash is given in Table 1.
Table 1 — Results of duplicate sampling, % ash, dry basis
Duplicate values
Difference between duplicates
%
Sample pair no.
A B |A − B| = d d
1 11,1 10,5 0,6 0,36
2 12,4 11,9 0,5 0,25
3 12,2 12,5 0,3 0,09
4 10,6 10,3 0,3 0,09
5 11,6 12,5 0,9 0,81
6 11,8 12,0 0,2 0,04
7 11,8 12,2 0,4 0,16
8 10,8 10,0 0,8 0,64
9 7,9 8,2 0,3 0,09
10 10,8 10,3 0,5 0,25
Total 2,78
The number of pairs, n is 10. The variance of the ash content is therefore
p
d
∑
s =
2n
p
27, 8
==0,139
and the standard deviation is:
s 0,,13900 373
6 © ISO 2016 – All rights reserved
==
Key
increment from regular scheme
extra increment for precision check scheme
Figure 1 — Example of a plan of duplicate sampling
The precision of the result for a single sub-lot is therefore:
Ps= 2
= 20,,373 = 075 % ash
()
The precision achieved for the mean ash of a normal lot sampled as m sub-lots is given by 2sm . For
example, if m = 10, then:
20,373
()
P = = 0,235 9 %
These values of P have been calculated using point estimates for the standard deviation and represent
the best estimate for precision.
If an interval estimate for the standard deviation is used, then on a 95 % confidence level, the precision
is within an interval with upper and lower limits. These limits are calculated from the point estimate
of precision and factors which depend on the degrees of freedom (f) used in calculating the standard
deviation (see Table 2).
Table 2 — Factors used for calculation of precision intervals
ƒ (number of observations) 5 6 7 8 9 10 15 20 25 50
Lower limit 0,62 0,64 0,66 0,68 0,69 0,70 0,74 0,77 0,78 0,84
Upper limit 2,45 2,20 2,04 1,92 1,83 1,75 1,55 1,44 1,38 1,24
NOTE The factors in Table 2 are derived from the estimate of s obtained from the squared differences of n
pairs of observations. Since there is no constraint in this case, the estimate as well as d will have n degrees of
freedom. The values in Table 2 are derived from the relationship:
2 2
ns ns
< 2 2
χχ
nn,,0025 ,,00975
The body of Table 2 gives the values for n/χ , which are multiplied by s to obtain the confidence limits.
For example, for the lot with 10 sub-lots used in the example above:
Upper limit = 1,75 (0,235 9) = 0,41 %
Lower limit = 0,70 (0,235 9) = 0,17 %
where the factors are obtained from Table 2 using ƒ = n , i.e. 10. The true precision lies between 0,17 %
P
and 0,41 % ash at the 95 % confidence level.
7.3 Duplicate sampling during routine sampling
If operational conditions do not allow the taking of 2n increments from each normal sub-lot or
precision is to be determined during normal sampling, then, provided that all increments can be kept
separate, adopt the following procedure for estimating precision.
Take the normal number of increments, n , from each sub-lot and combine them as duplicate samples
each comprising n /2 increments (see Figure 2). Repeat this process, if necessary, over several lots of
the same fuel until at least 10 pairs of duplicate samples have been obtained. In this case, the precision
obtained using the procedure in 7.2 will be for n /2 increments. This estimate of precision is divided by
the square root of 2 to obtain the estimate of precision for sub-lot samples comprising n increments.
8 © ISO 2016 – All rights reserved

Figure 2 — Example of a plan of duplicate sampling where no additional increments are taken
7.4 Alternatives to duplicate sampling
At some locations, operational conditions of a sampling system do not allow duplicate samples to be
collected with the assurance that no cross-contamination of sample material from adjacent primary
increments occurs. In such cases, other methods have been found useful. An example of such a method,
using Grubbs estimators, is given for information in Annex B.
This method involves collecting three samples from each of a minimum of 30 sub-lots of fuel. One sample
is collected using the normal sampling scheme and two mutually independent systematic samples are
collected by stopping a main fuel handling belt for collection of stopped-belt increments at preselected
intervals.
7.5 Precision adjustment procedure
If the desired level of precision, P , for the lot lies within the confidence limits, then there is no evidence
that this precision is not being achieved. However, if the confidence interval is wide enough to include
both P and P , the test is inconclusive and further data shall be obtained. The results shall be combined
0 W
with the original data and the calculation done on the total number of duplicate samples.
NOTE The expected effect is reduction of the width of the confidence limits since the value of f in Table 2 will
be greater.
This process can be continued until either P is above the upper confidence limit or the value of P falls
W 0
outside the confidence limits. In the latter case, adjustment may be necessary.
NOTE If the precision obtained differs from the desired precision, a cost/benefit analysis will indicate
whether it is worthwhile to proceed with any modifications to the sampling system and sampling programme
because the costs incurred in making the changes and retesting may not be worthwhile.
Before making changes to the sampling scheme, the errors of preparation and testing shall be examined
using the procedures given in Clause 9. It should then be possible to decide whether to make the changes
to the sampling or the sample preparation using the formulae in 5.2.
If it is decided to design a new sampling scheme, the first step is the calculation of the primary
increment variance. This can be done using Formula (12) which is derived by rearranging Formula (4)
and substituting n for n.
mn P
V =−nV (12)
IP0 T
where
P is the measured precision obtained from the test and is not P ;
V is either the original value or one estimated using the methods in Clause 9.
PT
Using the new value for the primary increment variance, design a new scheme following the procedures
specified in ISO 13909-2, ISO 13909-3 or ISO 13909-5, as relevant, depending on whether the sampling
is of coal or coke and from moving or stationary fuels.
When the new scheme is in operation, carry out a new precision check, discarding the previous results
and continue in this fashion until the precision is satisfactory.
Thereafter, it is not necessary to check the precision for every lot but periodic checks should be carried
out. For example, one sub-lot in five may be examined or, alternatively, 10 consecutive sub-lots if using
method 7.2, or the equivalent if using method 7.3.
When 10 pairs of results have been accumulated, they shall be examined as described in 7.2, ignoring
any intervening samples not taken in duplicate.
8 Calculation of precision
8.1 Replicate sampling
Establish the parameter to be analysed, e.g. ash (dry basis), and establish the sampling scheme for
the required precision in accordance with ISO 13909-2, ISO 13909-3 or ISO 13909-5 as appropriate,
depending on whether the sampling is of coal or coke and from moving streams or stationary lots.
Instead of forming a sample from each sub-lot, combine the total number of increments, n⋅m, as replicate
samples. The number of replicate samples, j, shall be not less than the number of sub-lots, m, used in the
calculation (see the relevant part of ISO 13909), and not less than 10.
If there are 10 such samples and the sample containers are labelled A, B, C, D, . J, then successive
increments will go into the containers as follows: A, B, C, D, E, F, G, H, I, J, A, B, C, D, . .
A typical calculation for coal is given below using the results in Table 3.
The number of replicate samples, j, is 10.
The mean result is 165/10 = 16,5 % ash
10 © ISO 2016 – All rights reserved

Table 3 — Results of single lot sampling, % ash, dry basis
Sample value (Sample value)
Sample no.
%
A 15,3 234,09
B 17,1 292,41
C 16,5 272,25
D 17,2 295,84
E 15,8 249,64
F 16,4 268,96
G 15,7 246,49
H 16,3 265,69
I 18,0 324,00
J 16,7 278,89
Totals 165,0 2 728,26
The sample estimate of the population standard deviation, s, is:
 
 
x
()
∑
i
 2 
x −
 
∑
i
n
 
 
 
s =
n−1
()
2728,26−
= = 0,800
The best estimate for the precision, P, achieved for the lot is given by:
2s
P= (13)
j
i.e.
20, 800
()
P = = 0,506 % ash
Hence, using Table 2, the true precision lies between 0,35 % and 0,89 % at the 95 % confidence level. It
should be noted, however, that the procedure given in this subclause tends to overstate the variance to
the extent that it includes variance components of sample preparation and analysis.
8.2 Normal sampling scheme
If it is desired to design a regular sampling scheme based on the results of the procedure specified
in 8.1, the estimate of precision obtained, the number of increments per sample and the number of
replicate samples can be substituted into Formula (12) and the value for increment variance estimated.
The procedures specified in ISO 13909-2, ISO 13909-3 or ISO 13909-5, as appropriate, can then be
followed to design the regular sampling scheme.
9 Methods of checking sample preparation and testing errors
9.1 General
The methods described in this Clause, for checking the precision of sample preparation and testing,
are designed to estimate the variance of random errors arising in the various stages of the process.
The errors are expressed in terms of variance. Separate tests are necessary to ensure that bias
is not introduced either by contamination or by losses during the sample preparation process
(see ISO 13909-8).
As described in ISO 13909-4, sample preparation for general analysis of coal will normally be carried
out in at least two stages, each stage consisting of a reduction in particle size, possible mixing, and
division of the sample into two parts, one of which is retained and one rejected. All the errors occur in
the course of the division, in the selection of the final 1 g of 212 µm size and in the analysis. The most
important factors are the size distribution of the samples before division and the masses retained after
division.
The preparation of coke samples is generally carried out with fewer stages but the same basic principle
of checking for errors applies.
For convenience, the remainder of this Clause refers to coal ash only. If the variance is satisfactory
for ash, it will normally be so for the other characteristics of the proximate and ultimate analyses,
except possibly for errors in moisture and calorific value, which should be checked. If desired, all
characteristics may be checked.
Methods are described for checking the overall errors of preparation and testing and also the errors
incurred at individual stages.
The methods were originally developed for manual and non-integrated mechanical preparation. If some
sample preparation is carried out within an integrated primary sampling/sample preparation system,
it may not be practicable to determine the errors for the individual components, except by artificial
means such as re-feeding reject streams through the system, which would be totally unrepresentative
of normal operations. The variances of the integrated preparation stages may therefore have to be
compounded with the primary increment variance and measured as such.
9.2 Target value for variance of sample preparation and analysis
9.2.1 General
The overall preparation and testing variance, V , estimated by the procedure described in 9.3, is
PT
evaluated in relation to a previously determined target, V . This target is normally laid down by the
PT
body responsible for sample preparation.
The individual division errors are estimated directly. These may be evaluated either in relation to a
target or as a proportion of the overall variance.
NOTE As a rough guide, a division-stage variance is generally twice the analytical variance so that, for
example, for a three-stage preparation and testing process, the overall value of V is divided in the ratio 2:2:1 to
PT
obtain the two-division stage variance targets and the analytical variance.
The final-stage analysis variance target can be determined from the relevant analytical standard from
Formula (14):
r
V = (14)
T
where
12 © ISO 2016 – All rights reserved

is the final sample extraction and analytical variance target;
V
T
r is the repeatability limit of the analytical method.
The division errors for moisture content may be unavoidably greater than those for ash content because
of the need to avoid excessive handling which could in turn result in bias. Such errors may, however,
be acceptable if the overall precision can be achieved due to the lower primary increment variances
normally encountered for moisture content.
9.2.2 Off-line preparation
The methods of sample preparation recommended for coal in ISO 13909-4, using the masses specified,
should achieve, for coal ash, a sample preparation and testing variance of 0,2 or less. For many coals,
much lower variances will be achievable, particularly, if mechanical dividers are used that take a great
many more than the minimum number of cuts. Similar considerations will apply to the methods of
preparation for coke in ISO 13909-6. If possible, therefore, a more stringent overall target should be set
in the light of experience with similar coals prepared on similar equipment.
Smaller preparation errors will reduce the number of samples required to be taken and tested.
The worst-case individual division-stage variance (for coal 0,08) should be treated as a maximum
which may be improved by using mechanical division.
9.2.3 On-line preparation
Where some elements of sample preparation are carried out in a system integral with the primary
sampler, the errors involved may be compounded with the primary increment variance, V . In such
l
cases, it should be expected that the residue of V will be less than it would have been had all the
PT
sample preparation been done off-line.
It is recommended that realistic overall targets be obtained from relevant experience. As a worst-case
target, however, use the worst-case individual division-stage variance for each division stage plus the
appropriate analytical variance (see 9.2.1).
9.3 Checking procedure as a whole
The first step is to check that the overall variance of preparation and testing does not exceed the target
set, V (see 9.2). The method provides a test of whether the difference between the estimated value
PT
and the target value is statistically significant.
This is done by taking duplicate samples at the first division of the sample; these are thereafter treated
entirely separately to give the two test samples (see Figure 3). The two samples provide an unbiased
estimate of the variance of sample preparation and analysis. Ten pairs of test samples are obtained in
this way.
If the mean observed absolute difference between the 10 pairs of results is y, then 0,886 2 y should lie
0 0
between 07, V and 17, 5 V (see Table 2).
PT PT
NOTE The factor 0,886 2 is derived from the relationship for converting the mean differences between pairs
to the standard deviation.
Provided that the standard deviations of two successive sets of 10 duplicate samples fall between these
upper and lower limits, it may be assumed that the procedure is satisfactory.
If the standard deviation is below 07, V , the variance is low but no adjustment is necessary since it
PT
is always desirable to have the variance as low as possible.
If the standard deviation is greater than 17, 5 V , the variance is too high and the masses retained at
PT
various stages of the sample-preparation process are probably insufficient. Therefore, the variance of
the errors arising at each stage should be estimated as described in 9.4 so that steps may be taken to
improve the procedures shown to be necessary.
Key
reduce to particle size specified ( L is the nominal top size after first-stage reduction)
divide to mass specified (Y is the value give in Table 3)
Figure 3 — Overall test of sample preparation
9.4 Checking stages separately
9.4.1 General
The following two procedures are commonly used.
a) Procedure 1 (see 9.4.2), where analysis is inexpensive relative to the cost of sampling.
b) Procedure 2 (see 9.4.3), which is slightly less accurate but involves fewer analyses.
Using the principles of 9.4.2.2 or 9.4.3.2 as appropriate, schemes with more than two division stages
can normally be examined.
14 © ISO 2016 – All rights reserved

For example, the errors arising from a three-stage preparation scheme can be separated as follows:
a) the errors in taking Y kg from X kg = variance V ;
b) the errors in taking 60 g from Y kg = variance V ;
c) the analytical errors, which include the error of taking 1 g from the bottle of fuel crushed to
212 µm = variance V .
T
The total variance of the procedure, V, is given by Formula (15):
V =+VVV+ (15)
12 T
If duplicates are extracted at an intermediate stage, the total variance of these samples will be the sum
of errors at this and later stages. For example, if in a three-stage procedure, duplicates are taken at the
second stage, then the variance of the duplicates is V + V .
2 T
In order to separate the component variances, it is necessary to take duplicates at each stage, calculate
the total variance at each stage and then, by working backwards from the analysis stage, separate the
individual stage variances.
The same
...