ISO 14488:2007/Amd 1:2019

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First edition
Particulate materials — Sampling and
sample splitting for the determination
of particulate properties
Matériaux particulaires — Échantillonnage et division des
échantillons pour la caractérisation des propriétés particulaires
Reference number
ISO 14488:2007/Amd.1:2019(E)
ISO 2019
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ISO 14488:2007/Amd.1:2019(E)
© ISO 2019

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

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ii © ISO 2019 – All rights reserved
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ISO 14488:2007/Amd.1:2019(E)

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This document was prepared by Technical Committee ISO/TC 24, Particle characterization including

sieving, Subcommittee SC 4, Particle characterization.

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© ISO 2019 – All rights reserved iii
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ISO 14488:2007/Amd.1:2019(E)
Particulate materials — Sampling and sample splitting for
the determination of particulate properties
Annex B
Add the following additional clause.

B.7 Simple approach to the calculation of the fundamental sampling error (FSE) and minimum

mass required for a specified standard error

This clause provides a method to approximately determine the magnitude (mg/g/kg) of the minimum

mass required to meet a specific standard error. The approach approximates the precise calculations

described in the document. With a knowledge or assumption of the actual mass utilized in the particle

size analysis experiment, the best standard error achievable based solely on the heterogeneity of the

material can also be estimated.

The fundamental sampling error (FSE) is one of 8 errors (implies culpability) or variables (implies


statistical variation) originally described by Pierre Gy – see Table B.3. It represents the smallest

possible variation in sample to sample reproducibility based solely on the heterogeneity of the material

or distribution involved.
Table B.3 — Old (Gy) and new notations (Pitard/Esbensen)
Errors Old term New term
Heterogeneity fluctuation error CE HFE
Quality fluctuation error QE QFE
Fundamental sampling error FE FSE
Grouping and segregation error GE GSE
Increment weighting error WE IWE
Increment delimitation error DE IDE
Increment extraction error EE IEE
Increment preparation errors PE IPE

The FSE is identical to the standard error familiar to mathematicians and statisticians . The

standard error (SE) of a parameter is the standard deviation (σ, theoretical value) or an estimate of

the standard deviation (s, absolute value coming from measurements) of a sampled distribution. If the

parameter or the statistic is the mean, it is called the standard error of the mean (SEM). It represents

how close the result gets to the ‘true’ mean with repeated samplings or an increased proportion of the

actual distribution.

In particle size distribution considerations, the FSE is inversely proportional to the square root of the

number of particles present in the distribution or part of the distribution. In the following derivations,

no assumption is made of the form of the original particle size distribution; only, that the samples

withdrawn are normally distributed (as is the standard case).
© ISO 2019 – All rights reserved 1
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ISO 14488:2007/Amd.1:2019(E)
SEM α 1/√n or n α 1/σ
For 1 % SEM it can be shown that:
n = 1/(0,01) = 10 000

Thus, 10 000 particles in total will be needed to specify the mean to 1 % SE. See also Reference [18]. The

implication is that to specify any other point of the distribution to 1 % SE, at least 10 000 particles will

be needed in the portion of the distribution above that point. The worst-case situation is considered

first; specifying the x point in the distribution to a standard error of 1 %. This requires 10 000

particles in the x + part of the distribution. This x + part represents only 1/100 of the total sample

99 99

mass of the entire distribution. Thus, only the mass (= volume × density) of 10 000 particles needs to be

calculated at some known or assumed x point in the distribution and multiplied by the appropriate

value to compute the total mass of the distribution. Using the value of the x point is more convenient

than attempting to use a more correct midpoint between the x and (unknown) x point. It will

99 100

slightly underestimate the minimum mass required but calculations show this to be minor.

Making two assumptions, the minimum mass of the portion M can be calculated: the particles are

spherical and all particles of the portion have the minimum diameter x .
Mn=×(/π 6)××x ρ
Qmin Q
n is the minimum number of particles for the specified precision;
(π/6) is the shape factor for a sphere;
x is the largest point in

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