ISO 12745:1996
(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
Minerais et concentrés de cuivre, de plomb et de zinc — Justesse et erreurs systématiques des techniques de pesée
Bakrova, svinčeva in cinkova ruda ter koncentrati - Natančnost in pogrešek pri masnih merilnih tehnikah
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Standards Content (Sample)
0 IS0
IS0 12745:1996(E)
measured with a static scale such as a weighbridge, is
4.2 Belt scales
perfectly acceptable for settlement purposes. The
variance component that the measurement of wet
A belt scale is a continuous (dynamic) mass measure-
mass contributes to the variance for contained metal
ment device that integrates the variable load on a
is significantly lower than those for the measurement
suspended belt section over long periods of time.
of moisture and metal contents [3].
Precision and bias for belt scales depend on numer-
ous factors not the least of which is the environment
The suspended mass of the scale’s beam and its sup-
in which they operate. A belt scale can be calibrated
port structure is only a small part of gross loads. As a
with a chain that is trailed on the belt over the scale’s
result, the variance for tare loads is significantly lower
mechanism with a static weight that is suspended
than the variance for gross loads which implies that
from the scale’s frame, or with a quantity of material
the variance for the net wet mass of a single unit is
whose wet mass is measured with a static scale.
largely determined by the variance for its gross load.
Despite its relatively short time basis, the material-run
After each cycle the weighbridge is zero adjusted,
test is the most reliable calibration procedure for
either automatically or manually, to eliminate drift.
dynamic scales [2].
Regulatory agencies may use one or more wagons
A belt scale in series with a hopper scale integrated in
of certified weight to calibrate weighbridges. Each
a conveyor belt system can be calibrated, and its pre-
wagon gives only one calibration point so that devi-
cision estimated, by comparing paired wet masses
ations from linearity are impossible to detect. By plac-
(static versus dynamic). Many applications would
ing two wagons on a weighbridge a set of three (3)
benefit from a pair of belt scales in series. Particles
calibration points is obtained to provide useful but
that become wedged between the conveyor’s frame
limited information on its linearity. The most effective
and the suspended frame of a belt scale cause dis-
test for linearity is based on addition or subtraction of
crepancies between paired measurements. Identifi-
cation of anomalous differences permits corrective a set of certified weights that covers the working
action to be taken. Removal of spillage from a belt range of a weighbridge. Equally effective but more
scale’s mechanism at regular intervals reduces drift, time consuming is alternately adding a single certified
and thus the probability of a bias occurring. weight with a mass of 1 t-2 t and a quantity of ma-
terial until the weighbridge is tested in increments of
5 t-l 0 t over its working range.
A precision of 0,4 % in terms of a coefficient of vari-
ation has been observed for advanced belt scales
under optimum conditions but under adverse conditions Precision parameters for weighbridges can be
the coefficient of variation may well exceed 3,5 %. measured and monitored by weighing in duplicate
Reliable and realistic estimates for the precision of once per shift, a truck or a wagon. After the gross
belt scales under routine conditions are obtained by weight of a randomly selected truck or wagon is
measuring and monitoring variances between ob-
measured in the usual manner, it is removed from the
served spans prior to each calibration. Frequent cali-
weighbridge. Next, the zero is checked and adjusted if
brations ensure that belt scales will generate unbiased
required, and then the unit is moved on to the weigh-
estimates for wet mass. The central limit theorem
bridge and weighed again. The mean for sets of four
implies that continuous weighing with dynamic scales (4) or more absolute differences between duplicates
gives a significantly lower precision for wet mass than can be used to calculate the variance for a single test
batch weighing with static scales does. result at gross loads. In terms of a coefficient of vari-
ation the precision for a weighbridge at gross loads
generally ranges from 0,l % up to 0,5 %.
Under routine conditions the linearity of belt scales is
difficult to measure. Manufacturers of load cells test
the linearity of response over 4 mA-20 mA ranges.
The precision can also be estimated by placing on the
However, linearity under test conditions does not
weighbridge, in addition to the gross load, a test mass
necessarily ensure linear responses to applied loads
of five (5) times up to ten (10) times the scale’s read-
under routine conditions. Nonetheless, deviations
ability or sensitivity. Measurements with and without
from linearity are not likely to add more uncertainties
this test mass are recorded and the variance for gross
to this mass measurement technique than other
loads calculated from a set of six (6) data points up to
sources of variability such as belt tension and stiff-
twelve (12) data points. Such estimates tend to be
ness, stickiness of wet material or wind forces.
marginally but not significantly lower than the pre-
cision between duplicates that are generated by first
weighing, and then removing and reweighing a loaded
truck or wagon.
4.3 Weighbridges
This procedure can be repeated without a load on the
scale. A test mass is placed on the scale and its mass
The wet mass of cargoes or shipments of mineral
recorded. Next, the test mass is removed, and the
concentrate is often measured by weighing trucks or
zero adjusted if required. This process is repeated no
wagons in empty and loaded condition at mines or
less than six (6) times, and the variance at near-zero
ports, and in loaded and empty condition at ports
loads calculated.
or smelters. The precision for wet mass that is
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stratum in a cargo space will partial loads be encoun-
4.4 Hopper scales
tered so that neither the precision for partial loads nor
The wet mass of cargoes or shipments can also be the linearity of the gantry scale are matters of much
determined with a single hopper scale or with a pair of concern.
parallel hopper scales. Upon completion of each dis-
In terms of a coefficient of variation the precision of
charge cycle a hopper scale is often automatically zero
gantry scales at gross loads generally ranges from
adjusted so that a bias caused by build-up of wet ma-
0,15 % up to 0,4 %. The variance for the net wet
terial and dislodgement at random times is eliminated.
mass of single grabs is equal to the sum of the
Otherwise, tare loads for each weighing cycle should
variances at gross and tare loads.
be recorded to allow for changes in accumulated
mass.
A hopper scale is calibrated by suspending from its
4.6 Platform scales
frame a set of certified weights with a mass of 1 t-2 t
each to cover its entire working range. It is possible The wet mass of shipments of contained mineral con-
but more time-consuming to calibrate a hopper scale centrate can be measured by weighing bulk bags or
with a single certified weight of 1 t-2 t by alternatively other containers on a platform scale, either in the
adding a quantity of material, recording the applied empty and the loaded condition at mines, or in the
mass, suspending the certified weight and recording loaded and the empty condition at smelters. Platform
the applied load again. scales are often used to measure the wet mass of
valuable mineral concentrates so that a proper state of
The precision can be estimated by placing on the hop-
calibration is extremely important.
per scale a test mass of five (5) times up to ten (IO)
times a scale’s readability or sensitivity, recording The suspended mass of the scale’s beam and its sup-
measurements with and without this test mass, and port structure is only a small part of the suspended
mass at gross loads. As a result, the variance for the
calculating the variance for a single weighing cycle
tare mass is significantly lower than the variance for
from six (6) test results up to twelve (12) test results.
the gross mass. The variance for the net wet mass of
This check can be repeated after the discharge cycle
a container is equal to the sum of the high variance for
to determine whether the precision is a function of
load. In terms of a coefficient of variation the precision the gross mass and the low variance for the tare mass
which implies that the variance for the wet mass of a
at gross loads generally ranges from 0,l % up to
0,25 %. shipment is largely determined by the variance for the
gross mass of containers. Unless gross masses differ
Even though the hopper’s suspended mass in the
substantially from the certified weight required to cali-
loaded condition adds most to the variance for net
brate a platform scale, the linearity of this mass
wet mass, its suspended mass in the empty condition
measurement device is not a matter of concern.
is large enough to add to the variance for the net wet
mass measured during each weighing cycle. The precision of platform scales (near zero and at rated
capacity) can be estimated by placing a test mass of
five (5) times up to ten (IO) times its readability or
sensitivity on its platform, recording measurements
4.5 Gantry scales
with and without this test mass and calculating the
variance for single weighing cycles from sets of six (6)
The wet mass of cargoes or shipments of concen-
replicate test results up to twelve (12) replicate test
trates in bulk can be determined with a gantry scale.
results. In terms of a coefficient of variation the pre-
This mass measurement device is also zero adjusted,
cision for platform scales ranges from 0,05 % up to
either manually or automatically, after each load is
0,2 % at gross loads. The variance for the net wet
discharged. The wet mass contained in a fully loaded
mass is equal to the sum of the variances at gross
clamshell bucket is of the same order of magnitude as
and tare loads.
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.
5 Certified weights
Only a single certified weight is required on location to
maintain a gantry scale in a proper state of calibration.
The traceability of certified weights to the Inter-
The precision of a gantry scale can be estimated by
national Unit of Mass through National Prototype Kilo-
placing on the loaded clamshell a test mass of five (5)
grams and a hierarchy of verifiable calibrations is of
times up to ten (10) times its readability or sensitivity,
critical importance. The integrity of certified weights
recording measurements with and without this test
can be ensured by storing them in a clean and dry
mass and calculating the variance for single weighing
environment, preferably on platforms or pallets, by
cycles from sets of six (6) test results up to twelve
covering them with tarpaulins to avoid corrosion and
(12) test results. It is possible to estimate the pre-
accumulation of dirt and by handling them carefully to
cision of a gantry scale with partially loaded clam-
avoid mechanical damage.
shells. However, only during removal of the lowest
5
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Based on how a traceable mass is compared with a invariably based on a draft survey at the port of loading,
draft survey or a measurement with a belt scale, or should not be disclosed to the marine surveyor at dis-
how a certified weight is compared with test results charge until the draft survey is completed. Otherwise,
for a static mass measurement device, calibration the precision between draft surveys at loading and dis-
methods can be divided into four (4) categories, charge cannot be estimated in an unbiased manner.
namely:
- a single certified weight of appropriate mass;
6.21 Draft surveys at loading and discharge
- a set of certified weights to cover a typical work-
rng range;
An example of draft surveys at loading and discharge
- a single, but preferably two (2) wagons of certi-
can be found in table A.1 of annex A. Table A.1 lists a
fied weight;
set of ten (IO) paired wet masses that are determined
by draft surveys at loading and discharge. Each ship-
- a mass traceable to a properly calibrated static
ment was loaded into a single cargo space so that
scale.
these results are typical for draft surveys of partially
ioaded vessels. Table 1 lists the statistical parameters
Weighbridges (including in-motion and coupled-in-
for this paired data set.
motion weighing devices) can also be calibrated with
hydraulic pressure gauges. The use of a hydraulic
pressure gauge adds to the calibration hierarchy a link
that is based on a completely different technology.
Table 1 - Precision and bias between draft
surveys
Parameter Symbol Value
6 Methods of operation
Mean - load (t) 4111,z
a)
Mean - discharge (t)
33 4 106,9
Mean difference (t) AX
6.1 General - 4,3
Mean difference (%) AX
- 0,l
Precision and bias for mass measurement devices
Variance of differences (t*) s*( Ax) I 410,92
and techniques can be estimated and monitored as
a function of time. Calibration data for static and
Coefficient of Variation (%) cv 0,91
dynamic scales not only generate information on
Student’s t-value t 0,361
bias but also reliable precision estimates for mass
measurements. Calibrations require more time than
Bias Detection Limits:
simple precision checks with a test mass, therefore a
Type I risk only (%) BDL(I) ?I 0,7
case can be made that precision checks be carried out
Type I & II risks (%) BDL(I&II) &I,2
at regular intervals, and that precision be monitored on
control charts. Sudden changes in precision may be
indicative of mechanical failures or malfunctioning
electronics, and require testing for conformance with
The variance of differences of 1 410,92 t* is the most
the manufacturer’s specifications.
basic measure for the precision between draft sur-
veys at loading and discharge while the coefficient of
Testing for bias, estimating precision and checking
variation of 0,91 % is a more transparent measure for
linearity are based on applied statistics, and in particu-
precision. The question is whether this estimate for
lar on Student’s t-test, Fisher’s F-test (analysis of
the precision between draft surveys is unbiased, and
variance) and correlation-regression analysis.
thus whether draft surveys at loading and discharge
are statistically independent.
Annex B reviews tests and formulae required to calcu-
late relevant para meters.
If the marine surveyor at the port of discharge were to
have prior knowledge of the vessel’s bill of lading, the
draft survey at discharge would no longer be
statistically independent which implies that the coef-
6.2 Draft surveys
ficient of variation of 0,91 % is not expected to be an
Precision and bias of draft surveys can be estimated
unbiased estimate for the precision between draft
and monitored by comparing wet masses that are de-
surveys at loading and discharge. Therefore, the ves-
termined at loading and discharge, by comparing wet
sel’s bill of lading should be kept confidential until
masses determined by draft survey (either at loading
the draft survey at discharge is completed to ensure
or at discharge) or with a properly calibrated static
that the wet mass measured at the port of discharge
weighing device in close proximity to the port of loading is also an unbiased estimate for the unknown true
or discharge. The vessel’s bill of lading, which is almost mass.
6
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Table 2 - Precision for wet mass by draft survey
If the draft surveys at loading and discharge were
equally precise, the variance for a single draft survey
would be:
Parameter Symbol 1 Value
Mean (t) 4109
1 410,92
M,
= 705,46 t*
Variance (P) 705,46
2 s*(M,,,)
Standard deviation (t) 26,56
&K,,,)
for standard deviation of:
Coefficient of Variation (%) cv 0,65
= 26,56 t 95 % Confidence Interval (t) 1) 95 % Cl + 60,l
,/705,46
95 % Cl + 1,5
95 % Confidence Interval (%)
and a coefficient of variation of:
95 % Confidence Range:
26,56 x 100 95 % CRL 4049
lower limit (t)
= 0,65%
95 % CRU 4169
[(4 Ill,2 + 4 106,9) /2] upper limit (t)
1) Based on to,g5;g x s(M,,J.
I I
Means of 4 Ill,2 t and 4 106,2 t are used to calculate
the coefficient of variation. In this case the means are
statistically identical but the mean of statistically dif-
If the long-term coefficient of variation were 0,8 %,
ferent means can still be used to calculate the coeffi-
the 95 % confidence interval for a wet mass of
cient of variation. However, numerically it is not the
4 109 t would be:
most reliable precision estimate.
Because such a large set of variables interact in this
1,96x4109x0,8=+644t
-
I
mass measurement technique, the probability that
100
displacement surveys at loading and discharge are
equally precise is remote. In 6.2.2 evidence will be
for a 95 % confidence range from 4 109 - 64,4 =
presented to show that this variance of differences of
4 045 t up to 4 109 + 64,4 = 4 173 t. The z-value of
1 410,92 t* is not an unbiased estimated for the pre-
I,96 from the normal or Gaussian distribution is often
cision between draft surveys at loading and at dis-
rounded to 2 which would change the 95 % confi-
charge.
dence interval from + 64 t to + 66 t, a difference that
is well within the precision of this mass measurement
The calculated t-value of 0,361 for a mean differ-
technique.
ence of 4,3 t does not exceed the tabulated value of
= 2,262 which implies that means of 4 11 I,2 t
t0,95;9 The precision estimates in table 2 are only valid if the
at loading and 4 106,9 t at discharge are statistically
variance of differences is unbiased, and if the draft
identical. Hence, each draft survey appears to gen-
surveys at loading and discharge are equally precise.
erate an unbiased estimate for the unknown true wet
The question whether the draft surveys at loading and
mass of the shipment in question. The probability of
discharge are indeed equally precise could be solved
this t-value of 0,361 being caused by random vari-
by estimating the precision at loading and at discharge
ations falls between 20 % and 30 % so that the
from statistically independent draft surveys. In other
closeness of agreement is not suspect.
words, were two (2) or more marine surveyors to
measure independently a vessel’s draft in the light
Bias Detection Limits of + 0,7 % or zfr 27 t for the
and loaded condition a set of no less than four (4)
Type I risk only, and + I,2 % or + 49 t for Type I and II
duplicate or replicate draft surveys, on similar vessels
risks, are different measures for the sensitivity or
and under comparable conditions, would be required
power of Student’s t-test to detect a bias. Bias Detec-
to estimate the precision of draft surveys at a particu-
tion Limits are also measures for symmetrical risks of
lar port.
losing and probabilities of gaining if the settlements
between trading partners were based on measuring
The question whether a variance of differences is an
the wet mass of shipments by draft surveys.
unbiased estimate for the precision between draft
surveys at loading and discharge can be solved by
Based on a standard deviation of 26,56 t* for a
comparing the results of draft surveys with wet
single displacement survey and a tabulated t-value of:
masses measured with a static scale. In draft surveys
to 95.9 = 2,262, the 95 % Confidence Interval (95 % Cl)
at discharge are compared with wet masses
for a cargo or shipment with a wet mass of 4 109 t is:
estimated with a weighbridge at discharge.
2,262 x 26,56 = + 60 t
6.2.2 Draft survey versus weig hbridge
for a 95 % Confidence Range (95 % CR) from 4 109 -
A comparison of wet masses by draft surveys and
60=4049tupto4109+60=4169t.Table2lists
with a weighbridge can be found in table A.2 of an-
precision estimates based on the mean of means of
nex A. Table A.2 lists a set of ten (10) pairs of wet
4 109 t and a variance of 705,46 t*.
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masses for the same shipments that were also re- Thus it would appear that knowledge of the vessel’s
ported in table A.1 . In this case wet masses that were bill of lading before the draft survey at discharge is
completed, results in statistical dependencies be-
measured by draft surveys at the port of discharge are
compared with wet masses that were measured with tween draft surveys at loading and discharge. There-
a weighbridge for trucks at the smelter. fore, the coefficient of variation of 0’91 % is a biased
estimate for the precision between draft surveys and
The set of paired mass measurements is tested for
the coefficient of variation of 2,8 % is a better estimate
bias by calculating the t-value for the mean difference,
for the precision of single draft surveys for partially
the variance of differences and the number of paired
loaded vessels.
data in the set. In this example the variance of differ-
ences and the number of paired data in the set. In this
The weighbridge’s precision is expected to add sig-
example the variance of differences is a measure for
nificantly less than
the precision between mass measurement tech-
niques with vastly different precision characteristics.
1 410,92
Under such conditions the variance of differences is
= 705,46 t*
2
virtually identical to the variance for the least precise
mass measurement technique (draft surveys at dis-
to the variance of differences of 13 243 t* so that a
charge).
variance of 13 243 - 705,46 = 12 500 t* would be
Table 3 lists the most relevant statistics for this set. a better estimate for the precision of a single draft
survey than the variance of 705,46 t? In terms of a
coefficient of variation the precision for draft surveys
Precision and bias between different
Table 3 -
for a single cargo space would then be
techniques
12500 x100
Parameter 1 Symbol 1 Value J
= 2,7 %
[(4 106,9 + 4 134,3) / 21
4 106,9
Mean - draft survey (t) WI
4 134,3
Mean - weighbridge (t) WV
A calculated t-value of 0,753 for a mean difference
AX -I- 27,4
Mean difference (t) of 27,4 t does not exceed the tabulated value of
= 2,262 which implies that means of 4 106,9 t
AX + 0,7 t0,95;9
Mean difference (%)
at loading and 4 134,3 t at discharge are statistically
Variance of differences (t*) s*( Ax) 13243
identical. Hence, the draft survey at discharge and
the weighbridge at discharge apparently generate un-
Coefficient of Variation (%) cv
218
biased estimates for the unknown true wet mass
Student’s t-value t 0,753
of each shipment. Nonetheless, the precision of a
static scale such as a weighbridge installs a signifi-
Bias Detection Limits:
cantly higher degree of confidence in a cumulative
Type I risk only (%) BDL(I) + 2,0
wet mass of 4 134,4 t than the precision of draft sur-
Type I & II risks (%) BDL(I&II) + 3,6
veys does.
Bias Detection Limits of & 2,0 % or + 82 t for the
The coefficient of variation of 2,8 % is a measure for
Type I risk only, and + 3,6 % or + 149 t for Type I and
the precision between draft surveys at discharge and
Type II risks, are measures of the power or sensitivity
wet masses determined with a weighbridge at the
of this test to detect a bias. Generally, Bias Detection
smelter. In 6.2.1 the precision between draft surveys
Limits are also estimates for the risk of one trading
at loading and discharge in terms of a coefficient of
partner to losing, and an identical probability of the
variation came out at 0,91 %. The question whether
other trading partner to gaining. In this case, however,
coefficients of variation of 2,8 % and 0,91 % are
the settlements were based on wet masses deter-
compatible can be solved by comparing the calculated
mined with the weighbridge so that the risk was
F-ratio of
much less than BDLs of + 2,0 % and + 3,6 % imply.
13243 =g3g Precision estimates for the wet mass of a single cargo
1 410,92 ' space or a complete cargo, and for the cumulative
mass of a set, are calculated in the same manner. For
(the variance between draft surveys at discharge and
example, a variance of 12 500 t* and a single wet
wet masses measured with a weighbridge at a mass of 4 107 t for draft surveys at discharge are
smelter, divided by the variance between draft sur- equivalent to a 95 % confidence interval of:
veys at loading and discharge) with tabulated values of
= 5,35. The calculated
= 3,18 and Fo,sg;g;s
Fo,95;9;9
2x,/12500 =f224t
value of 9,39 exceeds tabulated values at the 95 %
and 99 % probability levels. Hence, the probability that
224 = 3 883 t
coefficients of variation of 2,8 % and 0,91 % are sta- for a 95 % confidence range from 4 107 -
tistically identical is much less than 1 %. up to 4 107 + 224 = 4 331 t.
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@ IS0 IS0 12745:1996(E)
the basic statistical parameters for each moving data
Table 4 lists precision estimates that are based on a
base.
single wet mass of 4 107 t, a cumulative wet mass of
41 343 t, a variance of 12 500 t* for the single wet
Coefficients of variation of 0’39 % and 0’1 1 % are
mass, and the sum of variances of 125 000 t* for the
both measures for the precision of this belt scale.
cumulative wet mass.
However, the calculated F-ratio of
The coefficient of variation of 2’7 %, when divided by
0’1976
fi, becomes:
- = 13,00
0,015 2
2’7
- = 0’9 %
between the variances before and after calibration ex-
3’16
ceeds the tabulated values of FO 95.11.11 = 2,82 and
= 4’64 which implies that these variances
p;b,99;1 I;1 1
This relationship is based on the Central Limit Theo-
differ significantly. The long-term variance of 0,197 6
rem, an important theorem in mathematical probability
between chain spans prior to calibration more truly re-
and applied statistics.
flects the magnitude of random variations in mass
measurement with this belt scale as a function of
time. Therefore, the coefficient of variation of 0’39 %
is the more reliable estimate for its precision under
routine conditions.
6.3 Belt scales
The question whether the belt scale generates un-
An example of how to calculate the precision of wet
biased estimates for wet mass can be solved by ap-
masses measured with belt scales can be found in
plying Student’s t-test to the difference between the
table A.3 of annex A. This table lists a set of twelve
required span (115,25 for this belt scale), and the
(12) chain spans, recorded at weekly intervals prior to
mean of observed spans for a set that constitutes a
calibration, and a similar set of spans that were ob-
tained immediately following its calibration. Table 5 lists moving data base. Table 6 lists the results of this test.
- Precision for wet mass by draft survey
Table 4
Parameter Symbol Single Cumulative
41 343
WV 4107
Mean (t)
125000
s*@%,,,) 12500
Variance (t*)
Standard deviation (t) s&C,,,) Ill,8 353,6
Coefficient of Variation (%) cv 2,7
0'9
95 % Cl +224 +707
95 % Confidence Interval (t) 1)
&I,7
(%) 95 % Cl + 5,4
95 % Confidence Interval
95 % Confidence Range:
3883 40636
lower limit (t) 95 % CRL
42050
(t) 95 % CRU 4331
upper limit
1) Based onz0,g5xs(M,),orz0,g5xs
&J.
Precision of a belt scale
Table 5 -
Symbol Before After
Parameter
x 115,12 115,36
Mean (scale units) I I I I
0,197 6 0,015 2
Variance (scale units) 2 s* (4
s(x) 0,444 6 0,123 4
Standard deviation (scale units)
cv 0,39 0,ll
Coefficient of Variation (%)
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IS0 12745:1996(E) @ IS0
Table 7 - Precision for wet mass with a belt scale
Table 6 - Testing a belt scale for bias
Parameter 1 Symbol 1 Value Parameter 1 Symbol 1 Value
Mean - required span 115,25 Mean (t) 25000
x(R)
ww
Mean - observed span 115,12 Coefficient of Variation (%) CV
30) 0,39
Mean difference (span units) AX - 0,13 Standard deviation (t)
d4,J 97,5
Student’s t-value t 1,013 95 % Confidence Interval (t) 95 % Cl +195
Significance ns 1) 95 % Confidence Interval (%) 95 % Cl + 0,8
- I
95 % Confidence Range:
Bias Detection Limits:
lower limit (t) 95 % CRL 24805
Type I risk only (span units) BDL(I) rfI 0,28
upper limit (t) 95 % CRU 25195
Type I & II risks (span units) BDL(I&I I) + 0,51
1) ns = not significant.
6.4 Weighbridges
The difference of - 0,13 scale units between the re-
quired span of 11525 and the mean of 115,lZ for all
Table A.4 of annex A presents an example of how to
test data, results in a calculated t-value of 1,013 which
check the state of calibration for a weighbridge and
is below the tabulated value of t0,95;11 = 2,201 so that
how to estimate its precision. Table A.4 lists a set of
the belt scale is in a proper state of calibration. Bias
paired test data for a weighbridge that was calibrated
Detection Limits of + 028 for the Type I risk, and
with a pair of wagons with certified weights of
+ 0,51 for Type I and II risks, indicate that a mean dif-
31 890 kg and 70 810 kg respectively. Two (2) subsets
ference of 0,13 span units is most probably due to
of four (4) test data were generated by determining
random variations.
the mass of each wagon while the third subset was
obtained by weighing both wagons simultaneously.
A belt scale need not be adjusted if the difference be-
tween the required span and the moving average of
Table 8 summarizes the most important statistical
the running data base does not exceed the Bias De-
parameters for this set of calibration da
...
SLOVENSKI STANDARD
SIST ISO 12745:1998
01-november-1998
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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
Ta slovenski standard je istoveten z: ISO 12745:1996
ICS:
73.060.99 Druge rude Other metalliferous minerals
SIST ISO 12745:1998 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO 12745:1998
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SIST ISO 12745:1998
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SIST ISO 12745:1998
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SIST ISO 12745:1998
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SIST ISO 12745:1998
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SIST ISO 12745:1998
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SIST ISO 12745:1998
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SIST ISO 12745:1998
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SIST ISO 12745:1998
0 IS0
IS0 12745:1996(E)
measured with a static scale such as a weighbridge, is
4.2 Belt scales
perfectly acceptable for settlement purposes. The
variance component that the measurement of wet
A belt scale is a continuous (dynamic) mass measure-
mass contributes to the variance for contained metal
ment device that integrates the variable load on a
is significantly lower than those for the measurement
suspended belt section over long periods of time.
of moisture and metal contents [3].
Precision and bias for belt scales depend on numer-
ous factors not the least of which is the environment
The suspended mass of the scale’s beam and its sup-
in which they operate. A belt scale can be calibrated
port structure is only a small part of gross loads. As a
with a chain that is trailed on the belt over the scale’s
result, the variance for tare loads is significantly lower
mechanism with a static weight that is suspended
than the variance for gross loads which implies that
from the scale’s frame, or with a quantity of material
the variance for the net wet mass of a single unit is
whose wet mass is measured with a static scale.
largely determined by the variance for its gross load.
Despite its relatively short time basis, the material-run
After each cycle the weighbridge is zero adjusted,
test is the most reliable calibration procedure for
either automatically or manually, to eliminate drift.
dynamic scales [2].
Regulatory agencies may use one or more wagons
A belt scale in series with a hopper scale integrated in
of certified weight to calibrate weighbridges. Each
a conveyor belt system can be calibrated, and its pre-
wagon gives only one calibration point so that devi-
cision estimated, by comparing paired wet masses
ations from linearity are impossible to detect. By plac-
(static versus dynamic). Many applications would
ing two wagons on a weighbridge a set of three (3)
benefit from a pair of belt scales in series. Particles
calibration points is obtained to provide useful but
that become wedged between the conveyor’s frame
limited information on its linearity. The most effective
and the suspended frame of a belt scale cause dis-
test for linearity is based on addition or subtraction of
crepancies between paired measurements. Identifi-
cation of anomalous differences permits corrective a set of certified weights that covers the working
action to be taken. Removal of spillage from a belt range of a weighbridge. Equally effective but more
scale’s mechanism at regular intervals reduces drift, time consuming is alternately adding a single certified
and thus the probability of a bias occurring. weight with a mass of 1 t-2 t and a quantity of ma-
terial until the weighbridge is tested in increments of
5 t-l 0 t over its working range.
A precision of 0,4 % in terms of a coefficient of vari-
ation has been observed for advanced belt scales
under optimum conditions but under adverse conditions Precision parameters for weighbridges can be
the coefficient of variation may well exceed 3,5 %. measured and monitored by weighing in duplicate
Reliable and realistic estimates for the precision of once per shift, a truck or a wagon. After the gross
belt scales under routine conditions are obtained by weight of a randomly selected truck or wagon is
measuring and monitoring variances between ob-
measured in the usual manner, it is removed from the
served spans prior to each calibration. Frequent cali-
weighbridge. Next, the zero is checked and adjusted if
brations ensure that belt scales will generate unbiased
required, and then the unit is moved on to the weigh-
estimates for wet mass. The central limit theorem
bridge and weighed again. The mean for sets of four
implies that continuous weighing with dynamic scales (4) or more absolute differences between duplicates
gives a significantly lower precision for wet mass than can be used to calculate the variance for a single test
batch weighing with static scales does. result at gross loads. In terms of a coefficient of vari-
ation the precision for a weighbridge at gross loads
generally ranges from 0,l % up to 0,5 %.
Under routine conditions the linearity of belt scales is
difficult to measure. Manufacturers of load cells test
the linearity of response over 4 mA-20 mA ranges.
The precision can also be estimated by placing on the
However, linearity under test conditions does not
weighbridge, in addition to the gross load, a test mass
necessarily ensure linear responses to applied loads
of five (5) times up to ten (10) times the scale’s read-
under routine conditions. Nonetheless, deviations
ability or sensitivity. Measurements with and without
from linearity are not likely to add more uncertainties
this test mass are recorded and the variance for gross
to this mass measurement technique than other
loads calculated from a set of six (6) data points up to
sources of variability such as belt tension and stiff-
twelve (12) data points. Such estimates tend to be
ness, stickiness of wet material or wind forces.
marginally but not significantly lower than the pre-
cision between duplicates that are generated by first
weighing, and then removing and reweighing a loaded
truck or wagon.
4.3 Weighbridges
This procedure can be repeated without a load on the
scale. A test mass is placed on the scale and its mass
The wet mass of cargoes or shipments of mineral
recorded. Next, the test mass is removed, and the
concentrate is often measured by weighing trucks or
zero adjusted if required. This process is repeated no
wagons in empty and loaded condition at mines or
less than six (6) times, and the variance at near-zero
ports, and in loaded and empty condition at ports
loads calculated.
or smelters. The precision for wet mass that is
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SIST ISO 12745:1998
@ IS0
IS0 12745:1996(E)
stratum in a cargo space will partial loads be encoun-
4.4 Hopper scales
tered so that neither the precision for partial loads nor
The wet mass of cargoes or shipments can also be the linearity of the gantry scale are matters of much
determined with a single hopper scale or with a pair of concern.
parallel hopper scales. Upon completion of each dis-
In terms of a coefficient of variation the precision of
charge cycle a hopper scale is often automatically zero
gantry scales at gross loads generally ranges from
adjusted so that a bias caused by build-up of wet ma-
0,15 % up to 0,4 %. The variance for the net wet
terial and dislodgement at random times is eliminated.
mass of single grabs is equal to the sum of the
Otherwise, tare loads for each weighing cycle should
variances at gross and tare loads.
be recorded to allow for changes in accumulated
mass.
A hopper scale is calibrated by suspending from its
4.6 Platform scales
frame a set of certified weights with a mass of 1 t-2 t
each to cover its entire working range. It is possible The wet mass of shipments of contained mineral con-
but more time-consuming to calibrate a hopper scale centrate can be measured by weighing bulk bags or
with a single certified weight of 1 t-2 t by alternatively other containers on a platform scale, either in the
adding a quantity of material, recording the applied empty and the loaded condition at mines, or in the
mass, suspending the certified weight and recording loaded and the empty condition at smelters. Platform
the applied load again. scales are often used to measure the wet mass of
valuable mineral concentrates so that a proper state of
The precision can be estimated by placing on the hop-
calibration is extremely important.
per scale a test mass of five (5) times up to ten (IO)
times a scale’s readability or sensitivity, recording The suspended mass of the scale’s beam and its sup-
measurements with and without this test mass, and port structure is only a small part of the suspended
mass at gross loads. As a result, the variance for the
calculating the variance for a single weighing cycle
tare mass is significantly lower than the variance for
from six (6) test results up to twelve (12) test results.
the gross mass. The variance for the net wet mass of
This check can be repeated after the discharge cycle
a container is equal to the sum of the high variance for
to determine whether the precision is a function of
load. In terms of a coefficient of variation the precision the gross mass and the low variance for the tare mass
which implies that the variance for the wet mass of a
at gross loads generally ranges from 0,l % up to
0,25 %. shipment is largely determined by the variance for the
gross mass of containers. Unless gross masses differ
Even though the hopper’s suspended mass in the
substantially from the certified weight required to cali-
loaded condition adds most to the variance for net
brate a platform scale, the linearity of this mass
wet mass, its suspended mass in the empty condition
measurement device is not a matter of concern.
is large enough to add to the variance for the net wet
mass measured during each weighing cycle. The precision of platform scales (near zero and at rated
capacity) can be estimated by placing a test mass of
five (5) times up to ten (IO) times its readability or
sensitivity on its platform, recording measurements
4.5 Gantry scales
with and without this test mass and calculating the
variance for single weighing cycles from sets of six (6)
The wet mass of cargoes or shipments of concen-
replicate test results up to twelve (12) replicate test
trates in bulk can be determined with a gantry scale.
results. In terms of a coefficient of variation the pre-
This mass measurement device is also zero adjusted,
cision for platform scales ranges from 0,05 % up to
either manually or automatically, after each load is
0,2 % at gross loads. The variance for the net wet
discharged. The wet mass contained in a fully loaded
mass is equal to the sum of the variances at gross
clamshell bucket is of the same order of magnitude as
and tare loads.
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.
5 Certified weights
Only a single certified weight is required on location to
maintain a gantry scale in a proper state of calibration.
The traceability of certified weights to the Inter-
The precision of a gantry scale can be estimated by
national Unit of Mass through National Prototype Kilo-
placing on the loaded clamshell a test mass of five (5)
grams and a hierarchy of verifiable calibrations is of
times up to ten (10) times its readability or sensitivity,
critical importance. The integrity of certified weights
recording measurements with and without this test
can be ensured by storing them in a clean and dry
mass and calculating the variance for single weighing
environment, preferably on platforms or pallets, by
cycles from sets of six (6) test results up to twelve
covering them with tarpaulins to avoid corrosion and
(12) test results. It is possible to estimate the pre-
accumulation of dirt and by handling them carefully to
cision of a gantry scale with partially loaded clam-
avoid mechanical damage.
shells. However, only during removal of the lowest
5
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SIST ISO 12745:1998
IS0 12745:1996(E) @ IS0
Based on how a traceable mass is compared with a invariably based on a draft survey at the port of loading,
draft survey or a measurement with a belt scale, or should not be disclosed to the marine surveyor at dis-
how a certified weight is compared with test results charge until the draft survey is completed. Otherwise,
for a static mass measurement device, calibration the precision between draft surveys at loading and dis-
methods can be divided into four (4) categories, charge cannot be estimated in an unbiased manner.
namely:
- a single certified weight of appropriate mass;
6.21 Draft surveys at loading and discharge
- a set of certified weights to cover a typical work-
rng range;
An example of draft surveys at loading and discharge
- a single, but preferably two (2) wagons of certi-
can be found in table A.1 of annex A. Table A.1 lists a
fied weight;
set of ten (IO) paired wet masses that are determined
by draft surveys at loading and discharge. Each ship-
- a mass traceable to a properly calibrated static
ment was loaded into a single cargo space so that
scale.
these results are typical for draft surveys of partially
ioaded vessels. Table 1 lists the statistical parameters
Weighbridges (including in-motion and coupled-in-
for this paired data set.
motion weighing devices) can also be calibrated with
hydraulic pressure gauges. The use of a hydraulic
pressure gauge adds to the calibration hierarchy a link
that is based on a completely different technology.
Table 1 - Precision and bias between draft
surveys
Parameter Symbol Value
6 Methods of operation
Mean - load (t) 4111,z
a)
Mean - discharge (t)
33 4 106,9
Mean difference (t) AX
6.1 General - 4,3
Mean difference (%) AX
- 0,l
Precision and bias for mass measurement devices
Variance of differences (t*) s*( Ax) I 410,92
and techniques can be estimated and monitored as
a function of time. Calibration data for static and
Coefficient of Variation (%) cv 0,91
dynamic scales not only generate information on
Student’s t-value t 0,361
bias but also reliable precision estimates for mass
measurements. Calibrations require more time than
Bias Detection Limits:
simple precision checks with a test mass, therefore a
Type I risk only (%) BDL(I) ?I 0,7
case can be made that precision checks be carried out
Type I & II risks (%) BDL(I&II) &I,2
at regular intervals, and that precision be monitored on
control charts. Sudden changes in precision may be
indicative of mechanical failures or malfunctioning
electronics, and require testing for conformance with
The variance of differences of 1 410,92 t* is the most
the manufacturer’s specifications.
basic measure for the precision between draft sur-
veys at loading and discharge while the coefficient of
Testing for bias, estimating precision and checking
variation of 0,91 % is a more transparent measure for
linearity are based on applied statistics, and in particu-
precision. The question is whether this estimate for
lar on Student’s t-test, Fisher’s F-test (analysis of
the precision between draft surveys is unbiased, and
variance) and correlation-regression analysis.
thus whether draft surveys at loading and discharge
are statistically independent.
Annex B reviews tests and formulae required to calcu-
late relevant para meters.
If the marine surveyor at the port of discharge were to
have prior knowledge of the vessel’s bill of lading, the
draft survey at discharge would no longer be
statistically independent which implies that the coef-
6.2 Draft surveys
ficient of variation of 0,91 % is not expected to be an
Precision and bias of draft surveys can be estimated
unbiased estimate for the precision between draft
and monitored by comparing wet masses that are de-
surveys at loading and discharge. Therefore, the ves-
termined at loading and discharge, by comparing wet
sel’s bill of lading should be kept confidential until
masses determined by draft survey (either at loading
the draft survey at discharge is completed to ensure
or at discharge) or with a properly calibrated static
that the wet mass measured at the port of discharge
weighing device in close proximity to the port of loading is also an unbiased estimate for the unknown true
or discharge. The vessel’s bill of lading, which is almost mass.
6
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SIST ISO 12745:1998
@ IS0 IS0 12745:1996(E)
Table 2 - Precision for wet mass by draft survey
If the draft surveys at loading and discharge were
equally precise, the variance for a single draft survey
would be:
Parameter Symbol 1 Value
Mean (t) 4109
1 410,92
M,
= 705,46 t*
Variance (P) 705,46
2 s*(M,,,)
Standard deviation (t) 26,56
&K,,,)
for standard deviation of:
Coefficient of Variation (%) cv 0,65
= 26,56 t 95 % Confidence Interval (t) 1) 95 % Cl + 60,l
,/705,46
95 % Cl + 1,5
95 % Confidence Interval (%)
and a coefficient of variation of:
95 % Confidence Range:
26,56 x 100 95 % CRL 4049
lower limit (t)
= 0,65%
95 % CRU 4169
[(4 Ill,2 + 4 106,9) /2] upper limit (t)
1) Based on to,g5;g x s(M,,J.
I I
Means of 4 Ill,2 t and 4 106,2 t are used to calculate
the coefficient of variation. In this case the means are
statistically identical but the mean of statistically dif-
If the long-term coefficient of variation were 0,8 %,
ferent means can still be used to calculate the coeffi-
the 95 % confidence interval for a wet mass of
cient of variation. However, numerically it is not the
4 109 t would be:
most reliable precision estimate.
Because such a large set of variables interact in this
1,96x4109x0,8=+644t
-
I
mass measurement technique, the probability that
100
displacement surveys at loading and discharge are
equally precise is remote. In 6.2.2 evidence will be
for a 95 % confidence range from 4 109 - 64,4 =
presented to show that this variance of differences of
4 045 t up to 4 109 + 64,4 = 4 173 t. The z-value of
1 410,92 t* is not an unbiased estimated for the pre-
I,96 from the normal or Gaussian distribution is often
cision between draft surveys at loading and at dis-
rounded to 2 which would change the 95 % confi-
charge.
dence interval from + 64 t to + 66 t, a difference that
is well within the precision of this mass measurement
The calculated t-value of 0,361 for a mean differ-
technique.
ence of 4,3 t does not exceed the tabulated value of
= 2,262 which implies that means of 4 11 I,2 t
t0,95;9 The precision estimates in table 2 are only valid if the
at loading and 4 106,9 t at discharge are statistically
variance of differences is unbiased, and if the draft
identical. Hence, each draft survey appears to gen-
surveys at loading and discharge are equally precise.
erate an unbiased estimate for the unknown true wet
The question whether the draft surveys at loading and
mass of the shipment in question. The probability of
discharge are indeed equally precise could be solved
this t-value of 0,361 being caused by random vari-
by estimating the precision at loading and at discharge
ations falls between 20 % and 30 % so that the
from statistically independent draft surveys. In other
closeness of agreement is not suspect.
words, were two (2) or more marine surveyors to
measure independently a vessel’s draft in the light
Bias Detection Limits of + 0,7 % or zfr 27 t for the
and loaded condition a set of no less than four (4)
Type I risk only, and + I,2 % or + 49 t for Type I and II
duplicate or replicate draft surveys, on similar vessels
risks, are different measures for the sensitivity or
and under comparable conditions, would be required
power of Student’s t-test to detect a bias. Bias Detec-
to estimate the precision of draft surveys at a particu-
tion Limits are also measures for symmetrical risks of
lar port.
losing and probabilities of gaining if the settlements
between trading partners were based on measuring
The question whether a variance of differences is an
the wet mass of shipments by draft surveys.
unbiased estimate for the precision between draft
surveys at loading and discharge can be solved by
Based on a standard deviation of 26,56 t* for a
comparing the results of draft surveys with wet
single displacement survey and a tabulated t-value of:
masses measured with a static scale. In draft surveys
to 95.9 = 2,262, the 95 % Confidence Interval (95 % Cl)
at discharge are compared with wet masses
for a cargo or shipment with a wet mass of 4 109 t is:
estimated with a weighbridge at discharge.
2,262 x 26,56 = + 60 t
6.2.2 Draft survey versus weig hbridge
for a 95 % Confidence Range (95 % CR) from 4 109 -
A comparison of wet masses by draft surveys and
60=4049tupto4109+60=4169t.Table2lists
with a weighbridge can be found in table A.2 of an-
precision estimates based on the mean of means of
nex A. Table A.2 lists a set of ten (10) pairs of wet
4 109 t and a variance of 705,46 t*.
7
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SIST ISO 12745:1998
0 IS0
IS0 12745:1996(E)
masses for the same shipments that were also re- Thus it would appear that knowledge of the vessel’s
ported in table A.1 . In this case wet masses that were bill of lading before the draft survey at discharge is
completed, results in statistical dependencies be-
measured by draft surveys at the port of discharge are
compared with wet masses that were measured with tween draft surveys at loading and discharge. There-
a weighbridge for trucks at the smelter. fore, the coefficient of variation of 0’91 % is a biased
estimate for the precision between draft surveys and
The set of paired mass measurements is tested for
the coefficient of variation of 2,8 % is a better estimate
bias by calculating the t-value for the mean difference,
for the precision of single draft surveys for partially
the variance of differences and the number of paired
loaded vessels.
data in the set. In this example the variance of differ-
ences and the number of paired data in the set. In this
The weighbridge’s precision is expected to add sig-
example the variance of differences is a measure for
nificantly less than
the precision between mass measurement tech-
niques with vastly different precision characteristics.
1 410,92
Under such conditions the variance of differences is
= 705,46 t*
2
virtually identical to the variance for the least precise
mass measurement technique (draft surveys at dis-
to the variance of differences of 13 243 t* so that a
charge).
variance of 13 243 - 705,46 = 12 500 t* would be
Table 3 lists the most relevant statistics for this set. a better estimate for the precision of a single draft
survey than the variance of 705,46 t? In terms of a
coefficient of variation the precision for draft surveys
Precision and bias between different
Table 3 -
for a single cargo space would then be
techniques
12500 x100
Parameter 1 Symbol 1 Value J
= 2,7 %
[(4 106,9 + 4 134,3) / 21
4 106,9
Mean - draft survey (t) WI
4 134,3
Mean - weighbridge (t) WV
A calculated t-value of 0,753 for a mean difference
AX -I- 27,4
Mean difference (t) of 27,4 t does not exceed the tabulated value of
= 2,262 which implies that means of 4 106,9 t
AX + 0,7 t0,95;9
Mean difference (%)
at loading and 4 134,3 t at discharge are statistically
Variance of differences (t*) s*( Ax) 13243
identical. Hence, the draft survey at discharge and
the weighbridge at discharge apparently generate un-
Coefficient of Variation (%) cv
218
biased estimates for the unknown true wet mass
Student’s t-value t 0,753
of each shipment. Nonetheless, the precision of a
static scale such as a weighbridge installs a signifi-
Bias Detection Limits:
cantly higher degree of confidence in a cumulative
Type I risk only (%) BDL(I) + 2,0
wet mass of 4 134,4 t than the precision of draft sur-
Type I & II risks (%) BDL(I&II) + 3,6
veys does.
Bias Detection Limits of & 2,0 % or + 82 t for the
The coefficient of variation of 2,8 % is a measure for
Type I risk only, and + 3,6 % or + 149 t for Type I and
the precision between draft surveys at discharge and
Type II risks, are measures of the power or sensitivity
wet masses determined with a weighbridge at the
of this test to detect a bias. Generally, Bias Detection
smelter. In 6.2.1 the precision between draft surveys
Limits are also estimates for the risk of one trading
at loading and discharge in terms of a coefficient of
partner to losing, and an identical probability of the
variation came out at 0,91 %. The question whether
other trading partner to gaining. In this case, however,
coefficients of variation of 2,8 % and 0,91 % are
the settlements were based on wet masses deter-
compatible can be solved by comparing the calculated
mined with the weighbridge so that the risk was
F-ratio of
much less than BDLs of + 2,0 % and + 3,6 % imply.
13243 =g3g Precision estimates for the wet mass of a single cargo
1 410,92 ' space or a complete cargo, and for the cumulative
mass of a set, are calculated in the same manner. For
(the variance between draft surveys at discharge and
example, a variance of 12 500 t* and a single wet
wet masses measured with a weighbridge at a mass of 4 107 t for draft surveys at discharge are
smelter, divided by the variance between draft sur- equivalent to a 95 % confidence interval of:
veys at loading and discharge) with tabulated values of
= 5,35. The calculated
= 3,18 and Fo,sg;g;s
Fo,95;9;9
2x,/12500 =f224t
value of 9,39 exceeds tabulated values at the 95 %
and 99 % probability levels. Hence, the probability that
224 = 3 883 t
coefficients of variation of 2,8 % and 0,91 % are sta- for a 95 % confidence range from 4 107 -
tistically identical is much less than 1 %. up to 4 107 + 224 = 4 331 t.
8
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4 SIST ISO 12745:1998
@ IS0 IS0 12745:1996(E)
the basic statistical parameters for each moving data
Table 4 lists precision estimates that are based on a
base.
single wet mass of 4 107 t, a cumulative wet mass of
41 343 t, a variance of 12 500 t* for the single wet
Coefficients of variation of 0’39 % and 0’1 1 % are
mass, and the sum of variances of 125 000 t* for the
both measures for the precision of this belt scale.
cumulative wet mass.
However, the calculated F-ratio of
The coefficient of variation of 2’7 %, when divided by
0’1976
fi, becomes:
- = 13,00
0,015 2
2’7
- = 0’9 %
between the variances before and after calibration ex-
3’16
ceeds the tabulated values of FO 95.11.11 = 2,82 and
= 4’64 which implies that these variances
p;b,99;1 I;1 1
This relationship is based on the Central Limit Theo-
differ significantly. The long-term variance of 0,197 6
rem, an important theorem in mathematical probability
between chain spans prior to calibration more truly re-
and applied statistics.
flects the magnitude of random variations in mass
measurement with this belt scale as a function of
time. Therefore, the coefficient of variation of 0’39 %
is the more reliable estimate for its precision under
routine conditions.
6.3 Belt scales
The question whether the belt scale generates un-
An example of how to calculate the precision of wet
biased estimates for wet mass can be solved by ap-
masses measured with belt scales can be found in
plying Student’s t-test to the difference between the
table A.3 of annex A. This table lists a set of twelve
required span (115,25 for this belt scale), and the
(12) chain spans, recorded at weekly intervals prior to
mean of observed spans for a set that constitutes a
calibration, and a similar set of spans that were ob-
tained immediately following its calibration. Table 5 lists moving data base. Table 6 lists the results of this test.
- Precision for wet mass by draft survey
Table 4
Parameter Symbol Single Cumulative
41 343
WV 4107
Mean (t)
125000
s*@%,,,) 12500
Variance (t*)
Standard deviation (t) s&C,,,) Ill,8 353,6
Coefficient of Variation (%) cv 2,7
0'9
95 % Cl +224 +707
95 % Confidence Interval (t) 1)
&I,7
(%) 95 % Cl + 5,4
95 % Confidence Interval
95 % Confidence Range:
3883 40636
lower limit (t) 95 % CRL
42050
(t) 95 % CRU 4331
upper limit
1) Based onz0,g5xs(M,),orz0,g5xs
&J.
Precision of a belt scale
Table 5 -
Symbol Before After
Parameter
x 115,12 115,36
Mean (scale units) I I I I
0,197 6 0,015 2
Variance (scale units) 2 s* (4
s(x) 0,444 6 0,123 4
Standard deviation (scale units)
cv 0,39 0,ll
Coefficient of Variation (%)
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SIST ISO 12745:1998
IS0 12745:1996(E) @ IS0
Table 7 - Precision for wet mass with a belt scale
Table 6 - Testing a belt scale for bias
Parameter 1 Symbol 1 Value Parameter 1 Symbol 1 Value
Mean - required span 115,25 Mean (t) 25000
x(R)
ww
Mean - observed span 115,12 Coefficient of Variation (%) CV
30) 0,39
Mean difference (span units) AX - 0,13 Standard deviation (t)
d4,J 97,5
Student’s t-value t 1,013 95 % Confidence Interval (t) 95 % Cl +195
Significance ns 1) 95 % Confidence Interval (
...
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