SIST-TP CEN ISO/TR 16491:2014

Guidelines for the evaluation of uncertainty of measurement in air conditioner and heat pump cooling and heating capacity tests (ISO/DTR 16491:2012)

This Technical Specification gives guidance on the practical applications of the principles of performance measurement of air-cooled air-conditioners and air-to-air heat pumps as described in ISO 5151, ISO 13253, and ISO 15042.

Leitfaden zur Bestimmung der Messunsicherheit von Kälte- und Heizleistungsprüfungen bei Luftkonditionierern und Wärmepumpen (ISO/DTR 16491:2012)

Diese Technische Spezifikation enthält eine Anleitung zu den praktischen Anwendungen jener Prinzipien bei der Leistungsbemessung von luftgekühlten Luftkonditionierungsgeräten und Luft/Luft-Wärmepumpen, die in ISO 5151, ISO 13253 und ISO 15042 beschrieben sind.

Lignes directrices pour l'évaluation de l'incertitude de mesure lors des essais de puissance frigorifique et calorifique des climatiseurs et des pompes à chaleur (ISO/DTR 16491:2012)

L'ISO/TS 16491:2012 donne des lignes directrices pour les applications pratiques des principes de mesure de la performance des climatiseurs à condensation par air et des pompes à chaleur air/air tels que décrits dans l'ISO 5151, l'ISO 13253 et l'ISO 15042.

Smernice za vrednotenje merilne negotovosti preskusov učinkovitosti hlajenja in ogrevanja klimatskih naprav in toplotnih črpalk (ISO/DTR 16491:2012)

Ta tehnična specifikacija vsebuje navodila za praktično uporabo načel za oceno delovanja zračno hlajenih klimatskih naprav in toplotnih črpalk zrak-zrak, kot je opisano v standardih ISO 5151, ISO 13253 in ISO 15042.

General Information

• Status: Published
• Publication Date: 15-Dec-2013
• ICS: 23.120 - Ventilators. Fans. Air-conditioners
• ICS: 27.080 - Heat pumps
• Technical Committee: OGS - Heating for buildings
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 04-Dec-2013
• Due Date: 08-Feb-2014
• Completion Date: 16-Dec-2013
• Ref Project: CEN ISO/TS 16491:2012 - Guidelines for the evaluation of uncertainty of measurement in air conditioner and heat pump cooling and heating capacity tests (ISO/TS 16491:2012)

Standards Content (Sample)

SLOVENSKI STANDARD
SIST-TP CEN ISO/TR 16491:2014
01-januar-2014
6PHUQLFH]DYUHGQRWHQMHPHULOQHQHJRWRYRVWLSUHVNXVRYXþLQNRYLWRVWLKODMHQMDLQ
RJUHYDQMDNOLPDWVNLKQDSUDYLQWRSORWQLKþUSDON,62'75
Guidelines for the evaluation of uncertainty of measurement in air conditioner and heat
pump cooling and heating capacity tests (ISO/DTR 16491:2012)
Leitfaden zur Bestimmung der Messunsicherheit von Kälte- und Heizleistungsprüfungen
bei Luftkonditionierern und Wärmepumpen (ISO/DTR 16491:2012)
Lignes directrices pour l'évaluation de l'incertitude de mesure lors des essais de
puissance frigorifique et calorifique des climatiseurs et des pompes à chaleur (ISO/DTR
16491:2012)
Ta slovenski standard je istoveten z: CEN ISO/TS 16491:2012
ICS:
23.120 =UDþQLNL9HWUQLNL.OLPDWVNH Ventilators. Fans. Air-
QDSUDYH conditioners
27.080 7RSORWQHþUSDONH Heat pumps
SIST-TP CEN ISO/TR 16491:2014 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST-TP CEN ISO/TR 16491:2014

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SIST-TP CEN ISO/TR 16491:2014


TECHNICAL SPECIFICATION
CEN ISO/TS 16491

SPÉCIFICATION TECHNIQUE

TECHNISCHE SPEZIFIKATION
December 2012
ICS 23.120; 27.080
English Version
Guidelines for the evaluation of uncertainty of measurement in
air conditioner and heat pump cooling and heating capacity tests
(ISO/TS 16491:2012)
Lignes directrices pour l'évaluation de l'incertitude de Leitlinien für die Beurteilung der Messunsicherheit bei der
mesure lors des essais de puissance frigorifique et Prüfung der Kühl- und Heizleistung von Klimaanlagen und
calorifique des climatiseurs et des pompes à chaleur Wärmepumpen (ISO/TS 16491:2012)
(ISO/TS 16491:2012)
This Technical Specification (CEN/TS) was approved by CEN on 20 November 2012 for provisional application.

The period of validity of this CEN/TS is limited initially to three years. After two years the members of CEN will be requested to submit their
comments, particularly on the question whether the CEN/TS can be converted into a European Standard.

CEN members are required to announce the existence of this CEN/TS in the same way as for an EN and to make the CEN/TS available
promptly at national level in an appropriate form. It is permissible to keep conflicting national standards in force (in parallel to the CEN/TS)
until the final decision about the possible conversion of the CEN/TS into an EN is reached.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United
Kingdom.





EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2012 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN ISO/TS 16491:2012: E
worldwide for CEN national Members.

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CEN ISO/TS 16491:2012 (E)
Contents Page
Foreword . 3

2

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CEN ISO/TS 16491:2012 (E)
Foreword
This document (CEN ISO/TS 16491:2012) has been prepared by Technical Committee ISO/TC 86
"Refrigeration and air-conditioning" in collaboration with Technical Committee CEN/TC 113 “Heat pumps and
air conditioning units” the secretariat of which is held by AENOR.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to announce this Technical Specification: Austria, Belgium, Bulgaria, Croatia, Cyprus,
Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany,
Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland,
Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
Endorsement notice
The text of ISO/TS 16491:2012 has been approved by CEN as a CEN ISO/TS 16491:2012 without any
modification.
3

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SIST-TP CEN ISO/TR 16491:2014

TECHNICAL ISO/TS
SPECIFICATION 16491
First edition
2012-12-01

Guidelines for the evaluation of
uncertainty of measurement in air
conditioner and heat pump cooling and
heating capacity tests
Lignes directrices pour l'évaluation de l'incertitude de mesure lors des
essais de puissance frigorifique et calorifique des climatiseurs et des
pompes à chaleur




Reference number
ISO/TS 16491:2012(E)
©
ISO 2012

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ISO/TS 16491:2012(E)

COPYRIGHT PROTECTED DOCUMENT


©  ISO 2012
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56  CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail [e-mail]
Web www.iso.org
Published in Switzerland

ii © ISO 2012 – All rights reserved

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ISO/TS 16491:2012(E)
Contents Page
Foreword . iv
Introduction . v
1  Scope . 1
2  Normative references . 1
3  Terms and definitions . 1
4  Symbols . 3
5  Method of calculation . 4
5.1  Calibration . 4
5.2  Correction . 4
5.3  (Instrumental) drift . 4
5.4  Stability . 4
5.5  Uncertainty due to the lack of homogeneity . 4
6  Explanatory notes useful in laboratory application . 4
6.1  Uncertainty . 4
6.2  Confidence level . 4
6.3  Evaluation of errors . 5
6.4  Steps in evaluation of uncertainty in measurements . 5
6.5  Uncertainty of measurements . 5
7  Evaluation of uncertainty — Calorimeter room method . 7
7.1  Cooling capacity test . 8
7.2  Heating capacity test . 11
8  Evaluation of uncertainty — Air enthalpy method . 14
8.1  Cooling capacity test . 15
8.2  Heating capacity test . 16
8.3  Uncertainty of measurement on the air volume flow rate . 18
Annex A (normative) Uncertainty budget sheets . 19
Annex B (informative) Determination of indirect contribution to uncertainty, U(C ) . 27
I
Bibliography . 28

© ISO 2012 – All rights reserved iii

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ISO/TS 16491:2012(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In other circumstances, particularly when there is an urgent market requirement for such documents, a
technical committee may decide to publish other types of document:
 an ISO Publicly Available Specification (ISO/PAS) represents an agreement between technical experts in
an ISO working group and is accepted for publication if it is approved by more than 50 % of the members
of the parent committee casting a vote;
 an ISO Technical Specification (ISO/TS) represents an agreement between the members of a technical
committee and is accepted for publication if it is approved by 2/3 of the members of the committee casting
a vote.
An ISO/PAS or ISO/TS is reviewed after three years in order to decide whether it will be confirmed for a
further three years, revised to become an International Standard, or withdrawn. If the ISO/PAS or ISO/TS is
confirmed, it is reviewed again after a further three years, at which time it must either be transformed into an
International Standard or be withdrawn.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TS 16491 was prepared by Technical Committee ISO/TC 86, Refrigeration and air-conditioning,
Subcommittee SC 6, Air-cooled air conditioners and air-to-air heat pumps.
iv © ISO 2012 – All rights reserved

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ISO/TS 16491:2012(E)
Introduction
This Technical Specification is intended to be a practical guide to assist laboratory personnel in evaluating the
uncertainties in the measurement of the cooling and heating capacities of air conditioners and heat pumps. It
contains a brief introduction to the theoretical basis for the calculations, and contains examples of uncertainty
budget sheets that can be used as a basis for the determination of the uncertainty of measurement.

© ISO 2012 – All rights reserved v

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SIST-TP CEN ISO/TR 16491:2014
TECHNICAL SPECIFICATION ISO/TS 16491:2012(E)

Guidelines for the evaluation of uncertainty of measurement in
air conditioner and heat pump cooling and heating capacity
tests
1 Scope
This Technical Specification gives guidance on the practical applications of the principles of performance
measurement of air-cooled air-conditioners and air-to-air heat pumps as described in ISO 5151, ISO 13253,
and ISO 15042.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO/IEC Guide 99, International vocabulary of metrology — Basic and general concepts and associated terms
(VIM)
ISO/IEC Guide 98-3, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in
measurement (GUM:1995)
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 5151, Non-ducted air conditioners and heat pumps — Testing and rating for performance
ISO 13253, Ducted air-conditioners and air-to-air heat pumps — Testing and rating for performance
ISO 15042, Multiple split-system air-conditioners and air-to-air heat pumps — Testing and rating for
performance
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO/IEC Guide 99, ISO/IEC Guide 98-3,
ISO 3534-1, ISO 5151, ISO 13253 and ISO 15042 apply.
NOTE The definitions of terms 3.1, 3.2, 3.3, 3.4 and 3.5 are taken from ISO/IEC Guide 99:2007, 2.39, 4.14, 2.53,
4.21 and 4.19, respectively, and they are repeated here for easy reference.
3.1
calibration
operation that, under specified conditions, in a first step, establishes a relation between the quantity values
with measurement uncertainties provided by measurement standards and corresponding indications with
associated measurement uncertainties and, in a second step, uses this information to establish a relation for
obtaining a measurement result from an indication
[SOURCE: ISO/IEC Guide 99:2007, 2.39]
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ISO/TS 16491:2012(E)
3.2
resolution
smallest change in a quantity being measured that causes a perceptible change in the corresponding
indication
[SOURCE: ISO/IEC Guide 99:2007, 4.14]
NOTE In the case of a digital instrument, this value corresponds to the value of the least significant digit of the
reading of the instrument. This value might be different on the overall range of an instrument.
3.3
correction
modification applied to a measured quantity value to compensate for a known systematic effect
[SOURCE: ISO/IEC Guide 99:2007, 2.53, modified]
3.4
(instrumental) drift
continuous change in an indication, related neither to a change in the quantity being measured nor to a
change of any recognized influence quantity
[SOURCE: ISO/IEC Guide 99:2007, 4.21, modified]
3.5
stability
ability of a measuring instrument or measuring system to maintain its metrological properties constant with
time
[SOURCE: ISO/IEC Guide 99:2007, 4.19, modified]
3.6
uncertainty due to the lack of homogeneity
component specific to air temperature measurements where several probes are used simultaneously
NOTE In this case the air temperature value used in the calculation of heat power is the mean of the measurements
of the different probes.
3.7 Type of error evaluation
3.7.1
type A evaluation of standard uncertainty
evaluation of standard uncertainty based on any valid statistical method for treating data
NOTE Examples are calculating the standard deviation of the mean of a series of independent observations, using
the method of least squares to fit a curve to data in order to evaluate the parameters of the curve and their standard
deviations, and carrying out an analysis of variance in order to identify and quantify random effects in certain kinds of
measurements. If the measurement situation is especially complicated, one should consider obtaining the guidance of a
statistician.
3.7.2
type B evaluation of standard uncertainty
evaluation of standard uncertainty that is usually based on scientific judgment using all the relevant
information available
NOTE Relevant information can include
 previous measurement data,
 experience with, or general knowledge of, the behaviour and property of relevant materials and instruments,
 manufacturer’s specifications,
 data provided in calibration and other reports, and
 uncertainties assigned to reference data taken from handbooks.
2 © ISO 2012 – All rights reserved

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4 Symbols
For the purposes of this document, the symbols defined in ISO 5151, ISO 13253 and ISO 15042 and the
following apply.
Symbol Description Unit
e water vapour partial pressure Pa
e (T ) water vapour partial pressure at T Pa
w d d
f enhancement factor, considered as a constant value equal to 1 —
w
heat leakage coefficient between the indoor side compartment of the
-1
K W·K
S,i
calorimeter and its surroundings
heat leakage coefficient between the outdoor side compartment of the -1
K W·K
S,o
calorimeter and its surroundings
heat leakage coefficient between indoor side and outdoor side
-1
K W·K
S,p
compartments of the calorimeter through the separating partition
m dry air mass kg
a
-1
M dry air mass molar molar (kg·mol )
a
-1
M water vapour mass molar molar (kg·mol )
v
N number of sensors —
N number of values recorded during the acquisition time —
T
p atmospheric pressure Pa
p dry air partial pressure Pa
a
p water vapour partial pressure at wet-bulb temperature T Pa
w w
water flow rate through the coil of the indoor side compartment of the
q kg/s
iw
calorimeter
water flow rate through the coil of the outdoor side compartment of the
q kg/s
ow
calorimeter
R perfect gas constant —
T air dry bulb temperature °C
T air dew point temperature °C
d
T value measured by the sensor i —
i
T mean value measured by N sensors —
m
T air temperature in the indoor side compartment of the calorimeter °C
iam
T air temperature in the outdoor side compartment of the calorimeter °C
oam
air temperature in the surroundings of the indoor side compartment of the
T °C
iscm
calorimeter
air temperature in the surroundings of the outdoor side compartment of
T °C
oscm
the calorimeter
water inlet temperature to coil of the indoor side compartment of the
T °C
iwi
calorimeter
water outlet temperature to coil of the indoor side compartment of the
T °C
iwo
calorimeter
water inlet temperature to coil of the outdoor side compartment of the
T °C
owi
calorimeter
water outlet temperature to coil of the outdoor side compartment of the
T °C
owo
calorimeter
U(C ) indirect contribution to expanded uncertainty W
I
u(C ) indirect contribution to standard uncertainty W
I
3
V dry air volume m
 ratio of the water vapour mass molar to the dry air mass molar (0,62198) —
© ISO 2012 – All rights reserved 3

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ISO/TS 16491:2012(E)
5 Method of calculation
5.1 Calibration
This value is given in the calibration certificate.
This value is the calibration uncertainty which takes into account the reference instrument and the calibrated
instrument. The calibration uncertainty shall be at a confidence level of at least 95 %.
5.2 Correction
This quantity concerns here the calibration correction.
If this calibration correction is applied on the raw measurement of the instrument through a modelisation curve,
this term is the maximum difference between the correction model and the calibration results. If no correction
is applied on the raw measurement of the instrument, this correction is linearly added to the expanded
measurement uncertainty.
5.3 (Instrumental) drift
This value is calculated as the difference in successive calibration corrections.
5.4 Stability
The quantity is generally a mean of several instantaneous data measured in a given period of time. The
uncertainty component due to stability is calculated as the standard deviation of the instantaneous
measurements, and the standard uncertainty of the mean value is defined as this standard deviation divided
by the square root of the number of recorded data.
5.5 Uncertainty due to the lack of homogeneity
The uncertainty component due to homogeneity is calculated as the standard deviation of the individual
measurements, and the standard uncertainty of the mean value is defined as this standard deviation divided
by the square root of the number of probes.
6 Explanatory notes useful in laboratory application
6.1 Uncertainty
No measurement of a real quantity can be exact; there is always some error involved in the measurement.
Errors may arise because of measuring instruments not being exact, because the conditions of the test are
not precise, or for many other reasons, including human error. The likely magnitude of this error in
measurement is known as the uncertainty. Uncertainty may be expressed as a range of test results
(e.g. 10 kW  0,1 kW), or as a fraction or percentage of the test result (e.g. 10 kW  1 %).
6.2 Confidence level
Confidence level refers to the probability that the true result of a measurement lies within the range stated by
the uncertainty. For example, if the measurement of a power is given as 10,0 kW  1 % at a confidence level
of 95 %, this means that there is not more than 5 % probability that the true value of the power is outside the
range 9,90 kW to 10,10 kW. A confidence level of 95 % is usually used for engineering measurements; this
provides a good compromise between reliability of measurements and the cost of making those
measurements.
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ISO/TS 16491:2012(E)
6.3 Evaluation of errors
Two types of error evaluation are recognized by ISO Guide 98-3. A type A evaluation involves statistical
methods of evaluation of the errors, and may only be used where there are repeated measurements of the
same quantity. A type B evaluation is one using any other means, and may require the use of knowledge of
the measurement system, such as calibration certificates for instruments and experience in determining what
factors may produce errors in the measurement.
6.4 Steps in evaluation of uncertainty in measurements
To evaluate the uncertainty in a measurement, it is necessary to follow a series of steps.
a) A model of the measurement system must be developed, that lists all the factors that contribute to the
measurement.
b) Examination of this model will determine the magnitude of the contribution of each source of error to the
final measurement error.
c) In many cases the units of the final measurement will differ from the units of the various measurements
involved. For example, the measurement of the cooling capacity of an air-conditioner (in kilowatts, kW)
will involve the measurement of temperatures (in degrees Celsius, °C) or temperature differences
(in Kelvin, K). In these cases, it is necessary to determine weighting factors to describe the effect that
errors in these measurements will have on the final measurement of capacity. These weighting factors
are known as sensitivity coefficients.
d) Once all the factors contributing to the final measurement are evaluated, together with their sensitivity
coefficients, they must be combined to give the overall uncertainty in the final measurement.
6.5 Uncertainty of measurements
6.5.1 Uncertainty of individual measurements
The uncertainty of measurement of each individual measurement shall take into account the different
components of uncertainties as described below, where appropriate.
Table 1 — Components of uncertainties for individual measurements
Value from
Coverage factor, k
Source of Evaluation calibration Probability
[ISO/IEC Guide Standard uncertainty
uncertainty basis certificate or distribution
a
99:2007, 2.38]
actual value
U
Calibration
1
u 
Calibration U Normal 2
1
1
certificate
2
U
2
u 
Resolution Specifications U Rectangular
2 23
2
23
— — u
3
Calibration
Correction U (see 6.5.1 NOTE 1 (see 6.5.1 NOTE 1 (see 6.5.1 NOTE 1
3
certificate
and NOTE 2) and NOTE 2) and NOTE 2)
U
Calibration
4
u 
Drift U Rectangular
4 3
4
certificate
3
S
5
Standard deviation

S N
Stability (in time) Mean 5
T
on a mean value N
T
a
Number larger than one by which a combined standard measurement uncertainty is multiplied to obtain an expanded measurement
uncertainty.
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SIST-TP CEN ISO/TR 16491:2014
ISO/TS 16491:2012(E)
The expanded uncertainty, U, is thus calculated as follows.
a) If the calibration correction is applied:
2

S
22 222
5

U 2uuuuu (1)
12 3 4 i

N
T

NOTE 1 If the calibration correction value U is applied directly, then the evaluated value of u = 0. In case that the
3 3
averaged value of deviations at several calibration points is applied as correction factor, the value of u arising from
3
incomplete correction is evaluated from the variance of deviations remaining after the correction value has been applied to
each calibration data.
b) If the calibration correction is not applied:
2

S
22 22 5
U 2uuuuU (2)
12 4 i 3

N
T

NOTE 2 It should be avoided that the uncertainty is enlarged with no correction. However, if the correction value is
small compared to the uncertainty, there may be a case where correction is not needed. If the value of the calibration
correction U is entered in Equation (2), then u = 0.
3 3
6.5.2 Uncertainty of a mean value from several measurements
If several sensors are used for determining a mean value, this mean value is calculated with the following
equation:
N
T
 i
i1
T  (3)
m
N
The uncertainty of this mean value shall be calculated from the uncertainty of each individual measurement to
which an additional component for homogeneity is added as follows, assuming the individual measurements
to be correlated:
2
N

uT

 i 2

s
i1
uT ,

m  
N
N




leading to:
22
NN
  
UT

i
  
UT

22i
2
  
s s
ii11
(4)
UT22uT   2 
  
mm   
NN2
NN
  
  
  
  
where
u(T ) is the standard uncertainty on the mean value;
m
U(T ) is the expanded uncertainty on the mean value;
m
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ISO/TS 16491:2012(E)
u(T ) is the standard measurement uncertainty of the sensor i, determined according to Table 1;
i
U(T ) is the expanded measurement uncertainty of the sensor i, determined according to Table 1;
i
s is the standard deviation on the mean value (calculating from the N individual measurements, T ).
i
NOTE According to ISO/IEC Guide 98-3:2008, 5.2.2 NOTE 1, for the very special case where all of the input
estimates are correlated with correlation coefficients equal to 1, the uncertainty of measurements with the following
equation:
2
N

2

uy cux
cii

i1
22
NN
  

  
leads to, for the mean value, uT uT N uT N .

mii
  

ii11 

6.5.3 Uncertainty of a value obtained by using a smoothing curve
If a value, V(m), is determined from a measurement m and the use of a smoothing curve, then the term:
2
uV()m
shall be replaced by:
2

V
22
 
mum u V()m (5)
  
i i smooth
m



where
um is the standard uncertainty on each measurement m (determined according to Table 1);
i
i
uV ()m is the st
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