IEC 61788-11:2011

IEC 61788-11 ®
Edition 2.0 2011-07
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Superconductivity –
Part 11: Residual resistance ratio measurement – Residual resistance ratio of
Nb Sn composite superconductors
Supraconductivité –
Partie 11: Mesure du rapport de résistance résiduelle – Rapport de résistance
résiduelle des supraconducteurs composites de Nb Sn
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IEC 61788-11 ®
Edition 2.0 2011-07
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Superconductivity –
Part 11: Residual resistance ratio measurement – Residual resistance ratio of
Nb Sn composite superconductors
Supraconductivité –
Partie 11: Mesure du rapport de résistance résiduelle – Rapport de résistance
résiduelle des supraconducteurs composites de Nb Sn
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
CODE PRIX S
ICS 17.220; 29.050 ISBN 978-2-88912-581-4

– 2 – 61788-11  IEC:2011
CONTENTS
FOREWORD . 3
INTRODUCTION . 5
1 Scope . 6
2 Normative references . 6
3 Terms and definitions . 6
4 Requirements . 7
5 Apparatus . 7
5.1 Material of measuring base plate . 7
5.2 Length of the measuring base plate . 7
5.3 Cryostat for the resistance, R , measurement . 7
6 Specimen preparation. 8
7 Data acquisition and analysis . 8
7.1 Resistance (R ) at room temperature . 8
7.2 Resistance (R ) just above the superconducting transition . 8
7.3 Residual resistance ratio (RRR) . 10
8 Uncertainty and stability of the test method . 11
8.1 Temperature . 11
8.2 Voltage measurement. 11
8.3 Current . 11
8.4 Dimension . 11
9 Test report. 11
9.1 RRR value . 11
9.2 Specimen . 11
9.3 Test conditions . 12
Annex A (informative) Additional information relating to the measurement of RRR . 13
Annex B (informative) Uncertainty considerations . 15
Annex C (informative) Uncertainty evaluation in test method of RRR for Nb Sn . 19
Figure 1 – Relationship between temperature and resistance  . 7
Figure 2 – Voltage (U) versus temperature (T) curves and definitions of each voltage . 9

Table B.1 – Output signals from two nominally identical extensometers . 16
Table B.2 – Mean values of two output signals . 16
Table B.3 – Experimental standard deviations of two output signals. 16
Table B.4 – Standard uncertainties of two output signals . 17
Table B.5 – Coefficient of variations of two output signals. 17
Table C.1 – Uncertainty of each measurement . 20
Table C.2 – Obtained values of R , R and RRR for three Nb Sn samples. 21
1 2 3
61788-11  IEC:2011 – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SUPERCONDUCTIVITY –
Part 11: Residual resistance ratio measurement –
Residual resistance ratio of Nb Sn composite superconductors
FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
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9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 61788-11 has been prepared by IEC Technical Committee 90:
Superconductivity.
This second edition cancels and replaces the first edition published in 2003. It constitutes a
technical revision. The main revisions are the addition of two new annexes, "Uncertainty
considerations" (Annex B) and "Uncertainty evaluation in test method of RRR for Nb Sn"
(Annex C).
– 4 – 61788-11  IEC:2011
The text of this standard is based on the following documents:
FDIS Report on voting
90/268/FDIS 90/279/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
A list of all parts of the IEC 61788 series, published under the general title Superconductivity,
can be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until
the stability date indicated on the IEC web site under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
61788-11  IEC:2011 – 5 –
INTRODUCTION
Copper or aluminium is used as stabilizer material in multifilamentary Nb Sn superconductors
and works as an electrical shunt when the superconductivity is interrupted. It also contributes
to recovery of the superconductivity by conducting the heat generated in the superconductor
to the surrounding coolant. The resistivity of copper used in the composite superconductor in
the cryogenic temperature region is an important quantity which influences the stability of
the superconductor. The residual resistance ratio is defined as a ratio of the resistance of the
superconductor at room temperature to that just above the superconducting transition.
In this International Standard, the test method for the residual resistance ratio of Nb Sn
composite superconductors is described. The curve method is employed for the measurement
of the resistance just above the superconducting transition. Other methods are described in
Clause A.3.
– 6 – 61788-11  IEC:2011
SUPERCONDUCTIVITY –
Part 11: Residual resistance ratio measurement –
Residual resistance ratio of Nb Sn composite superconductors
1 Scope
This part of IEC 61788 covers a test method for the determination of the residual resistance
ratio (RRR) of Nb Sn composite superconductors. This method is intended for use with
superconductor specimens that have a monolithic structure with rectangular or round cross-
section, RRR less than 350 and cross-sectional area less than 3 mm , and have received a
reaction heat-treatment. Ideally, it is intended that the specimens be as straight as possible;
however, this is not always the case, thus care must be taken to measure the specimen in its
as received condition. All measurements are done without an applied magnetic field.
The method described in the body of this standard is the “reference” method and optional
acquisition methods are outlined in Clause A.3.
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.
IEC 60050-815, International Electrotechnical Vocabulary – Part 815: Superconductivity
3 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60050-815 and the
following apply.
3.1
residual resistance ratio
RRR
the ratio of resistance at room temperature to the resistance just above the superconducting
transition
NOTE In this standard for Nb Sn composite superconductors, the room temperature is defined as 293 K (20 °C),
and the residual resistance ratio is obtained in Equation (1) below, where the resistance (R ) at 293 K is divided by
the resistance (R ) just above the superconducting transition.
R
RRR = (1)
R
Figure 1 shows schematically a resistance versus temperature curve acquired on a specimen while measuring
cryogenic resistance. Draw a line in Figure 1 where the resistance sharply increases (a), and draw also a line in
Figure 1 where the resistance increases gradually (b) with temperature. The value of resistance at the intersection
of these two lines at T=T *, A, is defined as resistance (R ) just above the superconducting transition.
c 2
61788-11  IEC:2011 – 7 –
(b)
A
R
(a)
Temperature
T *
c
IEC  1603/11
Temperature T * is that at the intersection point.
c
Figure 1 – Relationship between temperature and resistance
4 Requirements
The resistance measurement both at room and cryogenic temperatures shall be performed
with the four-terminal technique.
The target relative combined standard uncertainty of this method is defined as an expanded
uncertainty (k = 2) not to exceed 10 % based on the coefficient of variation (COV) of 5 % in
the intercomparison test (see Clause C.2).
5 Apparatus
5.1 Material of measuring base plate
Material of the measuring base plate shall be copper, aluminum, silver or the like whose
thermal conductivity is equal to or better than 100 W/(m⋅K) at liquid helium temperature
(4,2 K). The surface of the material shall be covered with an insulating layer (tape or a layer
made of polyethylene terephthalate, polyester, polytetrafluoroethylene, etc.) whose thickness
is 0,1 mm or less.
5.2 Length of the measuring base plate
The measuring base plate shall be at least 30 mm long in one dimension.
5.3 Cryostat for the resistance, R , measurement
The cryostat shall include a specimen support structure and a liquid helium reservoir for the
resistance, R , measurement. The specimen support structure shall allow the specimen,
which is mounted on a measurement base plate, to be lowered and raised into and out of a
liquid helium bath. In addition, the specimen support structure shall be made so that a current

Resistance
– 8 – 61788-11  IEC:2011
can flow through the specimen and the resulting voltage generated along the specimen can
be measured.
6 Specimen preparation
The test specimen shall have no joints or splices, and shall be 30 mm or longer. The distance
between two voltage taps (L) shall be 25 mm or longer. A thermometer for measuring
cryogenic temperature shall be attached near the specimen.
Some mechanical method shall be used to hold the specimen against the insulated layer of
the measurement base plate. Special care shall be taken during instrumentation and
installation of the specimen on the measurement base plate so that no excessive force, which
may cause undesired bending strain or tensile strain, shall be applied to the specimen.
The specimen shall be instrumented with current contacts near each end of the specimen and
a pair of voltage contacts over a central portion of the specimen. The specimen shall be
mounted on a measurement base plate for these measurements. Both resistance measure-
ments, R and R , shall be made on the same specimen and the same mounting.
1 2
7 Data acquisition and analysis
7.1 Resistance (R ) at room temperature
The mounted specimen shall be measured at room temperature (T (K)), where T satisfies
m m
the following condition 273 ≤ T ≤ 308. A specimen current (I (A)) shall be applied so that
m 1
2 2
the current density is in the range of 0,1 A/mm to 1 A/mm based on the total wire
cross-sectional area, and the resulting voltage (U (V)), I and T shall be recorded.
1 1 m
Equation (2) below shall be used to calculate the resistance (R ) at room temperature. The
m
resistance (R ) at 293 K shall be calculated using equation (3) for a wire with Cu stabilizer.
The value of R shall be set equal to R , without any temperature correction, for wires that do
1 m
not contain a pure Cu component.
U
R = (2)
m
I
R
m
R = (3)
[1+ 0,00393⋅ (T − 293)]
m
7.2 Resistance (R ) just above the superconducting transition
7.2.1 The specimen, which is still mounted as it was for the room temperature measurement,
shall be placed in the cryostat for electrical measurement specified under 5.3. Alternate
cryostats that employ a heating element to sweep the specimen temperature are described in
Clause A.2.
7.2.2 The specimen shall be slowly lowered into the liquid helium bath and cooled to liquid
helium temperature over a time period of at least 5 min.
7.2.3 During the acquisition phases of the low-temperature R measurements, a specimen
current (I ) shall be applied so that the current density is in the range of 0,1 A/mm to
10 A/mm based on the total wire cross-sectional area and the resulting voltage (U(V)), I (A),
and specimen temperature (T (K)) shall be recorded. In order to keep the ratio of signal to
noise high enough, the measurement shall be carried out under the condition that the

61788-11  IEC:2011 – 9 –
absolute value of resulting voltage above the superconducting transition exceeds 10 µV. An
illustration of the data to be acquired and its analysis is shown in Figure 2.

U
(b)
U*
2+
A
(a)
U
U
0+
20+
U
U
20–
0rev
T
U
0–
U*
2– IEC  1604/11
Voltages with subscripts + and – are those obtained in the first and second measurements under positive and
negative currents, respectively, and U and U are those obtained at zero current. For clarity, U is not
20+ 20– 0rev
shown coincident with U . Voltages U * and U * with asterisk are those at the intersection points.
2+ 2-
0–
Figure 2 – Voltage (U) versus temperature (T) curves
and definitions of each voltage
7.2.4 When the specimen is in superconducting state and test current (I ) is applied, two
voltages shall be measured nearly simultaneously: U (the initial voltage recorded with a
0+
positive current polarity) and U (the voltage recorded during a brief change in applied
0rev
current polarity). A valid R measurement requires that excessive interfering voltages are not
present and that the specimen is initially in the superconducting state. Thus, the following
condition shall be met for a valid measurement:
|U −U |
0+ 0rev
< 1 % (4)
U
where U is the average voltage for the specimen in the normal state at cryogenic
temperature, which is defined in 7.2.10.
7.2.5 The specimen shall be gradually warmed so that it changes to the normal state
completely. When the cryostat for the resistance measurement specified under 5.3 is used,
this can be achieved simply by raising the specimen to an appropriate position above the
liquid helium level.
– 10 – 61788-11  IEC:2011
7.2.6 The specimen voltage versus temperature curve shall be acquired with the rate of
temperature increase maintained between 0,1 K/min and 10 K/min.
7.2.7 The voltage versus temperature curve shall continue to be recorded during the
transition into the normal state, up to a temperature somewhat less than 25 K. Then, the
specimen current shall be decreased to zero and the corresponding voltage, U , shall be
20+
recorded at a temperature below 25 K.
7.2.8 The specimen shall then be slowly lowered into the liquid helium bath and cooled to
the same temperature, within ± 1 K, where the initial voltage signal U was recorded. A
0+
specimen current, I , with the same magnitude but negative polarity (polarity opposite that
used for the initial curve) shall be applied and the voltage U shall be recorded at this
0–
temperature. The procedural steps 7.2.5 to 7.2.7 shall be repeated to record the voltage
versus temperature curve with this negative current. In addition, the recording of U shall be
20–
made at the same temperature, within ± 1 K, where U was recorded.
20+
7.2.9 Each of the two voltages versus temperature curves shall be analyzed by drawing a
line (a) through the data where the absolute value of voltage sharply increases with
temperature (see Figure 2) and drawing a second line (b) through the data above the
transition where the voltage is raised gradually and almost linearly with temperature increase.
U * and U * in Figure 2 shall be determined at the intersection of these two lines for the
2+ 2–
positive and negative polarity curves respectively.
7.2.10 The corrected voltages, U and U , shall be calculated using the following
2+ 2–
equations, U = U * – U and U = U * – U . The average voltage, U , shall be defined
2+ 2+ 0+ 2– 2– 0– 2
as
| U −U |
2+ 2
−
U =   (5)
7.2.11 A valid R measurement requires that the shift of thermoelectric voltage be within
acceptable limits during the measurements of the U and U . Thus, the following condition
2+ 2–
shall be met for a valid measurement,
|∆ −∆ |
+ −
< 3 % (6)
U
where ∆ and ∆ are defined as ∆ = U – U and ∆ = U – U If the R measurement
+ – + 20+ 0+ – 20– 0–. 2
does not meet the validity requirements in 7.2.4 and this subclause, then improvement steps
either in hardware or experimental operation shall be taken to meet these requirements
before results are reported.
7.2.12 Equation (7) shall be used to calculate the measured resistance (R ) just above the
superconducting transition.
U
R =   (7)
I
7.3 Residual resistance ratio (RRR)
The RRR shall be calculated using Equation (1).

61788-11  IEC:2011 – 11 –
8 Uncertainty and stability of the test method
8.1 Temperature
The room temperature shall be determined with a standard uncertainty not to exceed 0,6 K,
while holding the specimen, which is mounted on the measuring base plate, at room
temperature.
8.2 Voltage measurement
For the resistance measurement, the voltage signal shall be measured with a relative
standard uncertainty not to exceed 0,5 %.
8.3 Current
When the current is directly applied to the specimen with a programmable DC current source,
the specimen test current shall be determined with a standard uncertainty not to exceed 0,3 %.
When the specimen test current is determined from a voltage-current characteristic of a
standard resistor by the four-terminal technique, the standard resistor, with a relative
combined standard uncertainty not to exceed 0,3 %, shall be used .
The fluctuation of d.c. specimen test current, provided by a d.c. power supply, shall be less
than 0,5 % during every resistance measurement.
8.4 Dimension
The distance along the specimen between the two voltage taps, (L), shall be determined with
a relative combined standard uncertainty not to exceed 5 %.
9 Test report
9.1 RRR value
The obtained RRR value shall be reported as
RRR(1±U ) (n = ∙∙∙ ), (8)
re
where U = 2u (k = 2) is the expanded relative uncertainty with u denoting the uncertainty, k
re r r
is a coverage factor and n is the sampling number. It is desired that n be larger than 4 so that
the normal distribution can be assumed for the estimation of the standard deviation. If n is not
sufficiently large, a square distribution shall be assumed. In case of n = 1 the analytic method
–2
described in Annex C shall be used with b/R = 1,46 × 10 estimated from the
intercomparison test.
9.2 Specimen
The test report for the result of the measurements shall also include the following items, if
known:
a) manufacturer;
b) classification and/or symbol;
c) shape and area of the cross-section;
d) dimensions of the cross-sectional area;
e) number of filaments;
– 12 – 61788-11  IEC:2011
f) diameter of the filaments;
g) Cu to non-copper ratio.
9.3 Test conditions
9.3.1 The following test conditions shall be reported for the measurements of R and R :
1 2
a) total length of the specimen;
b) distance between the voltage taps (L) ;
c) length of the current contacts;
d) transport currents (I and I );
1 2
e) current densities (I and I divided by the total wire cross-sectional area);
1 2
f) voltages (U , U , U , U *, U , U , U *, U , and U );
1 0+ 0rev 2+ 20+ 0– 2– 20– 2
g) resistances (R , R , and R ) ;
m 1 2
h) material, shape, and dimensions of the base plate;
i) installation method of the specimen in the base plate;
j) insulating material of the base plate.
9.3.2 The following test conditions shall be reported for the measurements of R :
a) temperature setting and holding method of the specimen;
b) T : Temperature for measurement of R
m m.
9.3.3 The following test conditions shall be reported for the measurements of R :
a) rate of increasing temperature;
b) method of cooling down and heating up.

61788-11  IEC:2011 – 13 –
Annex A
(informative)
Additional information relating to the measurement
of the residual resistance ratio (RRR)
A.1 Recommendation on specimen mounting orientation
Horizontal mounting of the wire on the base plate is recommended, since this mounting
orientation can reduce possible thermal gradient along the wire compared to the vertical
mounting orientation. Here the horizontal mounting orientation means that the wire axis is
parallel to the surface of liquid helium.
A.2 Alternate methods for increasing temperature of specimen above
superconducting transition temperature
The following methods are also recommended for increasing temperature above the
superconducting transition of the specimen. The rate of increasing temperature of the whole
specimen within a range between 0,1 K/min and 10 K/min should be applied for these
methods. In order to dampen the rate of increasing temperature and to avoid a large
temperature gradient, special care should be taken in selecting heater power, heat capacity
(the specimen with the measuring base plate) and the distance between the heater and the
specimen.
a) Heater method
The specimen can be heated above the superconducting transition by a heater installed in
the measuring base plate after taking the specimen out of the liquid helium bath in the
cryostat.
b) Adiabatic methods
1) Adiabatic method
In this method, the cryostat holds a chamber in which the specimen, a sample holder,
a heater and so on are contained. Before the chamber is immersed in the liquid helium
bath, air inside the chamber is pumped out and helium gas is filled. Then, the chamber
is immersed in the liquid helium bath and the specimen will be cooled to a temperature
of 5 K or lower. After the helium gas is pumped out, the specimen can be heated
above the superconducting transition by the heater under adiabatic condition.
2) Quasi-adiabatic method
In this method, the cryostat holds the specimen a certain distance above the liquid
helium bath for the entire cryogenic measurement. A thermal anchor from the
measuring base plate to the liquid helium bath allows the specimen to be cooled to a
temperature of 5 K or lower. The specimen can be heated above the superconducting
transition by a heater located in the measuring base plate under quasi-adiabatic
condition.
c) Refrigerator method
In this method, an electromechanical apparatus (a refrigerator) is used to cool the
specimen, which is mounted to a measuring base plate, to a temperature of 5 K or lower.
The specimen can be heated above the superconducting transition by a heater or by
controlling the refrigerator power.
A.3 Alternative R measurement method
The following methods can optionally be used for acquisition of R .
– 14 – 61788-11  IEC:2011
a) Fixed temperature method
In this method R is directly determined at a fixed temperature of 20 K, which is above
and near the transition temperature, instead of the method described in 7.2. In this case, it
is desirable that the whole specimen is at a uniform temperature and the fixed temperature
of 20 K should be determined with a combined standard uncertainty not to exceed 0,6 K.
The fixed temperature and the combined standard uncertainty should be noted in the test
report. Also the U and U , which are defined in the body of the text, should be recorded
0+ 0–
as the zero voltage level in the fixed method. In order to eliminate the influence of
thermoelectric voltage, two voltage signals of the specimen, say U and U , should be
2+ 2–
acquired nearly simultaneously by reversal of the test current. For the fixed method, the
effect of thermoelectric voltage on determination of cryogenic resistance R can well be
eliminated.
b) Computer-based method
A computer can be used to control the current direction and warming of the specimen and
to measure the voltage-temperature curve. Changes in current direction by periodic
current reversals or periodic current on and off cycles are used to correct for off-set
voltages in order that the measurements can be made during one cycle of changing the
specimen temperature. This method is useful when the transition to the normal state is not
too fast. The effect of thermoelectric voltage should also be checked.
c) Other simplified methods with periodic checks
Simplified methods without temperature measurement might also be accepted, if an
operator with sufficient experience performs the measurement using a given apparatus
and if the following condition is satisfied. If a simplified laboratory practice can be shown,
through periodic checks, to achieve the same result as the method in this standard, within
its stated uncertainty, then the simplified practice can be used in place of this reference
method. These periodic checks could be accomplished by doing one of the following:
1) an interlaboratory comparison where one laboratory uses the reference method and
another laboratory uses their simplified method;
2) a single laboratory comparison where one laboratory “checks” its simplified method
against the reference method;
3) periodic measurement of a small set of reference samples with well-known RRR values
using the simplified method.
61788-11  IEC:2011 – 15 –
Annex B
(informative)
Uncertainty considerations
B.1 Overview
In 1995, a number of international standards organizations, including IEC, decided to unify the
use of statistical terms in their standards. It was decided to use the word “uncertainty” for all
quantitative (associated with a number) statistical expressions and eliminate the quantitative
use of “precision” and “accuracy.” The words “accuracy” and “precision” could still be used
qualitatively. The terminology and methods of uncertainty evaluation are standardized in the
Guide to the Expression of Uncertainty in Measurement (GUM) [1] .
It was left to each TC to decide if they were going to change existing and future standards to
be consistent with the new unified approach. Such change is not easy and creates additional
confusion, especially for those who are not familiar with statistics and the term uncertainty. At
the June 2006 TC 90 meeting in Kyoto, it was decided to implement these changes in future
standards.
Converting “accuracy” and “precision” numbers to the equivalent “uncertainty” numbers
requires knowledge about the origins of the numbers. The coverage factor of the original
number may have been 1, 2, 3 or some other number. A manufacturer’s specification that can
sometimes be described by a rectangular distribution will lead to a conversion number of
1/ 3 . The appropriate coverage factor was used when converting the original number to the
equivalent standard uncertainty. The conversion process is not something that the user of the
standard needs to address for compliance to TC 90 standards, it is only explained here to
inform the user about how the numbers were changed in this process. The process of
converting to uncertainty terminology does not alter the user’s need to evaluate their
measurement uncertainty to determine if the criteria of the standard are met.
The procedures outlined in TC 90 measurement standards were designed to limit the
uncertainty of any quantity that could influence the measurement, based on the Convener’s
engineering judgment and propagation of error analysis. Where possible, the standards have
simple limits for the influence of some quantities so that the user is not required to evaluate
the uncertainty of such quantities. The overall uncertainty of a standard was then confirmed
by an interlaboratory comparison.
B.2 Definitions
Statistical definitions can be found in three sources: the GUM, the International Vocabulary of
Basic and General Terms in Metrology (VIM)[2], and the NIST Guidelines for Evaluating and
Expressing the Uncertainty of NIST Measurement Results (NIST)[3]. Not all statistical terms
used in this standard are explicitly defined in the GUM. For example, the terms “relative
standard uncertainty” and “relative combined standard uncertainty” are used in the GUM
(5.1.6, Annex J), but they are not formally defined in the GUM (see [3]).
B.3 Consideration of the uncertainty concept
Statistical evaluations in the past frequently used the Coefficient of Variation (COV) which is
the ratio of the standard deviation and the mean (N.B. the COV is often called the relative
standard deviation). Such evaluations have been used to assess the precision of the
measurements and give the closeness of repeated tests. The standard uncertainty (SU)
___________
The figures in square brackets refer to the reference documents in Clause B.5 of this Annex.

– 16 – 61788-11  IEC:2011
depends more on the number of repeated tests and less on the mean than the COV and
therefore in some cases gives a more realistic picture of the data scatter and test judgment.
The example below shows a set of electronic drift and creep voltage measurements from two
nominally identical extensometers using same signal conditioner and data acquisition system.
The n = 10 data pairs are taken randomly from the spreadsheet of 32 000 cells. Here,
extensometer number one (E ) is at zero offset position whilst extensometer number two (E )
1 2
is deflected to 1 mm. The output signals are in volts.

Table B.1 – Output signals from two nominally identical extensometers
Output signal [V]
E E
1 2
0,001 220 70 2,334 594 73
0,000 610 35 2,334 289 55
0,001 525 88 2,334 289 55
0,001 220 70 2,334 594 73
0,001 525 88 2,334 594 73
0,001 220 70 2,333 984 38
0,001 525 88 2,334 289 55
0,000 915 53 2,334 289 55
0,000 915 53 2,334 594 73
0,001 220 70 2,334 594 73
Table B.2 – Mean values of two output signals
Mean ( X ) [V]
E E
1 2
0,001 190 19 2,334 411 62
n
X
∑ i
i=1
X= [V]
(B.1)
n
Table B.3 – Experimental standard deviations of two output signals
Experimental standard deviation (s) [V]
E E
1 2
0,000 303 48 0,000 213 381
n
s= ⋅ (X − X) [V] (B.2)
∑ i
n−1
i=1
61788-11  IEC:2011 – 17 –
Table B.4 – Standard uncertainties of two output signals
Standard uncertainty (u) [V]
E E
1 2
0,000 095 97 0,000 067 48
s
(B.3)
u= [V]
n
Table B.5 – Coefficient of variations of two output signals
Coefficient of variation (COV) [%]
E E
1 2
25,498 2 0,009 1
s
(B.4)
COV=
X
The standard uncertainty is very similar for the two extensometer deflections. In contrast, the
coefficient of variation COV is nearly a factor of 2 800 different between the two data sets.
This shows the advantage of using the standard uncertainty which is independent of the mean
value.
B.4 Uncertainty evaluation example for TC 90 standards
The observed value of a measurement does not usually coincide with the true value of the
measurand. The observed value may be considered as an estimate of the true value. The
uncertainty is part of the "measurement error" which is an intrinsic part of any measurement.
The magnitude of the uncertainty is both a measure of the metrological quality of the
measurements and improves the knowledge about the measurement procedure. The result of
any physical measurement consists of two parts: an estimate of the true value of the
measurand and the uncertainty of this “best” estimate. The GUM, within this context, is a
guide for a transparent, standardized documentation of the measurement procedure. One can
attempt to measure the true value by measuring “the best estimate” and using uncertainty
evaluations which can be considered as two types: Type A uncertainties (repeated
measurements in the laboratory in general expressed in the form of Gaussian distributions)
and Type B uncertainties (previous experiments, literature data, manufacturer’s information,
etc. often provided in the form of rectangular distributions).
The calculation of uncertainty using the GUM procedure is illustrated in the following example:
a) The user must derive in a first step a mathematical measurement model in form of
identified measurand as a function of all input quantities. A simple example of such a
model is given for the uncertainty of a force measurement using a load cell:
Force as measurand = W (weight of standard as expected) + d (manufacturer’s data) +
W
d (repeated checks of standard weight/day) + d (reproducibility of checks at different
R Re
days).
Here the input quantities are: the measured weight of standard weights using different
balances (Type A), manufacturer’s data (Type B), repeated test results using the digital
electronic system (Type B), and reproducibility of the final values measured on different
days (Type B).
b) The user should identify the type of distribution for each input quantity (e.g. Gaussian
distributions for Type A measurements and rectangular distributions for Type B
measurements).
– 18 – 61788-11  IEC:2011
c) Evaluate the standard uncertainty of the Type A measurements,
s
u = where, s is the experimental standard deviation and n is the total number of
A
n
measured data points.
d) Evaluate the standard uncertainties of the Type B measurements:
u = ⋅ d + . where, d is the range of rectangular distributed values
B W W
e) Calculate the combined standard uncertainty for the measurand by combining all the
standard uncertainties using the expression:
2 2
u = u + u
c A B
In this case, it has been assumed that there is no correlation between input quantities. If
the model equation has terms with products or quotients, the combined standard
uncertainty is evaluated using partial derivatives and the relationship becomes more
complex due to the sensitivity coefficients [4, 5].
f) Optional – the combined standard uncertainty of the estimate of the referred measurand
can be multiplied by a coverage factor (e. g. 1 for 68 % or 2 for 95 % or 3 for 99 %) to
increase
...