ISO 12745:2008
(Main)Copper, lead and zinc ores and concentrates — Precision and bias of mass measurement techniques
Copper, lead and zinc ores and concentrates — Precision and bias of mass measurement techniques
ISO 12745:2008 provides guidelines to test for bias over a wide range of mass measurement techniques, to estimate the precision for each technique and to calculate the precision for wet mass when estimated by applying one of those techniques. The guidelines are based on the application of statistical tests to verify that a mass measurement technique is unbiased, to estimate the variance as the most basic measure for its precision and to check the linearity of a static scale over its working range. Calibration methods and performance tests for compliance with applicable regulations generate test results that can be used to quantify precision and bias for each of these mass measurement techniques and to verify linearity for static weighing devices. The guidelines apply to mass measurement techniques used to estimate the wet mass for cargoes or shipments of mineral concentrate as the basis for freight and insurance charges and for preliminary payments or for final settlements between trading partners.
Minerais et concentrés de cuivre, de plomb et de zinc — Justesse et erreurs systématiques des techniques de pesée
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INTERNATIONAL ISO
STANDARD 12745
Second edition
2008-10-01
Copper, lead and zinc ores and
concentrates — Precision and bias of
mass measurement techniques
Minerais et concentrés de cuivre, de plomb et de zinc — Justesse et
erreurs systématiques des techniques de pesée
Reference number
ISO 12745:2008(E)
©
ISO 2008
---------------------- Page: 1 ----------------------
ISO 12745:2008(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
COPYRIGHT PROTECTED DOCUMENT
© ISO 2008
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 either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2008 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 12745:2008(E)
Contents Page
Foreword. iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 1
4 General remarks. 4
4.1 Draft surveys . 4
4.2 Belt scales . 5
4.3 Weighbridges . 5
4.4 Hopper scales . 6
4.5 Gantry scales . 6
4.6 Platform scales . 7
5 Certified weights. 7
6 Methods of operation . 8
6.1 General. 8
6.2 Draft surveys . 8
6.3 Belt scales . 12
6.4 Weighbridges . 14
6.5 Hopper scales . 16
6.6 Gantry scales . 18
6.7 Platform scales . 20
Annex A (informative) Tables. 22
Annex B (informative) Statistics .32
Annex C (informative) Draft surveys . 41
Annex D (informative) Procedure for the testing of static scales . 44
Bibliography . 47
© ISO 2008 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO 12745:2008(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.
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 12745 was prepared by Technical Committee ISO/TC 183, Copper, lead, zinc and nickel ores and
concentrates.
This second edition cancels and replaces the first edition (ISO 12745:1996), which has been technically
revised.
iv © ISO 2008 – All rights reserved
---------------------- Page: 4 ----------------------
INTERNATIONAL STANDARD ISO 12745:2008(E)
Copper, lead and zinc ores and concentrates — Precision and
bias of mass measurement techniques
1 Scope
This International Standard provides guidelines to test for bias over a wide range of mass measurement
techniques, to estimate the precision for each technique and to calculate the precision for wet mass when
estimated by applying one of those techniques.
The guidelines are based on the application of statistical tests to verify that a mass measurement technique is
unbiased, to estimate the variance as the most basic measure for its precision and to check the linearity of a
static scale over its working range. Calibration methods and performance tests for compliance with applicable
regulations generate test results that can be used to quantify precision and bias for each of these mass
measurement techniques and to verify linearity for static weighing devices.
The guidelines apply to mass measurement techniques used to estimate the wet mass for cargoes or
shipments of mineral concentrate as the basis for freight and insurance charges and for preliminary payments
or for final settlements between trading partners.
The application of static scales requires that at least one certified weight with a mass of no less than one (1)
tonne be either available on location or brought in for calibration purposes, and that this certified weight be
applicable to the scale in accordance with the manufacturer’s recommendations. A set of certified weights
covering the entire working range of a weighing device simplifies the process of verifying its state of calibration,
estimating its precision as a function of applied load and testing its linearity over the working range.
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 3534-1:2006, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 3534-2:2006, Statistics — Vocabulary and symbols — Part 2: Applied statistics
ISO 5725-1:1994, Accuracy (trueness and precision) of measurement methods and results — Part 1: General
principle and definitions
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
2
NOTE 1 In authoritative textbooks on applied statistics the use of the sigma squared (σ ) symbol is restricted to
2
unknown population variances for which a measurement procedure gives an estimate only. By contrast, the symbol s
applies to variances of samples, and thus to finite sets of measurements. Standard methods on sampling of bulk materials
2
often apply sigma-symbols (σ or σ) indiscriminately.
© ISO 2008 – All rights reserved 1
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ISO 12745:2008(E)
NOTE 2 Following are definitions for the most relevant concepts and terms in mass measurement technology. They
are presented to clarify the difference between this standard method, which quantifies the risk of losing and the probability
of gaining in commercial transactions, and other methods that deal with mass measurement techniques from the
perspective of regulatory agencies.
3.1
accuracy
generic term that implies closeness of agreement between an observed mass and its unknown true value
NOTE Accuracy is an abstract concept that cannot be quantified, but a lack of accuracy can be measured and
quantified in terms of a bias or systematic error.
3.2
bias
difference between the expectation of the test result and an accepted reference value
NOTE This definition is only valid if the accepted reference value is known with absolute certainty (International Units
of Mass and Length). Given that most accepted reference values are known within finite confidence limits, the difference
between the expectation of a test result and an accepted reference value is only a bias if the expectation of the test result
1)
falls outside the confidence limits of an accepted reference value.
3.3
belt scale
mass measurement device that continuously integrates and records as a cumulative mass, the load on a belt
while it passes the suspended scale section in a conveyor belt
NOTE Belt scales are continuous mass measurement devices that are calibrated by applying a load such as a
calibrated chain on the belt above the scale section (dynamic), or a certified weight suspended from the scale’s frame
(static), for a specified integration period, or by measuring with the belt scale a quantity of material whose mass is
measured with a static scale (material-run method).
3.4
bias detection limit
BDL
measure for the power or sensitivity of Student’s t-test to detect a bias or systematic error between applied
and observed loads
3.5
coefficient of variation
CV
measure for random variations in a mass measurement technique, numerically equal to the standard deviation
as a percentage of the observed mass
3.6
confidence interval
Cl
interval within which a predetermined percentage of the differences between all possible measurements and
their mean is expected to cluster
3.7
confidence range
CR
range within which a predetermined percentage of all possible measurements is expected to cluster
NOTE In science and engineering 95 % confidence intervals and ranges are most frequently used.
1) For example, the mass of the lot is generally determined once only so that the measured value is not the expectation
of the test result. In this International Standard a bias is the statistically significant difference between independent
estimates of the wet mass of the lot (loading versus discharge, static versus dynamic scales) and mass measurements
should be traceable to National Prototype Kilograms, and thus to the International Unit of Mass, through the shortest
possible calibration hierarchy.
2 © ISO 2008 – All rights reserved
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ISO 12745:2008(E)
3.8
correlation coefficient
r
measure for the degree of association or interdependence between a set of certified weights and observed
loads
3.9
draft survey
mass measurement technique that is based on converting the difference between a vessel’s displacement
under different loads into a mass on the basis of its draft tables while taking into account the density and
temperature of water and ballast, and changes in ballast and supplies
NOTE Draft surveys are based on Archimedes’s Principle which states that a floating body displaces its own mass.
The wet mass of a cargo or shipment can be measured by converting changes in draft, trim, ballast and consumable
supplies into mass on the basis of the vessel’s draft table.
3.10
precision
generic term for the cumulative effect of random variations in a mass measurement technique
NOTE Precision is a generic qualifier, e.g. “a high degree of precision”, “the precision is poor or low” or “the precision
characteristics are excellent”, are valid statements albeit without quantitative implications.
3.11
probable bias range
PBR
limits within which a measured bias is expected to fall at predetermined probabilities, either for a type I risk
only or for type I and II risks
3.12
relative standard deviation
s
r
measure for random variations in a mass measurement technique, numerically equal to the standard deviation
divided by the observed mass
3.13
standard deviation
s
measure for random variations in a mass measurement technique, numerically equal to the square root of the
variance
3.14
static scale
mass measurement device that converts into a mass a static load on a weighbridge or on a platform, inside a
hopper or suspended from a gantry scale
NOTE Static scales are batch mass measurement devices that are calibrated either with a single certified weight or
with a set, and less frequently with a calibrated hydraulic press. Static scales may have automatic zero adjustment so that
the sum of the differences between tare and gross loads can be used to generate a cumulative mass. Dual hopper scales
allow a virtually continuous mass flow during loading and discharge operations without sacrificing the accuracy and
precision characteristics of the static scale.
3.15
Student’s t-value
t
ratio between the difference for the means for sets of applied and observed loads and the standard deviation
for the mean difference
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ISO 12745:2008(E)
3.16
type I risk
α
risk of rejecting the hypothesis that the means for sets of applied and observed loads are compatible when
their mean difference is, in fact, statistically identical to zero
3.17
type II risk
β
risk of accepting the hypothesis that the means for sets of applied and observed loads are compatible when
their mean difference is, in fact, statistically different from zero
3.18
variance
2
s
measure for random variations in a mass measurement technique, numerically equal to the sum of squared
deviations from the mean for a set of measurements divided by the number of measurements in the set
minus 1 (divided by the degrees of freedom)
NOTE In textbooks on applied statistics the term “mean squared deviation from the mean” is often used in reference
to the variance.
4 General remarks
International and national handbooks on weighing devices define uncertainties in mass measurement
techniques in different ways. In some handbooks the use of the term “error” is restricted to a bias or
systematic error while others refer to “maximum permissible risks”, which appears synonymous with
“tolerances”, as a measure for random variations in a mass measurement technique.
Unless “maximum permissible errors” or “tolerances” are, by definition, equal to 95 % or 99 % confidence
intervals, neither can be converted into a variance as the most basic measure for the precision of a
measurement process. However, an unbiased estimate for the variance of the wet mass of a cargo or
shipment of mineral concentrate is required before the precision for its dry mass and the masses of contained
metals can be calculated and reported in terms of 95 % confidence intervals and ranges as a measure for the
risk that trading partners encounter.
Annex D provides information for a step-by-step procedure for the testing of static scales.
4.1 Draft surveys
The difference between a vessel’s displacements, either before and after loading or before and after
discharge, is converted into a wet mass on the basis of its draft table. Corrections are applied for changes in
ballast and consumables such as fuel, potable water and supplies. Average densities of water, in ballast tanks
and in proximity to the vessel during draft surveys, are measured and taken into account when converting a
difference between the vessel’s displacements under different load conditions into a mass.
External factors, such as wind velocity and stratified salinity, limit the precision of draft surveys. Deformation of
vessels, while in a partially loaded condition, adds another element of uncertainty that may translate into a
bias. Displacement surveys for single cargo spaces are invariably less precise than displacement surveys for
full cargoes. The highest degree of precision can be obtained when a vessel is surveyed at loading in a light
(without ballast) and completely loaded condition, or at discharge in a completely loaded and light (without
ballast) condition.
Moisture migration during the voyage would cause discrepancies between surveys at loading and discharge if
drained water were removed with the bilge pumps. In such cases the wet mass measured at discharge may
well be significantly lower than the wet mass at loading but the dry masses at loading and discharge are
expected to be compatible. Oxidation often causes a small increase in mass that is difficult to estimate due to
the highly variable degree of precision for draft surveys.
4 © ISO 2008 – All rights reserved
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ISO 12745:2008(E)
Generally, precision estimates in terms of coefficients of variation range from a low of 0,5 % to a high of 2,5 %.
The lowest coefficients of variation were observed by comparing draft surveys at loading and discharge. If the
marine surveyor at discharge has knowledge of the vessel’s bill of lading (B/L), the draft surveys at the ports
[1]
of discharge and loading are no longer statistically independent .
Draft surveys at loading are based on consensus between an officer of the vessel, a marine surveyor
representing the shipper, and sometimes a marine surveyor representing the buyer. Under such conditions
the precision of the draft surveys at loading cannot possibly be estimated. Only in the case that two or more
qualified marine surveyors each complete their own draft surveys for the vessel, at the same time but
independently, can the precision of this mass measurement technique be estimated in an unbiased manner.
The precision for a draft survey can also be estimated if the wet mass of a cargo or shipment is measured with
a static scale with known precision characteristics, provided that it be located in close proximity to the vessel
to ensure that loss of moisture and mechanical loss do not cause a bias. Unlike linearity for static mass
measurement devices linearity for draft surveys cannot be defined in a meaningful manner due to the
differences in the deformation of vessels over a wide range of loading conditions.
Annex C provides an example of a displacement calculation for a draft survey.
4.2 Belt scales
A belt scale is a continuous (dynamic) mass measurement device that integrates the variable load on a
suspended belt section over long periods of time. Precision and bias for belt scales depend on numerous
factors not the least of which is the environment in which they operate. A belt scale can be calibrated with a
chain that is trailed on the belt over the scale’s mechanism with a static weight that is suspended from the
scale’s frame, or with a quantity of material whose wet mass is measured with a static scale. Despite its
[2]
relatively short time basis, the material-run test is the most reliable calibration procedure for dynamic scales .
A belt scale in series with a hopper scale integrated in a conveyor belt system can be calibrated, and its
precision estimated, by comparing paired wet masses (static versus dynamic). Many applications would
benefit from a pair of belt scales in series. Particles that become wedged between the conveyor’s frame and
the suspended frame of a belt scale cause discrepancies between paired measurements. Identification of
anomalous differences permits corrective action to be taken. Removal of spillage from a belt scale’s
mechanism at regular intervals reduces drift, and thus the probability of a bias occurring.
A precision of 0,4 % in terms of a coefficient of variation has been observed for advanced belt scales under
optimum conditions but under adverse conditions the coefficient of variation may well exceed 3,5 %. Reliable
and realistic estimates for the precision of belt scales under routine conditions are obtained by measuring and
monitoring variances between observed spans prior to each calibration. Frequent calibrations ensure that belt
scales will generate unbiased estimates for wet mass. The central limit theorem implies that continuous
weighing with dynamic scales gives a significantly lower precision for wet mass than batch weighing with static
scales does.
Under routine conditions the linearity of belt scales is difficult to measure. Manufacturers of load cells test the
linearity of response over 4 mA to 20 mA ranges. However, linearity under test conditions does not
necessarily ensure linear responses to applied loads under routine conditions. Nonetheless, deviations from
linearity are not likely to add more uncertainties to this mass measurement technique than other sources of
variability such as belt tension and stiffness, stickiness of wet material or wind forces.
4.3 Weighbridges
The wet mass of cargoes or shipments of mineral concentrate is often measured by weighing trucks or
wagons in empty and loaded condition at mines or ports, and in loaded and empty condition at ports or
smelters. The precision for wet mass that is measured with a static scale such as a weighbridge, is perfectly
acceptable for settlement purposes. The variance component that the measurement of wet mass contributes
to the variance for contained metal is significantly lower than those for the measurement of moisture and
[3]
metal contents .
© ISO 2008 – All rights reserved 5
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ISO 12745:2008(E)
The suspended mass of the scale’s beam and its support structure is only a small part of gross loads. As a
result, the variance for tare loads is significantly lower than the variance for gross loads which implies that the
variance for the net wet mass of a single unit is largely determined by the variance for its gross load. After
each cycle the weighbridge is zero adjusted, either automatically or manually, to eliminate drift.
Regulatory agencies may use one or more wagons of certified weight to calibrate weighbridges. Each wagon
gives only one calibration point so that deviations from linearity are impossible to detect. By placing two
wagons on a weighbridge a set of three [3] calibration points is obtained to provide useful but limited
information on its linearity. The most effective test for linearity is based on addition or subtraction of a set of
certified weighs that covers the working range of a weighbridge. Equally effective but more time consuming is
alternately adding a single certified weight with a mass of 1 t to 2 t and a quantity of material until the
weighbridge is tested in increments of 5 t to 10 t over its working range.
Precision parameters for weighbridges can be measured and monitored by weighing in duplicate once per
shift, a truck or a wagon. After the gross weight of a randomly selected truck or wagon is measured in the
usual manner, it is removed from the weighbridge. Next, the zero is checked and adjusted if required, and
then the unit is moved on to the weighbridge and weighed again. The mean for sets of four or more absolute
differences between duplicates can be used to calculate the variance for a single test result at gross loads. In
terms of a coefficient of variation the precision for a weighbridge at gross loads generally ranges from 0,1 %
up to 0,5 %.
The precision can also be estimated by placing on the weighbridge, in addition to the gross load, a test mass
of five times up to ten times the scale’s readability or sensitivity. Measurements with and without this test
mass are recorded and the variance for gross loads calculated from a set of six data points up to 12 data
points. Such estimates tend to be marginally but not significantly lower than the precision between duplicates
that are generated by first weighing, and then removing and reweighing a loaded truck or wagon.
This procedure can be repeated without a load on the scale. A test mass is placed on the scale and its mass
recorded. Next, the test mass is removed, and the zero adjusted if required. This process is repeated no less
than six times, and the variance at near-zero loads calculated.
4.4 Hopper scales
The wet mass of cargoes or shipments can also be determined with a single hopper scale or with a pair of
parallel hopper scales. Upon completion of each discharge cycle a hopper scale is often automatically zero
adjusted so that a bias caused by build-up of wet material and dislodgement at random times is eliminated.
Otherwise, tare loads for each weighing cycle should be recorded to allow for changes in accumulated mass.
A hopper scale is calibrated by suspending from its frame a set of certified weights with a mass of 1 t to 2 t
each to cover its entire working range. It is possible but more time-consuming to calibrate a hopper scale with
a single certified weight of 1 t to 2 t by alternatively adding a quantity of material, recording the applied mass,
suspending the certified weight and recording the applied load again.
The precision can be estimated by placing on the hopper scale a test mass of five times up to ten times a
scale’s readability or sensitivity, recording measurements with and without this test mass, and calculating the
variance for a single weighing cycle from six test results up to 12 test results. This check can be repeated after
the discharge cycle to determine whether the precision is a function of load. In terms of a coefficient of
variation the precision at gross loads generally ranges from 0,1 % up to 0,25 %.
Even though the hopper’s suspended mass in the loaded condition adds most to the variance for net wet
mass, its suspended mass in the empty condition is large enough to add to the variance for the net wet mass
measured during each weighing cycle.
4.5 Gantry scales
The wet mass of cargoes or shipments of concentrates in bulk can be determined with a gantry scale. This
mass measurement device is also zero adjusted, either manually or automatically, after each load is
discharged. The wet mass contained in a fully loaded clamshell bucket is of the same order of magnitude as
its suspended mass and support structure so that the variances for tare and gross loads both contribute to the
variance for the net wet mass of each weighing cycle.
6 © ISO 2008 – All rights reserved
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ISO 12745:2008(E)
Only a single certified weight is required on location to maintain a gantry scale in a proper state of calibration.
The precision of a gantry scale can be estimated by placing on the loaded clamshell a test mass of five times
up to ten times its readability or sensitivity, recording measurements with and without this test mass and
calculating the variance for single weighing cycles from sets of six test results up to 12 test resu
...
INTERNATIONAL ISO
STANDARD 12745
Second edition
2008-10-01
Copper, lead and zinc ores and
concentrates — Precision and bias of
mass measurement techniques
Minerais et concentrés de cuivre, de plomb et de zinc — Justesse et
erreurs systématiques des techniques de pesée
Reference number
ISO 12745:2008(E)
©
ISO 2008
---------------------- Page: 1 ----------------------
ISO 12745:2008(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
COPYRIGHT PROTECTED DOCUMENT
© ISO 2008
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 either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2008 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 12745:2008(E)
Contents Page
Foreword. iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 1
4 General remarks. 4
4.1 Draft surveys . 4
4.2 Belt scales . 5
4.3 Weighbridges . 5
4.4 Hopper scales . 6
4.5 Gantry scales . 6
4.6 Platform scales . 7
5 Certified weights. 7
6 Methods of operation . 8
6.1 General. 8
6.2 Draft surveys . 8
6.3 Belt scales . 12
6.4 Weighbridges . 14
6.5 Hopper scales . 16
6.6 Gantry scales . 18
6.7 Platform scales . 20
Annex A (informative) Tables. 22
Annex B (informative) Statistics .32
Annex C (informative) Draft surveys . 41
Annex D (informative) Procedure for the testing of static scales . 44
Bibliography . 47
© ISO 2008 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO 12745:2008(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.
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 12745 was prepared by Technical Committee ISO/TC 183, Copper, lead, zinc and nickel ores and
concentrates.
This second edition cancels and replaces the first edition (ISO 12475:1996), which has been technically
revised.
iv © ISO 2008 – All rights reserved
---------------------- Page: 4 ----------------------
INTERNATIONAL STANDARD ISO 12745:2008(E)
Copper, lead and zinc ores and concentrates — Precision and
bias of mass measurement techniques
1 Scope
This International Standard provides guidelines to test for bias over a wide range of mass measurement
techniques, to estimate the precision for each technique and to calculate the precision for wet mass when
estimated by applying one of those techniques.
The guidelines are based on the application of statistical tests to verify that a mass measurement technique is
unbiased, to estimate the variance as the most basic measure for its precision and to check the linearity of a
static scale over its working range. Calibration methods and performance tests for compliance with applicable
regulations generate test results that can be used to quantify precision and bias for each of these mass
measurement techniques and to verify linearity for static weighing devices.
The guidelines apply to mass measurement techniques used to estimate the wet mass for cargoes or
shipments of mineral concentrate as the basis for freight and insurance charges and for preliminary payments
or for final settlements between trading partners.
The application of static scales requires that at least one certified weight with a mass of no less than one (1)
tonne be either available on location or brought in for calibration purposes, and that this certified weight be
applicable to the scale in accordance with the manufacturer’s recommendations. A set of certified weights
covering the entire working range of a weighing device simplifies the process of verifying its state of calibration,
estimating its precision as a function of applied load and testing its linearity over the working range.
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 3534-1:2006, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 3534-2:2006, Statistics — Vocabulary and symbols — Part 2: Applied statistics
ISO 5725-1:1994, Accuracy (trueness and precision) of measurement methods and results — Part 1: General
principle and definitions
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
2
NOTE 1 In authoritative textbooks on applied statistics the use of the sigma squared (σ ) symbol is restricted to
2
unknown population variances for which a measurement procedure gives an estimate only. By contrast, the symbol s
applies to variances of samples, and thus to finite sets of measurements. Standard methods on sampling of bulk materials
2
often apply sigma-symbols (σ or σ) indiscriminately.
© ISO 2008 – All rights reserved 1
---------------------- Page: 5 ----------------------
ISO 12745:2008(E)
NOTE 2 Following are definitions for the most relevant concepts and terms in mass measurement technology. They
are presented to clarify the difference between this standard method, which quantifies the risk of losing and the probability
of gaining in commercial transactions, and other methods that deal with mass measurement techniques from the
perspective of regulatory agencies.
3.1
accuracy
generic term that implies closeness of agreement between an observed mass and its unknown true value
NOTE Accuracy is an abstract concept that cannot be quantified, but a lack of accuracy can be measured and
quantified in terms of a bias or systematic error.
3.2
bias
difference between the expectation of the test result and an accepted reference value
NOTE This definition is only valid if the accepted reference value is known with absolute certainty (International Units
of Mass and Length). Given that most accepted reference values are known within finite confidence limits, the difference
between the expectation of a test result and an accepted reference value is only a bias if the expectation of the test result
1)
falls outside the confidence limits of an accepted reference value.
3.3
belt scale
mass measurement device that continuously integrates and records as a cumulative mass, the load on a belt
while it passes the suspended scale section in a conveyor belt
NOTE Belt scales are continuous mass measurement devices that are calibrated by applying a load such as a
calibrated chain on the belt above the scale section (dynamic), or a certified weight suspended from the scale’s frame
(static), for a specified integration period, or by measuring with the belt scale a quantity of material whose mass is
measured with a static scale (material-run method).
3.4
bias detection limit
BDL
measure for the power or sensitivity of Student’s t-test to detect a bias or systematic error between applied
and observed loads
3.5
coefficient of variation
CV
measure for random variations in a mass measurement technique, numerically equal to the standard deviation
as a percentage of the observed mass
3.6
confidence interval
Cl
interval within which a predetermined percentage of the differences between all possible measurements and
their mean is expected to cluster
3.7
confidence range
CR
range within which a predetermined percentage of all possible measurements is expected to cluster
NOTE In science and engineering 95 % confidence intervals and ranges are most frequently used.
1) For example, the mass of the lot is generally determined once only so that the measured value is not the expectation
of the test result. In this International Standard a bias is the statistically significant difference between independent
estimates of the wet mass of the lot (loading versus discharge, static versus dynamic scales) and mass measurements
should be traceable to National Prototype Kilograms, and thus to the International Unit of Mass, through the shortest
possible calibration hierarchy.
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3.8
correlation coefficient
r
measure for the degree of association or interdependence between a set of certified weights and observed
loads
3.9
draft survey
mass measurement technique that is based on converting the difference between a vessel’s displacement
under different loads into a mass on the basis of its draft tables while taking into account the density and
temperature of water and ballast, and changes in ballast and supplies
NOTE Draft surveys are based on Archimedes’s Principle which states that a floating body displaces its own mass.
The wet mass of a cargo or shipment can be measured by converting changes in draft, trim, ballast and consumable
supplies into mass on the basis of the vessel’s draft table.
3.10
precision
generic term for the cumulative effect of random variations in a mass measurement technique
NOTE Precision is a generic qualifier, e.g. “a high degree of precision”, “the precision is poor or low” or “the precision
characteristics are excellent”, are valid statements albeit without quantitative implications.
3.11
probable bias range
PBR
limits within which a measured bias is expected to fall at predetermined probabilities, either for a type I risk
only or for type I and II risks
3.12
relative standard deviation
s
r
measure for random variations in a mass measurement technique, numerically equal to the standard deviation
divided by the observed mass
3.13
standard deviation
s
measure for random variations in a mass measurement technique, numerically equal to the square root of the
variance
3.14
static scale
mass measurement device that converts into a mass a static load on a weighbridge or on a platform, inside a
hopper or suspended from a gantry scale
NOTE Static scales are batch mass measurement devices that are calibrated either with a single certified weight or
with a set, and less frequently with a calibrated hydraulic press. Static scales may have automatic zero adjustment so that
the sum of the differences between tare and gross loads can be used to generate a cumulative mass. Dual hopper scales
allow a virtually continuous mass flow during loading and discharge operations without sacrificing the accuracy and
precision characteristics of the static scale.
3.15
Student’s t-value
t
ratio between the difference for the means for sets of applied and observed loads and the standard deviation
for the mean difference
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3.16
type I risk
α
risk of rejecting the hypothesis that the means for sets of applied and observed loads are compatible when
their mean difference is, in fact, statistically identical to zero
3.17
type II risk
β
risk of accepting the hypothesis that the means for sets of applied and observed loads are compatible when
their mean difference is, in fact, statistically different from zero
3.18
variance
2
s
measure for random variations in a mass measurement technique, numerically equal to the sum of squared
deviations from the mean for a set of measurements divided by the number of measurements in the set
minus 1 (divided by the degrees of freedom)
NOTE In textbooks on applied statistics the term “mean squared deviation from the mean” is often used in reference
to the variance.
4 General remarks
International and national handbooks on weighing devices define uncertainties in mass measurement
techniques in different ways. In some handbooks the use of the term “error” is restricted to a bias or
systematic error while others refer to “maximum permissible risks”, which appears synonymous with
“tolerances”, as a measure for random variations in a mass measurement technique.
Unless “maximum permissible errors” or “tolerances” are, by definition, equal to 95 % or 99 % confidence
intervals, neither can be converted into a variance as the most basic measure for the precision of a
measurement process. However, an unbiased estimate for the variance of the wet mass of a cargo or
shipment of mineral concentrate is required before the precision for its dry mass and the masses of contained
metals can be calculated and reported in terms of 95 % confidence intervals and ranges as a measure for the
risk that trading partners encounter.
Annex D provides information for a step-by-step procedure for the testing of static scales.
4.1 Draft surveys
The difference between a vessel’s displacements, either before and after loading or before and after
discharge, is converted into a wet mass on the basis of its draft table. Corrections are applied for changes in
ballast and consumables such as fuel, potable water and supplies. Average densities of water, in ballast tanks
and in proximity to the vessel during draft surveys, are measured and taken into account when converting a
difference between the vessel’s displacements under different load conditions into a mass.
External factors, such as wind velocity and stratified salinity, limit the precision of draft surveys. Deformation of
vessels, while in a partially loaded condition, adds another element of uncertainty that may translate into a
bias. Displacement surveys for single cargo spaces are invariably less precise than displacement surveys for
full cargoes. The highest degree of precision can be obtained when a vessel is surveyed at loading in a light
(without ballast) and completely loaded condition, or at discharge in a completely loaded and light (without
ballast) condition.
Moisture migration during the voyage would cause discrepancies between surveys at loading and discharge if
drained water were removed with the bilge pumps. In such cases the wet mass measured at discharge may
well be significantly lower than the wet mass at loading but the dry masses at loading and discharge are
expected to be compatible. Oxidation often causes a small increase in mass that is difficult to estimate due to
the highly variable degree of precision for draft surveys.
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Generally, precision estimates in terms of coefficients of variation range from a low of 0,5 % to a high of 2,5 %.
The lowest coefficients of variation were observed by comparing draft surveys at loading and discharge. If the
marine surveyor at discharge has knowledge of the vessel’s bill of lading (B/L), the draft surveys at the ports
[1]
of discharge and loading are no longer statistically independent .
Draft surveys at loading are based on consensus between an officer of the vessel, a marine surveyor
representing the shipper, and sometimes a marine surveyor representing the buyer. Under such conditions
the precision of the draft surveys at loading cannot possibly be estimated. Only in the case that two or more
qualified marine surveyors each complete their own draft surveys for the vessel, at the same time but
independently, can the precision of this mass measurement technique be estimated in an unbiased manner.
The precision for a draft survey can also be estimated if the wet mass of a cargo or shipment is measured with
a static scale with known precision characteristics, provided that it be located in close proximity to the vessel
to ensure that loss of moisture and mechanical loss do not cause a bias. Unlike linearity for static mass
measurement devices linearity for draft surveys cannot be defined in a meaningful manner due to the
differences in the deformation of vessels over a wide range of loading conditions.
Annex C provides an example of a displacement calculation for a draft survey.
4.2 Belt scales
A belt scale is a continuous (dynamic) mass measurement device that integrates the variable load on a
suspended belt section over long periods of time. Precision and bias for belt scales depend on numerous
factors not the least of which is the environment in which they operate. A belt scale can be calibrated with a
chain that is trailed on the belt over the scale’s mechanism with a static weight that is suspended from the
scale’s frame, or with a quantity of material whose wet mass is measured with a static scale. Despite its
[2]
relatively short time basis, the material-run test is the most reliable calibration procedure for dynamic scales .
A belt scale in series with a hopper scale integrated in a conveyor belt system can be calibrated, and its
precision estimated, by comparing paired wet masses (static versus dynamic). Many applications would
benefit from a pair of belt scales in series. Particles that become wedged between the conveyor’s frame and
the suspended frame of a belt scale cause discrepancies between paired measurements. Identification of
anomalous differences permits corrective action to be taken. Removal of spillage from a belt scale’s
mechanism at regular intervals reduces drift, and thus the probability of a bias occurring.
A precision of 0,4 % in terms of a coefficient of variation has been observed for advanced belt scales under
optimum conditions but under adverse conditions the coefficient of variation may well exceed 3,5 %. Reliable
and realistic estimates for the precision of belt scales under routine conditions are obtained by measuring and
monitoring variances between observed spans prior to each calibration. Frequent calibrations ensure that belt
scales will generate unbiased estimates for wet mass. The central limit theorem implies that continuous
weighing with dynamic scales gives a significantly lower precision for wet mass than batch weighing with static
scales does.
Under routine conditions the linearity of belt scales is difficult to measure. Manufacturers of load cells test the
linearity of response over 4 mA to 20 mA ranges. However, linearity under test conditions does not
necessarily ensure linear responses to applied loads under routine conditions. Nonetheless, deviations from
linearity are not likely to add more uncertainties to this mass measurement technique than other sources of
variability such as belt tension and stiffness, stickiness of wet material or wind forces.
4.3 Weighbridges
The wet mass of cargoes or shipments of mineral concentrate is often measured by weighing trucks or
wagons in empty and loaded condition at mines or ports, and in loaded and empty condition at ports or
smelters. The precision for wet mass that is measured with a static scale such as a weighbridge, is perfectly
acceptable for settlement purposes. The variance component that the measurement of wet mass contributes
to the variance for contained metal is significantly lower than those for the measurement of moisture and
[3]
metal contents .
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The suspended mass of the scale’s beam and its support structure is only a small part of gross loads. As a
result, the variance for tare loads is significantly lower than the variance for gross loads which implies that the
variance for the net wet mass of a single unit is largely determined by the variance for its gross load. After
each cycle the weighbridge is zero adjusted, either automatically or manually, to eliminate drift.
Regulatory agencies may use one or more wagons of certified weight to calibrate weighbridges. Each wagon
gives only one calibration point so that deviations from linearity are impossible to detect. By placing two
wagons on a weighbridge a set of three [3] calibration points is obtained to provide useful but limited
information on its linearity. The most effective test for linearity is based on addition or subtraction of a set of
certified weighs that covers the working range of a weighbridge. Equally effective but more time consuming is
alternately adding a single certified weight with a mass of 1 t to 2 t and a quantity of material until the
weighbridge is tested in increments of 5 t to 10 t over its working range.
Precision parameters for weighbridges can be measured and monitored by weighing in duplicate once per
shift, a truck or a wagon. After the gross weight of a randomly selected truck or wagon is measured in the
usual manner, it is removed from the weighbridge. Next, the zero is checked and adjusted if required, and
then the unit is moved on to the weighbridge and weighed again. The mean for sets of four or more absolute
differences between duplicates can be used to calculate the variance for a single test result at gross loads. In
terms of a coefficient of variation the precision for a weighbridge at gross loads generally ranges from 0,1 %
up to 0,5 %.
The precision can also be estimated by placing on the weighbridge, in addition to the gross load, a test mass
of five times up to ten times the scale’s readability or sensitivity. Measurements with and without this test
mass are recorded and the variance for gross loads calculated from a set of six data points up to 12 data
points. Such estimates tend to be marginally but not significantly lower than the precision between duplicates
that are generated by first weighing, and then removing and reweighing a loaded truck or wagon.
This procedure can be repeated without a load on the scale. A test mass is placed on the scale and its mass
recorded. Next, the test mass is removed, and the zero adjusted if required. This process is repeated no less
than six times, and the variance at near-zero loads calculated.
4.4 Hopper scales
The wet mass of cargoes or shipments can also be determined with a single hopper scale or with a pair of
parallel hopper scales. Upon completion of each discharge cycle a hopper scale is often automatically zero
adjusted so that a bias caused by build-up of wet material and dislodgement at random times is eliminated.
Otherwise, tare loads for each weighing cycle should be recorded to allow for changes in accumulated mass.
A hopper scale is calibrated by suspending from its frame a set of certified weights with a mass of 1 t to 2 t
each to cover its entire working range. It is possible but more time-consuming to calibrate a hopper scale with
a single certified weight of 1 t to 2 t by alternatively adding a quantity of material, recording the applied mass,
suspending the certified weight and recording the applied load again.
The precision can be estimated by placing on the hopper scale a test mass of five times up to ten times a
scale’s readability or sensitivity, recording measurements with and without this test mass, and calculating the
variance for a single weighing cycle from six test results up to 12 test results. This check can be repeated after
the discharge cycle to determine whether the precision is a function of load. In terms of a coefficient of
variation the precision at gross loads generally ranges from 0,1 % up to 0,25 %.
Even though the hopper’s suspended mass in the loaded condition adds most to the variance for net wet
mass, its suspended mass in the empty condition is large enough to add to the variance for the net wet mass
measured during each weighing cycle.
4.5 Gantry scales
The wet mass of cargoes or shipments of concentrates in bulk can be determined with a gantry scale. This
mass measurement device is also zero adjusted, either manually or automatically, after each load is
discharged. The wet mass contained in a fully loaded clamshell bucket is of the same order of magnitude as
its suspended mass and support structure so that the variances for tare and gross loads both contribute to the
variance for the net wet mass of each weighing cycle.
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Only a single certified weight is required on location to maintain a gantry scale in a proper state of calibration.
The precision of a gantry scale can be estimated by placing on the loaded clamshell a test mass of five times
up to ten times its readability or sensitivity, recording measurements with and without this test mass and
calculating the variance for single weighing cycles from sets of six test results up to 12 test resu
...
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