IEC GUIDE 115:2007

IEC GUIDE 115
Edition 1.0 2007-09
GUIDE 115
GUIDE 115
Application of uncertainty of measurement to conformity assessment activities
in the electrotechnical sector

Application de l’incertitude de mesure aux activités d’évaluation de la
conformité dans le secteur électrotechnique
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IEC GUIDE 115
Edition 1.0 2007-09
GUIDE 115
GUIDE 115
Application of uncertainty of measurement to conformity assessment activities
in the electrotechnical sector

Application de l’incertitude de mesure aux activités d’évaluation de la
conformité dans le secteur électrotechnique
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
T
CODE PRIX
ICS 17.020; 19.080 ISBN 2-8318-9307-0

– 2 – Guide 115 © IEC:2007
CONTENTS
FOREWORD.03
INTRODUCTION.5H1H4

1 Scope.6H2H5
2 Reference documents.7H3H5
3 Terms and definitions .8H4H5
4 Application of uncertainty of measurement principles .9H5H6
4.1 General .10H6H6
4.2 Uncertainty of measurement principles.11H7H7
4.3 Background .12H8H7
4.4 Uncertainty of measurement principles – Application of procedures .13H9H8
4.5 Conclusion .14H10H10
5 Guidance on making uncertainty of measurement calculations including examples
of how to perform the calculations .15H11H10
5.1 General principles .16H12H10
5.2 Summary of steps when estimating uncertainty .17H13H11
5.3 Simple example – Estimation of measurement uncertainty for a temperature-
rise test with thermocouples .18H14H14

Annex A (informative) Uncertainty of measurement calculations for product
conformity assessment testing – Examples 1 to 6 .19H15H16

Guide 115 © IEC:2007 – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
___________
APPLICATION OF UNCERTAINTY OF MEASUREMENT
TO CONFORMITY ASSESSMENT ACTIVITIES
IN THE ELECTROTECHNICAL SECTOR

FOREWORD
This first edition of IEC Guide 115 has been prepared in accordance with Annex A of Part 1 of
the ISO/IEC Directives by the IECEE/CTL.
The text of this guide is based on the following documents:
Approval document Report on voting
C/1446/DV C/1457/RV
Full information on the voting for the approval of this Guide can be found in the report on
voting indicated in the above table.

– 4 – Guide 115 © IEC:2007
INTRODUCTION
This Guide has been prepared by the IECEE Committee of Testing Laboratories (CTL) to
provide guidance on the practical application of the measurement uncertainty requirements of
ISO/IEC 17025 to the electrical safety testing conducted within the IECEE CB Scheme.
The IECEE CB Scheme is a multilateral, international agreement, among over 40 countries
and some 60 national certification bodies, for the acceptance of test reports on electrical
products tested to IEC standards.
The aim of the CTL is, among other tasks, to define a common understanding of the test
methodology with regard to the IEC standards as well as to ensure and continually improve
the repeatability and reproducibility of test results among the member laboratories.
The practical approach to measurement uncertainty outlined in this Guide has been adopted
for use in the IECEE Schemes, and is also extensively used around the world by testing
laboratories engaged in testing electrical products to national safety standards.
This guide is of particular interest to the following IEC Technical Committees which may
decide to make use of it if necessary:
TECHNICAL COMMITTEE 13: EQUIPMENT FOR ELECTRICAL ENERGY MEASUREMENT, TARIFF
AND LOAD CONTROL
TECHNICAL COMMITTEE 17: SWITCHGEAR AND CONTROLGEAR
TECHNICAL COMMITTEE 18: ELECTRICAL INSTALLATIONS OF SHIPS AND OF MOBILE
AND FIXED OFFSHORE UNITS
TECHNICAL COMMITTEE 20: ELECTRIC CABLES
TECHNICAL COMMITTEE 21: SECONDARY CELLS AND BATTERIES
TECHNICAL COMMITTEE 22: POWER ELECTRONIC SYSTEMS AND EQUIPMENT
TECHNICAL COMMITTEE 23: ELECTRICAL ACCESSORIES
TECHNICAL COMMITTEE 32: FUSES
TECHNICAL COMMITTEE 33: POWER CAPACITORS
TECHNICAL COMMITTEE 34: LAMPS AND RELATED EQUIPMENT
TECHNICAL COMMITTEE 35: PRIMARY CELLS AND BATTERIES
TECHNICAL COMMITTEE 38: INSTRUMENT TRANSFORMERS
TECHNICAL COMMITTEE 39: ELECTRONIC TUBES
TECHNICAL COMMITTEE 40: CAPACITORS AND RESISTORS FOR ELECTRONIC
EQUIPMENT
TECHNICAL COMMITTEE 47: SEMICONDUCTOR DEVICES
TECHNICAL COMMITTEE 59: PERFORMANCE OF HOUSEHOLD ELECTRICAL
APPLIANCES
TECHNICAL COMMITTEE 61: SAFETY OF HOUSEHOLD AND SIMILAR ELECTRICAL
APPLIANCES
TECHNICAL COMMITTEE 62: ELECTRICAL EQUIPMENT IN MEDICAL PRACTICE
TECHNICAL COMMITTEE 64: ELECTRICAL INSTALLATIONS AND PROTECTION
AGAINST ELECTRIC SHOCK
TECHNICAL COMMITTEE 65: INDUSTRIAL-PROCESS MEASUREMENT AND CONTROL
TECHNICAL COMMITTEE 66: SAFETY OF MEASURING, CONTROL AND LABORATORY
EQUIPMENT
TECHNICAL COMMITTEE 76: OPTICAL RADIATION SAFETY AND LASER EQUIPMENT
TECHNICAL COMMITTEE 77: ELECTROMAGNETIC COMPATIBILITY
TECHNICAL COMMITTEE 78: LIVE WORKING
TECHNICAL COMMITTEE 80: MARITIME NAVIGATION AND RADIOCOMMUNICATION
EQUIPMENT AND SYSTEMS
TECHNICAL COMMITTEE 82: SOLAR PHOTOVOLTAIC ENERGY SYSTEMS

Guide 115 © IEC:2007 – 5 –
APPLICATION OF UNCERTAINTY OF MEASUREMENT
TO CONFORMITY ASSESSMENT ACTIVITIES
IN THE ELECTROTECHNICAL SECTOR

1 Scope
This Guide presents a practical approach to the application of uncertainty of measurement to
conformity assessment activities in the electrotechnical sector . It is specifically conceived for
use in IECEE Schemes as well as by testing laboratories engaged in testing electrical
products to national safety standards. Clause 4 describes the application of uncertainty of
measurements principles. Clause 5 provides guidance on making uncertainty of measurement
calculations. Annex A gives some examples relating to uncertainty of measurement
calculations for product conformity assessment testing.
2 Reference documents
ISO/IEC 17025: General requirements for the competence of testing and calibration
laboratories
Guide to the expression of uncertainty in measurement (GUM) (1995)
[BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML]
International vocabulary of basic and general terms in metrology (VIM) (1996)
[BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML]
3 Terms and definitions
For the purposes of this Guide, the following terms and definitions apply.
3.1
coverage factor
number that, when multiplied by the combined standard uncertainty, produces an interval (the
expanded uncertainty) about the measurement result that may be expected to encompass a
large, specified fraction (e.g. 95 %) of the distribution of values that could be reasonably
attributed to the measurand
3.2
combined standard uncertainty
result of the combination of standard uncertainty components
3.3
error of measurement
result of a measurement minus a true value of the measurand (not precisely quantifiable
because true value lies somewhere unknown within the range of uncertainty)
3.4
expanded uncertainty
obtained by multiplying the combined standard uncertainty by a coverage factor
3.5
level of confidence
probability that the value of the measurand lies within the quoted range of uncertainty

– 6 – Guide 115 © IEC:2007
3.6
measurand
quantity subjected to measurement, evaluated in the state assumed by the measured system
during the measurement itself
[IEC 60359:2001]
3.7
quantity X
i
source of uncertainty
3.8
standard deviation
positive square root of the variance
3.9
standard uncertainty
estimated standard deviation
3.10
uncertainty (of measurement)
parameter, associated with the result of a measurement, that characterizes the dispersion of
the values that could reasonably be attributed to the measurand
[IEC 60359:2001, modified]
3.11
type A evaluation method
method of evaluation of uncertainty of measurement by the statistical analysis of series of
observations
3.12
type B evaluation method
method of evaluation of uncertainty of measurement by means other than the statistical
analysis of series of observations
4 Application of uncertainty of measurement principles
4.1 General
4.1.1 Qualification and acceptance of CB test laboratories (CBTL), e.g. in the IECEE, is
performed according to IEC/ISO 17025, which states in 5.4.6.2:
“Testing laboratories shall have and apply procedures for estimating uncertainty of measure-
ment. In certain cases, the nature of the test method may preclude rigourous, metrologically
and statistically valid, calculation of uncertainty of measurement. In these cases the
laboratory shall at least attempt to identify all the components of uncertainty and make a
reasonable estimation, and shall ensure that the form of reporting of the result does not give a
wrong impression of the uncertainty. Reasonable estimation shall be based on knowledge of
the performance of the method and on the measurement scope and shall make use of, for
example, previous experience and validation data.
NOTE 1 The degree of rigour needed in an estimation of uncertainty of measurement depends on factors
such as:
– the requirements of the test method;
– the requirements of the client;
– the existence of narrow limits on which decisions on conformance to a specification are based.
NOTE 2 In those cases where a well-recognized test method specifies limits to the values of the major
sources of uncertainty of measurement and specifies the form of presentation of calculated results, the
laboratory is considered to have satisfied this clause by following the test method and reporting
instructions (see 5.10).”
Guide 115 © IEC:2007 – 7 –
4.1.2 IEC/ISO 17025, 5.10.3.1, item c), states:
“Subclause 5.10.3.1 includes the following:
c) where applicable, a statement on the estimated uncertainty of measurement; information
on uncertainty is needed in test reports, when it is relevant to the validity of application of
the test results, when a client’s instruction so requires, or when the uncertainty affects
compliance to a specification limit.”
4.1.3 IEC/ISO 17025 was written as a general use document, for all industries. Uncertainty
of measurement principles are applied to laboratory testing and presentation of test results to
provide a degree of assurance that decisions made about conformance of the products tested
according to the relevant requirements are valid. Procedures and techniques for uncertainty of
measurement calculations are well established. This CB Testing Laboratory (CBTL) procedure
is written to provide more specific guidance on the application of uncertainty of measurement
principles to reporting of testing results under the CB Scheme.
4.1.4 This clause of CBTL procedure focuses on the application of uncertainty of
measurement principles under the CB Scheme, while, Clause 5 of CBTL procedure provides
guidance on making uncertainty of measurement calculations and includes examples.
4.2 Uncertainty of measurement principles
4.2.1 A challenge to applying uncertainty of measurement principles to conformity assess-
ment activities is managing the cost, time and practical aspects of determining the
relationships between various sources of uncertainty. Some relationships are either unknown
or would take considerable effort, time and cost to establish. There are a number of proven
techniques available to address this challenge. These techniques include eliminating from
consideration those sources of variability, which have little influence on the outcome and
minimizing significant sources of variability by controlling them.
4.3 Background
4.3.1 Test methods used under the IECEE CB Scheme are in essence consensus standards.
Criteria used to determine conformance with requirements are most often based on a
consensus of judgment of what the limits of the test result should be. Exceeding the limit by a
small amount does not result in an imminent hazard. Test methods used may have a precision
statement expressing the maximum permissible uncertainty expected to be achieved when the
method is used. Historically, test laboratories have used state-of-the-art equipment and not
considered uncertainty of measurement when comparing results to limits. Safety standards
have been developed in this environment and the limits in the standards reflect this practice.
4.3.2 Test parameters that influence the results of tests can be numerous. Nominal
variations in some test parameters have little effect on the uncertainty of the measurement
result. Variations in other parameters may have an effect. However, the degree of influence
can be minimized by limiting the variability of the parameter when performing the test.
4.3.3 A frequent way of accounting for the effects of test parameters on tests results is to
define the acceptable limits of variability of test parameters. When this is done, any variability
in measurement results obtained due to changes in the controlled parameters is not
considered significant if the parameters are controlled within the limits. Examples of the
application of this technique require:
a) input power source to be maintained: voltage ±2 %, frequency ±0,5 %, total harmonic
distortion maximum 3 %;
b) ambient temperature: 23 °C ± 2 °C;
c) relative humidity: 93 % ± 2 % (RH);
d) personnel: documented technical competency requirements for the test;
e) procedures: documented laboratory procedures;

– 8 – Guide 115 © IEC:2007
f) equipment accuracy: instrumentation with accuracy according to CTL decision 251A.
NOTE The acceptable limits in items a) through c) are given as examples and do not necessarily represent actual
limits established.
4.3.4 The end result of controlling sources of variability within prescribed limits is that the
measurement result can be used as the best estimate of the measurand. In effect, the
uncertainty of measurement about the measured result is negligible with regard to the final
pass/fail decision.
4.4 Uncertainty of measurement principles – Application of procedures
4.4.1 When a test results in measurement of a variable, there is uncertainty associated with
the test result obtained
4.4.2 Procedure 1, see Figure 1, is used when calculation of uncertainty of measurement is
required by IEC/ISO 17025, 5.4.6.2 and 5.10.3.1 item c). Calculate the uncertainty for
measurement (see Clause 5) and compare the measured result with the uncertainty band to a
defined acceptable limit. The measurement complies with the requirement if the probability of
its being within the limit is at least 50 %.

Limit
Fail
Fail
Pass
Measurement result
Pass
Upper limit of uncertainty
Lower limit of uncertainty
Measurement
Figure 1 – Procedure 1: uncertainty of measurement calculated
4.4.3 Procedure 2, see Figure 2, is used when IEC/ISO 17025, 5.4.6.2, Note 2, applies.
Procedure 2 is the traditional method used under the CB Scheme and has been referred to as
the “accuracy method”. The test performed is routine. Sources of uncertainty are minimized so
that the uncertainty of the measurement need not be calculated to determine conformance
with the limit. Variability in test parameters is within acceptable limits. Test parameters such
as power source voltage, ambient temperature and ambient humidity are maintained within
the defined acceptable limits for the test. Personnel training and laboratory procedures
minimize uncertainty of measurement due to human factors. Instrumentation used has an
uncertainty within prescribed limits.
Measured value
Guide 115 © IEC:2007 – 9 –
NOTE The name, accuracy method, comes from the concept of limiting uncertainty due to instrumentation by
using instruments within prescribed accuracy limits. For this purpose, the accuracy specification for an instrument
is considered the maximum uncertainty of measurement attributable to the instrument.

Limit
Fail
Pass
Pass
Measurement result
Measurement
Figure 2 – Procedure 2: accuracy method
4.4.4 The measurement result is considered in conformance with the requirement if it is
within the prescribed limit. It is not necessary to calculate the uncertainty associated with the
measurement result.
4.4.5 Example – Procedure 2
• Power supply output voltage measurement test
a) Method
Connect the power supply to a mains source of rated voltage, ±2 %, and rated
frequency. Measure output voltage from power supply while loaded to rated current,
±2 %, with a non-inductive resistive load. The test is to be performed in an ambient
temperature of 23 °C ± 2 °C.
Use metres having an accuracy conforming to CTL decision 251A.
The power supply conforms to the requirements if the output voltage is ±5 % of rated
value.
b) Results
Power supply rating: 240 V, 50 Hz input; 5 V d.c., 2 A output.
Input Output
U Frequency I U
V Hz A V
242 50 2,01 5,1
Test ambient temperature: 24 °C.
Measured value
– 10 – Guide 115 © IEC:2007
The accuracy of the instruments used is shown in the following table:
Metre Calibrated accuracy for scale CTL decision 251A, max.
used for measurement
Thermometer ±1,0 °C ±2,0 °C
Voltmeter ±0,5 % ±1,5 %
Frequency ±0,2 % ±0,2 %
Current ±0,5 % ±1,5 %
The conclusion of the test is that the power supply conforms to the requirement.
4.5 Conclusion
4.5.1 The traditional approach to addressing uncertainty of measurement for conformity
assessment activities under the CB Scheme, has been the application of the accuracy
method. This method minimizes sources of uncertainty associated with the performance of
routine tests so that the measurement result can be directly compared with the test limit to
determine conformance with the requirement. This method conforms to the requirements in
IEC/ISO 17025. The accuracy method takes less time and costs less to implement than
detailed uncertainty of measurement calculations and the conclusions reached are valid with
regard to the final pass/fail decision.
4.5.2 In situations where the traditional, accuracy method does not apply, uncertainty of
measurement values are calculated and reported along with the variables results obtained
during testing.
5 Guidance on making uncertainty of measurement calculations including
examples of how to perform the calculations
5.1 General principles
5.1.1 This clause is meant to be a short and simplified summary of the steps to be taken by
a CBTL when the need to estimate uncertainties arises. It also includes examples of how to
perform the calculations.
5.1.2 It is by no means a comprehensive paper about measurement uncertainty (MU), its
sources and estimation in general, but is supposed to offer a practical approach for most
applicable circumstances within a CBTL in the IECEE CB Scheme.
5.1.3 No measurement is perfect and the imperfections give rise to error of measurement in
the result. Consequently, the result of a measurement is only an approximation to the
measured value (measurand) and is only complete when accompanied by a statement of the
uncertainty of that approximation. Indeed, because of measurement uncertainty, a true value
can never be known.
5.1.4 The total uncertainty of a measurement is a combination of a number of component
uncertainties. Even a single instrument reading may be influenced by several factors. Careful
consideration of each measurement involved in the test is required to identify and list all the
factors that contribute to the overall uncertainty. This is a very important step and requires a
good understanding of the measuring equipment, the principles and practice of the test and
the influence of environment.
5.1.5 The Guide to the expression of uncertainty in measurement (GUM) has adopted the
approach of grouping uncertainty components into two categories based on their method of
evaluation, Type A and Type B. This categorization of the methods of evaluation, rather than
of the components themselves, avoids certain ambiguities.

Guide 115 © IEC:2007 – 11 –
5.1.6 Type A evaluation is carried out by calculation from a series of repeated observations,
using statistical methods.
5.1.7 Type B evaluation is carried out by means other than that used for Type A. For
example, by judgment based on the following table.
Data in calibration certificates This enables corrections to be made and type B
uncertainties to be assigned
Previous measurement data For example, history graphs can be constructed and
yield useful information about changes with time
Experience with or general knowledge Behaviour and properties of similar materials and
equipment
Accepted values of constants Associated with materials and quantities
Manufacturers’ specifications
All other relevant information

5.1.8 Individual uncertainties are evaluated by the appropriate method and each is
expressed as a standard deviation and is referred to as a standard uncertainty.
5.2 Summary of steps when estimating uncertainty
5.2.1 Identify the factors that may significantly influence the measured values and review
their applicability. There are many possible sources in practice, mainly including.
a) Contribution from calibration of the measuring instruments, including contribution from
reference or working standards.
b) Temperature error at the beginning and end of a test (e.g. winding resistance method).
c) Uncertainty related to the loading applied and the measurement of it.
d) Velocity of air flow over the test sample and uncertainty in measuring it.
e) For digital instruments, there are the number of displayed digits and the stability of the
display at the time the reading is taken. In addition, the reported uncertainty of an
instrument does not necessarily include the display.
f) Instrument resolution, limits in graduation of a scale.
g) Approximations and assumptions incorporated in the measurement method.
h) Uncertainty due to the procedures used to prepare the sample for test and actually testing
it.
i) If a computer is used to acquire the readings from the instrument, there is uncertainty
associated with the processing of the data due to calculations or other manipulations
within the computer such as analog to digital conversions, and conversions between
floating point and integer numbers.
k) Rounded values of constants and other parameters used for calculations.
m) Effects of environmental conditions (e.g. variation in ambient temperature) or
measurement of these on the measurement.
--> Negligible in case environmental conditions are stable (assumed and expected from a
CBTL).
n) Variability of the power supply source (voltage, current, frequency) the sample is
connected to and the uncertainty in measuring it.
--> Negligible in case stabilized supply sources are used (assumed and expected from a
CBTL).
o) Personal bias in reading analogue instruments
(e.g. parallax error or the number of significant figures that can be interpolated).
--> Negligible in case of digital displays or in case of appropriate training
(assumed and expected from a CBTL).
p) Variation between test samples and in case the samples are not fully representative.

– 12 – Guide 115 © IEC:2007
Unless the IEC standard specifies tests on multiple samples, only one sample is tested.
--> The variation between test samples is assumed to be negligible by CBTLs
NOTE This list does not state all of the items that can contribute to MU. Other factors may have to be identified
and considered by each laboratory respectively.
5.2.2 Transform influencing factors x to the unit of the measured value (quantify), for which
i
you are going to estimate the uncertainty, if not already given in that unit (e.g. if the unit of the
measured value is V and a resistor's tolerance in Ω is one of the influencing factors, transform
the change of resistance to the resulting contribution in V).
Once the uncertainty contributions associated with a measurement process have been
identified and quantified, it is necessary to combine them in some manner in order to provide
a single value of uncertainty that can be associated with the measurement result.
5.2.3 Determine the probability distribution
The probability distribution of the measured quantity describes the variation in probability of
the true value lying at any particular difference from the measured or assigned result. The
form of the probability distribution will often not be known, and an assumption has to be
made, based on prior knowledge or theory, that it approximates to one of the common forms.
It is then possible to calculate the standard uncertainty, U(x ), for the assigned form from
i
simple expressions. The four main distributions of interest are
– normal;
– rectangular;
– triangular;
– U-shaped.
5.2.4 Normal distribution is assigned when the uncertainty is taken from, for example, a
calibration certificate/report where the coverage factor, k, is stated. The standard uncertainty
is found by dividing the stated uncertainty from the calibration certificate by its coverage
factor k, which is k = 2 for a level of confidence of approximately 95 % (recommended for
CBTL in the IECEE CB scheme). It may be necessary to confirm k with the calibration
laboratory in case it is not stated on the certificate.
uncertainty
Normal: u(x ) =
i
k
5.2.5 Rectangular distribution means that the probability density is constant within the
prescribed limits. A rectangular distribution should be assigned where a manufacturer's
specification limits are used as the uncertainty, unless there is a statement of confidence
associated with the specification, in which case a normal distribution can be assumed.
a
i
Rectangular: u(x ) =
i
where a is the half width of the rectangular distribution.
i
5.2.6 U-shaped distribution is applicable to mismatch uncertainty. The value of the limit for
the mismatch uncertainty, M, associated with the power transfer at a junction is obtained from
100 ((1± Γ Γ ) − 1) % or 20 log (1 ± Γ Γ ) dB (logarithmic units)
G L 10 G L
where Γ and Γ are the reflection coefficients for the source and load.
G L
Guide 115 © IEC:2007 – 13 –
The mismatch uncertainty is asymmetric about the measured result; however, the difference
this makes to the total uncertainty is often insignificant, and it is acceptable to use the larger
of the two limits.
U-shaped distribution is used for EMC purposes but also for climatic control of temperature
and humidity.
M
U-shaped: u(x ) =
i
5.2.7 Triangular distribution means that the probability of the true value lying at a point
between two prescribed limits increases uniformly from zero at the extremities to the
maximum at the centre. A triangular distribution should be assigned where the contribution
has a distribution with defined limits and where the majority of the values between the limits
lie around the central point.
a
i
u x =
Triangular: ( )
i
5.2.8 A detailed approach to the determination of probability distribution can be found in the
Guide to the expression of uncertainty in measurement (GUM).
5.2.9 Correlation: For the statistical approach to the combination of individual uncertainty
contributions to be valid, there shall be no common factors associated with these
contributions.
5.2.10 The effect of correlated input quantities may be to increase or decrease the combined
standard uncertainty. For example, if the area of a rectangle is determined by measurement of
its width and height using the same measuring implement the correlation will increase the
uncertainty. On the other hand, if a gauge block were to be measured by comparison with
another of identical material, the effect of uncertainty due to temperature will depend on the
difference in temperature between the two blocks and will therefore tend to cancel.
5.2.11 If the correlation is such that the combined standard uncertainty is increased, the
most straightforward approach is to add the standard uncertainties for these quantities before
combining the result statistically with other contributions.
5.2.12 If, however, the correlation is such that the combined standard uncertainty will be
decreased, as in the gauge-block comparison above, the difference in standard uncertainty
would be used as the input quantity.
5.2.13 A detailed approach to the treatment of correlated input quantities can be found in the
GUM.
5.2.14 Establish the uncertainty budget m , containing the standard uncertainties of each
x
influencing factor (quantity) u(x). Usually u(x) will already represent the uncertainty
i i
contribution u (y) of each factor. A convenient way to do that is to write the identified and
i
potential contributing factors and their estimates into a table (see examples). The uncertainty
contribution u(m ) is calculated by the formula:
x
2 2 2
u(m ) = SQRT (u (y) + u (y) + . + u (y) )
x 1 2 i
5.2.15 Calculate the expanded uncertainty U, considering your level of confidence.
The expanded uncertainty is calculated by multiplying the standard uncertainty with the
coverage factor k, which is k = 2 for a level of confidence of approximately 95 %
(recommended for CBTL in the IECEE CB scheme), or k = 3 for approximately 99,7 % level of
confidence.
u = k × u(m )
x
– 14 – Guide 115 © IEC:2007
5.2.16 Report the result of the measurement comprising the measured value, the associated
expanded uncertainty U and the coverage factor k.
Example: 10,5 V ± 0,4 V (coverage factor k = 2, for a level of confidence of approximately
95 %).
5.3 Simple example – Estimation of measurement uncertainty for a temperature-rise
test with thermocouples
The following example has been chosen to demonstrate the basic method of evaluating the
uncertainty of measurement. It has been simplified in order to provide transparency for the
reader and intended to be general guidance on how to proceed. The contributions and values
are not intended to imply mandatory or preferred requirements. The input quantities are
regarded as being not correlated.
a) Identification of significant influencing factors
Quantity Source of uncertainty Source of error quantity
s (x )
X
p i
i
Uncertainty of thermocouple For example, from specifications
δ
TC
Uncertainty of hybrid recorder For example, from the calibration certificate of
δ
HR
a calibration laboratory, including their inherited
uncertainty and the listed coverage factor of
k = 3
Influence of fixing method of thermocouples For example, from the laboratory's own
δ
Fixing
investigation campaign
Uncertainty of ambient temperature For example, measured by a separate
δ
ambient
measurement instrument, data taken from the manufacturer's
specifications
b) Relating influencing factors to the measured value
The relationship between the influencing factor and the measured value evaluated at the
point of measurement is known as the sensitivity coefficient. In this simple example, there
is a 1-to-1 relationship between the influencing factors and the measured value.
Therefore, the sensitivity coefficient is 1. For more complex relationships, the sensitivity
coefficient can take on other values.
Quantity Estimate Sensitivity Error quantity
X x coefficient s (x )
i i p i
δ –40 °C to +350 °C 1 0,5 °C
TC
δ Worst case of calibrated items, e.g. –25 °C 1 1,8 °C
HR
to +250 °C
Worst case of investigated temperatures, 1 2,4 °C
δ
Fixing
e.g. 25 °C, 85 °C, 150 °C
Usually used in the vicinity of 25 °C 1 1,25 °C
δ
ambient
c) Uncertainty budget, m
x
Quantity Estimate Error Probability Standard Sensitivity Uncertainty
X x quantity distribution uncertainty coefficient contribution
i i
s (x ) u(x ) u (y)
p i i i
–40 °C to 0,5 °C Rectangular 0,29 °C 1 0,29 °C
δ
TC
+350 °C
–25 °C to 1,8 °C Normal 0,6 °C 1 0,6 °C
δ
HR
+250 °C
25 °C, 85 °C, 2,4 °C Normal 2,4 °C 1 2,4 °C
δ
Fixing
150 °C
– 1,25 °C Rectangular 0,72 °C 1 0,72 °C
δ
ambient
m 25 °C to 150 °C   u(m ) =
x x
2,63 °C
Guide 115 © IEC:2007 – 15 –
2 2 2
()
u()m = u + u + u +.
x 1 2 3
3 = 1,73, 6 = 2,45
d) Expanded uncertainty, U
U = k × u(m ) = 2 × 2,63 °C = 5,27 °C = approximately 5,3 °C
x
e) Reported result
The measured temperature rise is xx,x K ± 5,3 °C
The reported expanded uncertainty of measurement is stated as the standard uncertainty
of measurement multiplied by the coverage factor k = 2, which for a normal distribution
corresponds to a coverage probability of approximately 95 %.

– 16 – Guide 115 © IEC:2007
Annex A
(informative)
Uncertainty of measurement calculations for product
conformity assessment testing –
Examples 1 to 6
IECEE CTL WG 1 provides the following set of examples of calculations to illustrate the
application of uncertainty of measurement to conformity assessment activities carried out
under the IECEE CB Scheme.
Example 1 – Input test
Example 2 – Input power test
Example 3 – Leakage current measurement test
Example 4 – Distance measurement using caliper gauge
Example 5 – Torque measurement
Example 6 – Pre-conditioning for ball pressure test
These examples have been simplified to illustrate various steps of the process for performing
uncertainty of measurement calculations.

Guide 115 © IEC:2007 – 17 –
Example 1
Test name: input test.
Result: uncertainty of input current expressed in per cent of reading in amperes.
Description: Input current is measured to product connected to mains power source.
Input current to product is proportional to voltage applied.
Quan- Source of X Type Relative Probability Distri- Relative Sensitivity Relative
i
tity uncertainty error shape bution standard coefficient, uncertainty
X quantity, division uncer- C contribu-
i i
S (X ) factor, tainty, tion, u (y)
p i i
k u(X )
i
Repeatability X A Normal 0,2 % 1 0,2 %
δ
R
R
of
measurement
Specification X B 0,5 % Rectangular 0,3% 1 0,3 %
δ
instr
instr
for instrument
Reading error X B 0,3 % Rectangular 0,17 % 1 0,17 %
δ
reading
reading
Specification X B 0,17 % Rectangular 0,1 % 1 0,1 %
δ
power
power
for power
mains
fluctuation
Relative combined standard uncertainty, u 0,41 %
c
Coverage factor k = 2; confidence level: 95 % –
p
0,81 %
Relative expanded uncertainty, U = u × K
c P
Reported result – The measured input current is m (1 ± 0,0081) A, k = 2, 95 % confidence
x
level.
δ repeatability of measurement – uncertainty due to repeatedly making the same
R
measurement – Type A with normal distribution
()x − x
∑ i
u = σ = = 0,2 %
n−1
n(n − 1)
δ specification for instrument – uncertainty due to instrument used for
instr
measurements. Determined from specifications in instrument manual (MPE). Meter is
0,5 class. Error is ±0,5 %. Rectangular distribution, k = 3.
u = 0,5 / 3 = 0,3 %
δ reading of instrument – uncertainty due to technician reading the instrument. When
reading
testing meter is 0,5 A per graduation and 100 graduations, estimating reading error is
1/10 graduation. In the practice testing, reading value is 34,8 line. Rectangular
distribution, k = 3.
u [(0,1)(0,5)]/[(34,5)(0,5) 3] × 100 = 0,17 %
3 =
δ power mains fluctuation – uncertainty due to fluctuations in power mains voltage.
power
Uncertainty of the regulator is 0,2%. Rectangular distribution, k = 3 . Sensitivity
coefficient = 1.
u = 0,2 / 3 = 0,1 %
– 18 – Guide 115 © IEC:2007
Example 2
Test name: input power test.
Result: uncertainties expressed in per cent of input power in watts.
Description: input power is measured to product operating in stabile condition while connected
to regulated mains power source. Input power measured by analog or digital power meter.
Quan- Source of X Type Relative Probability Distri- Relative Sensitivity Relative
i
tity uncertainty error shape bution standard coefficient, uncertainty
X quantity, division uncer- C contribu-
i i
S (X ) factor, tainty, tion, u (y)
p i i
k u(X )
i
Repeatability X A Normal 0,2 % 1 0,2 %
δ
R
R
of
measurement
Specification X A 0,2 % Normal 2 0,1 % 1 0,1 %
δ
instr
instr
for instrument
Reading error X B 0,45 % Rectangular 0,26 % 1 0,26 %
δ
reading
reading
δ Specification X B 0,35 % Rectangular 0,2 % 1 0,20 %
power power
for power
mains
fluctuation
Relative combined standard uncertainty, u 0,40 %
c
Coverage factor k = 2; confidence level: 95 % –
p
0,80 %
Relative expanded uncertainty, U = u × k
c p
Reported Result – The measured input power is m (1 ± 0,008) W, k = 2, 95 % confidence
x
level.
δ repeating error repeatability of measurement – uncertainty due to repeatedly
R
making the same measurement – Type A with normal distribution
()
x − x
∑ i
u = σ = = 0,2 %
n−1
n(n − 1)
δ specification for instrument – uncertainty due to instrument used for measure-
instr
ments. Determined from calibration laboratory report. Expanded uncertainty
reported is ±0,2. Distribution is normal, k = 2.
u = 0,2/2 = 0,1 %
δ reading of instrument – uncertainty due to technician reading instrument –
reading
estimated.
δ specification of power mains fluctuation – uncertainty due to fluctuations in
power
power mains voltage.
Guide 115 © IEC:2007 – 19 –
Example 3
Test name: leakage current measurement.
Result: uncertainties of leakage current expressed in micro-amperes.
Description: leakage current is measured with product operating under normal working
conditions. Leakage current is measured directly by a leakage current metre. The measure-
ment is carried out under following conditions.
a) Between any pole of the power source and metal parts that can be easily touched or the
metal foil on the insulating materials that can be easily touched, not exceeding 20 cm by
10 cm.
b) Between any pole of the power source and the metal parts only using basic insulation to
separate live parts of 1 stage apparatus.
c) Before and after humidity conditioning.
Tested parts are
– between live parts and the enclosure isolated from the live part by only basic insulation;
– between th
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