ISO 13909-7:2016

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
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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
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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 n
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