Mueller 317 3487 1 Pb [603465]

ACTA IMEKO
ISSN: 2221- 870X
December 2017, Volume 6, Number 4, 95-99

ACTA IMEKO | www.imeko.org December 2017 | Volume 6 | Number 4 | 95
Assessment of Mass Comparator Sensitivity
Christian Müller -Schöll
Mettler -Toledo GmbH, Im Langacher 44, 8606 Greifensee, Switzerland

Section: RESEARCH PAPER
Keywords: mass calibration ; comparator sensitivity; uncertainty ; mass comparator ; OIML R111
Citation: Christian Müller- Schöll, Assessment of Mass Comparator Sensitivity, Acta IMEKO, vol. 6, no. 4, article 15, Decem ber 2017 , identifier: IMEKO -ACTA –
06 (2017 )-04-15
Editor: Paolo Carbone, University of Perugia, Italy
Received January 29, 2016 ; In final form November 18, 2017 ; Published December 2017
Copyright: © 2017 IMEKO. This is an open- access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Funding: Mettler -Toledo GmbH, Greifensee, Switzerland
Corresponding author: Christian Müller -Schöll, e -mail: christian.mueller- [anonimizat]

1. INTRODUCTION
When calibrating weight pieces, the difference between the
unknown weight and the reference weight is calculated from
the indications of the mass comparator display (or the data
interface signal) . This difference is then used to calculate the
conventiona l mass of the unknown weight. For common
industrial and laboratory applications, weight pieces are
calibrated in c onventional mass [1] and electronic balances and
mass comparators also indicate in this conventional unit.
The term sensitivity is defined in [2] as “quotient of the
change in an indication of a measuring system and the
corresponding change in a value of a quantity being measured” [2, 4.12]. A ccording to this definition the general equation for
sensitivity of a mass comparator is
𝑆=∆𝐼
∆𝑚𝑐 (1)
with change in indication ∆𝐼 and conventional mass of a weight
∆𝑚𝑐 (and not the reciprocal value as is sometimes used, e.g. in
[3] and [7 ]).
The general assumption is that for electronic balances and
mass comparators, the difference ∆ 𝐼 of the indications is equal
to the difference in conventional mass ∆𝑚𝑐. This corresponds
to a sensitivity e qual to 1.
However, there are sources that suggest that this is not
always the case. In earlier days, it was apparently usual that
comparators with an optical scale did not necessarily indicate

correct mass differences. Therefore, [3, SOP4] and [1, C.4.1.2 ],
for example, describe weighing cycles for mass calibrations including a sensitivity weight (S), e.g. of the form “A – B –
B+(S) – A+(S)”. With these cycles, the sensitivity is determined
in every single weighing cycle to convert the scale divisions into
a mass difference .
In Section 2 we will review existing literature on this subject.
Sections 3 and 4 d eal with uncertainty qu estions. In S ections 5
through 7 we derive a procedure for assessing comparator
sensitivity based on optimized uncertainty . Section 8 presents a
verification through experimental dat a. The conclusions finally
summarize the findings.
2. REVIEW OF THE LITERA TURE
2.1. Testing Procedures for Sensitivity
According to some sources in the literature, it is not
necessary to determine sensitivity in every weighing cycle for
modern electronic comparators :
• "A sensitivity weight is not required if the electronic mass comparator that is used has been tested (with supporting data available) to determine that the balanc e has sufficient
accuracy…" [3, GMP 14]. The uncertainty of this
assumption shall be included as an uncorrected systematic
error in the uncer tainty budget and acceptable limits are
"2 %" [3, SOP8 ]. ABSTRACT
For the calibration of weight pieces, the evaluation of comparator sensitivity and its associated uncertainty component is essential.
Yet, there is not much documented guidance on how to assess these values. This paper proposes a procedure for assessing, eval uating
and optimizing mass comparat or sensitivity.

ACTA IMEKO | www.imeko.org December 2017 | Volume 6 | Number 4 | 96 • Kochsiek et al. mention in the German edition of their
book “Massebestimmung” [4] (translated to English: “mass determination”) that for a “frequently adjusted
electromagnetica lly compensated balance ” sensitivity 𝑆 shall
be assumed to be 1 and an uncertainty in 𝑆 shall be assumed
to be less than 5 𝐸−04 or may even be neglected,
especially when using auxiliary weights …”.[4]. However, it
remains unclear how to adjust the comparator so that it
fulfils the condition of being “adjusted”, nor are there any
suggestions as to the accuracy and thus uncertainty of the
adjustment procedures, nor as to how often an adjustment
must take place to fulfil the requirement of being “frequently adjusted”. It is interesting to note that the cited
numerical value ( 5 𝐸−04) is omitted in the (later) English
edition of the same book [5].
• Chapter C.6.4.2 of [1] requires that an uncertainty
component for sensitivity be included in the budget when
calibrating weights, but gives no specific guidance on how
to assess the value of this component and especially on how
to select a proper sensitivity test weight regarding its size and its calibration quality.
In general, there are two ways to treat sensitivity: One is to
assume ideal sensitivity and set a limit for the deviation of the
sensitivity from "1" and test and verif y the sensitivity against
that limit. This limit value is considered in the uncertainty
budget as an uncorrected error. The other one is to evaluate a
value for sensitivity, correct all balance readings with this value,
calculate the uncertainty of this correction and have this
contribute to the uncertainty budget (which results in a smaller
uncertainty but requires a higher calculation effort) .
Since mass c alibrations involve a significant amount of
calculations, it is common practice today to use at least software
spreadsheets or even dedicated software for the calculations. If this is the case, the sensitivity value can easily be incorporated
as a correcti on in the calculation of the mass differences and its
uncertainty will then contribute to the uncertainty calculation.
In some commercially available calibration software (e.g.
Scalesnet, McLink), a numerical value of sensitivity is
determined in a separat e test for each comparator. But for its
uncertainty, the uncertainty value given in [4] is frequently used
without alteration . Where the mass difference between the
calibrated weight and the reference weight becomes large, this might have significant influ ence on the final combined
calibration uncertainty of the weight piece under test. One
result of this paper is to answer the question whether this worst
case estimation of a sensitivity uncertainty of 5 𝐸−04 is
justified.
2.2. Test Weights for Sensitivity Test ing
There seems to be common understanding that sensitivity of
mass comparators is tested with a “ small” weight: Reference [3,
SOP 2] mentions a “small weight”, [3, SOP 34] mentions a
maximum of 0.5 % of balance capacity, while [3, GMP 10]
mentions a maximum of 1 % of balance capacity. It remains
unclear if "balance capacity" means the full load value or the
electrical weighing range in this context. No standard method
for the selection of the sensitivity test weight appears to be
available.
3. ASSESSMENT OF SENSIT IVITY
The VIM [2] defines adjustment of a measuring system as
“set of operations carried out on a measuring system so that it provides prescribed indications corresponding to given values of a quantity to be measured” .
Today’s mass comparators with electromagnetic force
compensation are equipped with provisions for self -adjustment.
These consist of one (or more) internal weight piece(s) and an algorithm which can be time and/or temperature controlled or
manually triggered. Furthermore, external mass calibration
software allows for an additional “ adjustment ” of the reading
by applying a sensitivity fact or in the processing of the value
that was read from the comparator output. In this light, we
consider the calibration software a part of the “measuring system” together with the comparator (see Figure 1 ), and the
application of a sensitivity value is cons idered an adjustment of
this system .
The sensitivity factor applied by the software is gained from
the following test procedure: The comparator is loaded with a
pre-load (between zero and nominal load) which brings the
comparator into a typical working range and working state.
Then a test is carried out using an “ABBA” cycle which starts
with the mentioned pre-load (“A”), then a calibrated sensitivity
test weight with conventional mass ∆𝑚
𝑐,𝑆 is added (“B”), this
step is repeated (“B”) and finally the test weight is removed
(“A”). From the calibration value of the test weight and the
calculated, buoyancy-corrected difference of comparator
indication during the test ∆𝐼𝑆, the sensitivity value 𝑆 is
calculated according to (1). (Subscripts upper case "𝑆" are used
in this paper to indicate the context of a sensitivity test ).
Once this sensitivity value is determined, it must be used for
any further processing of a reading of that comparator. We
assume here that the self -adjustment procedure of the
comparator is run about once a day, so that any climate -induced
changes (air density, temperature) and their effect on the
comparator sensitivity are negligible, this means that the
sensitivity of the c ompara tor stays “the same” over time ( but
will not necessarily be 1 exactly) .
4. UNCERTAINTY OF SENSI TIVITY
4.1. General Considerations
Given the procedure above and (1) for the calculation of
sensitivity, we find the following sources of uncertainty when
determin ing S from a sensitivity test:
• Readability of the comparator 𝑢 𝑟𝑟𝑟𝑟
• Repeatability of the comparator 𝑢 𝑟𝑟𝑟𝑟𝑟𝑟
• Calibration uncertainty of the sensitivity test weight
𝑢𝑤𝑟𝑤𝑤ℎ𝑟

Figure 1. The measuring system. Measuring System:
delivers processed value
Software (external of comparator):
processes indication value with a factor
Comparator:
delivers indication value

ACTA IMEKO | www.imeko.org December 2017 | Volume 6 | Number 4 | 97 The uncertainty in 𝑆 can thus easily be derived as:
𝑢𝑆2= �1
∆𝑚𝑐,𝑆×𝑢𝑟𝑟𝑟𝑟�2
+�1
∆𝑚𝑐,𝑆×𝑢𝑟𝑟𝑟𝑟𝑟𝑟�2
+
+�∆𝐼𝑆
∆𝑚𝑐,𝑆2×𝑢𝑤𝑟𝑤𝑤ℎ𝑟�2
(2)
with the components
𝑢𝑟𝑟𝑟𝑟 = 𝑑
2×1
√3
for an ABBA cycle (derived from the calculation of an
ABBA difference) and with comparator indication readability 𝑑,
𝑢𝑟𝑟𝑟𝑟𝑟𝑟 =𝑠
√𝑛
with the repeatability standard deviation 𝑠 of the comparator
and the number of cycles of the sensitivity test 𝑛 and
𝑢𝑤𝑟𝑤𝑤ℎ𝑟=𝑈𝑐𝑟𝑐
𝑘
with coverage factor 𝑘 , taken from the calibration certificate of
the sensitivity test weight.

For simplification of the uncertainty calculation (only) we set
∆𝐼𝑆= ∆𝑚𝑐 so that (2) becomes for a sensitivity test:
𝑢𝑆2= �1
∆𝑚𝑐,𝑆×𝑟
2×√3�2
+�1
∆𝑚𝑐,𝑆×𝑠
�𝑛𝑆�2
+�1
∆𝑚𝑐,𝑆×𝑈𝑐𝑐𝑐
2�2
(3)
Please note that since 𝑆 is a relative number, its uncertainty
𝑢𝑆2 is also a relative number while its uncertainty contributors
are in mass units.
4.2. Uncertainty o f Conventional Mass – Connection to OIML R111
OIML R111 [1] requires an uncertainty contribution 𝑢𝑠
(note lower case “s” in the subscript) to be estimated that , as a
component of the balance uncertainty 𝑢𝑏𝑟, accounts for the
uncertainty of the sensitivity in the calculation of conventional
mass. In our case, where a factor 𝑆 is used to calculate the
conventional mass difference according to (1), this uncertainty
component of conventional mass is (with sensitivities 𝑆 close to
1):
𝑢𝑠2=�∆𝐼
𝑆2 ×u𝑆�2
≈[∆𝐼 ×u𝑆]2 (4)
Note that 𝑢𝑠2 (with lower case subscript s) is taken from [1]
while the last term (with upper case S ) is our concept .
5. INITIAL CHOICE OF A S ENSITIVITY TEST WE IGHT
As has been mentioned above, there i s only little literature
available on mass comparator sensitivity. The publication of
R. Davis [6] appears to have been written in the light of
comparators with optical scales and a sensitivity assessment in every mass calibration cycle and therefore provi des only a
rough direction for today’s questions. Lee Shih Mean’s paper [7] focuses on a very special problem (the calibration of
stainless steel against Pt- Ir standards and evaluating true mass)
and thus has its own reasons for the choice of the weight si ze.
All sources , however, agree in the general idea that the weight
should be “small” and in the magnitudes of the weighing
differences that will be obtained. The reason is probably, that
this procedure tries to approximate an ideal differential
sensitivity
𝜕𝐼
𝜕𝑚𝑐 from the test with finite values ∆𝐼𝑆
∆𝑚𝑐,𝑆 thus
avoiding any influence of non-linearities in the characteristic
curve of the comparator. As a first practical assumption, we chose calibrated test
weights with a nominal value of about 100 t imes the readability
𝑑 of the comparator, but not smaller than the smallest OIML –
weight which is 1 mg. The weights are made of stainless steel to
avoid any complications arising from buoyancy effects. As test
objects we chose the manual comparators in the mass
calibration laboratory of METTLER TOLEDO, accredited as
SCS 0032. ( Table 1 ).
We further assume for simplicity reasons that the sensitivity
test weights were calibrated with an uncertainty (k=2) of one
third of the MPE of class E 1 according to [1].
Thirdly, we used "datasheet repeatablities" for our
calculations and 𝑛𝑆=1 repetitions for the sensitivity test. For
each mass comparator used in our laboratory, we calculated the
uncertainty of the sensitivity as given in (3).
This revealed some unexpected results. Figure 2 shows the
sensitivity uncertainties (k=1) for each co mparator type listed in
Table 1. We note the following important findings:
• Although we applied the same basic idea for the choice of
the sensitivity test weight, the differences of the sensitivity
uncertainties between the comparators were of abou t 3
magnitudes, ranging from 6 E-04 to 2 E-02.
• The maximum uncertainty value observed (2 E-02) was
significantly higher than the simplified value of 5 E-04 from
the literature although our procedure uses a correction .
We conclude that a general assumption of an uncertainty of
comparator sensitivity of 5 E-04 (as can be found in the
literature) is not justified.
6. VARIATION AND OPTIMI ZATION OF PARAMETERS
6.1. Optimization to reach an Uncertainty of 5 E-04
Further investigation of the uncertainty budget of the
sensitivity revealed that in most cases (and especially in the case
Table 1. Mass comparators, datasheet repeatabilities and readabilities and test
weights nominal values of “initial choi ce”. Comparator
XP64003L
XP10003S
XP5003S
XP2004S
AX1005
AX106
XP6U
𝑑
(mg) 5 1 1 0.1 0.01 0.001 0.0001
𝑠
(mg) 8 1 0.8 0.1 0.02 0.003 0.0003
5
𝑚𝑐,𝑆
(mg) 500 100 100 10 1 1 1

Figure 2. Sensitivity uncertainties based on initial choice of the sensitivity
test weight (k=1).

ACTA IMEKO | www.imeko.org December 2017 | Volume 6 | Number 4 | 98 of the high values identified above ), the dominant contributor
to the uncertainty budget was the influence of repeatability
(which is the second component in (3)). The equation suggests
that this contributor could be reduced by an increase in the
number of weighing cycles used in the adjustment. However,
this has little effect since it is not practical to use more than
about 5 A BBA cycles. (For this publication, we will continue to
use datasheet repeatabilities. However, it is obvious that using
individually determined repeatabilities (which are usually
smaller ) will have a significant , improving impact on the
uncertainty.)
Re-visiting equation (3), we find that the nominal value of
the chosen sensitivity test weight influences all three uncertainty
contributors. This opens the door to optimizing the sensitivity uncertainty by adjusting number of cycles and nominal values of
the test weights . Increasing the nominal weight value will lead
to smaller sensitivity uncertainties. A massive increase would, however, violate the principle of “small” sensitivity test weights
(as explained above in Section 2.2 ), so we prefer to keep
nominal values small. Additionally , we will only use nominal
values that are specified in [1].
With these restrictions, we iteratively increased the nominal
values in the sensitivity test weight with the aim of reduc ing
uncertain ties of all sensitivities to approximately 5 E-04 or less
(which is the literature value) . In order to keep the procedures
easy to understand for all laboratory personnel, we fixed the
number of weighing cycles for the sensitivity test to 𝑛
𝑆=3
ABBA cycles for all types of compara tors. The new values are
shown in Figure 3 . Please note the difference in y-axis scale
compared to Figure 2 .
These results were achieved using the sensitivity test weights
for the comparator models as shown in Table 2 . The nominal
values of these weights a re below the maximum value of 0.5 %
of balance capacity as stipulated in [3], so this choice does not
violate the concept of a "small" weight.
6.2. Further Optimization to reach S maller Uncertainties
By increasing the number of cycles and by increasing the
nominal values of the weight pieces, it is possible to reach values for 𝑢𝑠 of e.g 1 E-04.
However, with an attempt to reach 1 E-05 (still using
datasheet repeatabilities) , the necessary test weight s approach
the "0.5 % of capacity limit" (see above) and thus are no longer
considered "small".
6.3. Variation of Sensitivity Test Weight Accuracy
Except for microbalance comparators, the calibration
uncertainty of the sensitivity test weight 𝑈𝑐𝑟𝑐 has litt le
influence on the uncertainty in 𝑆. So using weights calibrated in
E2 quality instead of E 1 weights is possible without major
disadvantage.
7. GENERAL COOKBOOK PROCEDURE FOR ASSESS ING
OPTIMIZED COMPARATOR SENSITIVITY AND ITS
UNCERTAINTY
The following proc edure for assessing sensitivity uncertainty
can be derived from the considerations above:
1. Set a maximum acceptable value for sensitivity uncertainty
(e.g. 5E-04 or 1 E-05).
2. Set a number of ABBA cycles for the sensitivity test , use (3)
and iteratively increase the nominal weight value until the
above condition is fulfilled for the comparator concerned .
3. Execute sensitivity test and apply the value found for 𝑆 to
all future readings.
4. Use the value of 𝑢𝑠 for the uncertainty estimation of mass
calibrations according to [1].
8. EXPERIMENTAL VERIFIC ATION
In order to verify the theoretical ideas outlined above, we
have done several tests. One series of tests was done on a n
XP2004S comparator balance. We have tested different weight
sizes and number s of test cycles. The results are found in Figure
4: the diagram shows 3 series of sensitivity values and their
calculated uncertainties. The first s eries was done with a 100 mg
sensitivity test weight and one cycle, while the second series was done with a 500 mg weight and three cycles. The third series
was done with a 1 g test weight and three cycles. The picture
confirms the theoretical consideratio ns:
• As could be expected, the variability of the values gained
with higher uncertainty is bigger. The larger the test weights
and the number of cycles, the smaller the variability.
• Most data points are consistent to each other : An En -Test
shows that most dat a points are consistent with every other
one, especially the points gained with more than one cycle
(i.e. 𝑛
𝑆>1 ) show excellent agreement with each other.

Figure 3. Sensitivity uncertainties with optimized procedure (k=1).
Table 2. Mass comparators and test weight nominal values for optimized
sensitivity. Com parato
r
XP64003L
XP10003S
XP5003S
XP2004S
AX1005
AX106
XP6U
𝑚𝑐
(mg) 10000 2000 1000 200 50 5 1
Figure 4. Three series of sensitivity test points together with calculated
uncertainties (k=2). Nominal values and number of cycles for each series:
100 mg (n=1), 500 mg (n=3), 1 g (n=3) .

ACTA IMEKO | www.imeko.org December 2017 | Volume 6 | Number 4 | 99 9. CONCLUSIONS
The sensitivity of mass comparators and its associated
uncertainty are both values with important significance in the
field of weight piece calibration. The literature does not provide
much guidance neither on procedures to be used for assessing
sensitivity and its uncertainty nor on the selection of suitable weights for sensitivity testing . We have presented a procedure
for assessing and the mathematics for evaluating sensitivity and
its associated uncertainty. By means of iterative application, a
weight for a sensitivity test can be selected so that relative
sensitivity uncertainties 𝑢
𝑠 of e.g. 1 E-04 are achieved with the
prerequisite that a correction for sensitivity is applied .
REFERENCES
[1] OIML: “OIML R111- 1:2004: Weights of classes E 1, E 2, F1, F2,
M1, M1–2, M 2, M 2–3 and M 3 – Part 1: Metrological and technical
requirements”: www.oiml.org . [2] JCGM 200: 2012: “International vocabulary of metrology – Basic
and general concepts and associated terms (VIM) 3rd edition”:
www.bipm.org.
[3] NIST: IR 6969: www.nist.gov.
[4] Kochsiek M, Glaeser M, Massebestimmung , VCH, Weinheim, 1997
[5] Kochsiek M, Glaeser M (eds.). Comprehensive Mass Metrology ,
Wiley -VCH, Berlin, 2000.
[6] R. Davis: “Note on the Choice of a Sensitivity Weight in Precision Weighing”, Journal of Research of the Natio nal Bureau
of Standards , Volume 92, Number 3, pp 239 -242, May-June
1987.
[7] S. M. Lee, R. Davis , L. K. Lim: “ Calibration of a 1 kg Stainless
Steel Standard with respect to a 1 kg Pt-Ir Prototype: A Survey of
Corrections and Their Uncertainties ”, Asia-Pacific Symposium
on Mass, Force and Torque (APMF 2007), Oct 24- 25 2007.

Certain commercial equipment, instruments, or materials are identified in this
paper in order to adequately describe the experimental procedure. Such identification does not imply recommend ation or endorsement by the author, nor does it imply that
the materials or equipment identified are the only or best available for the purpose.