IEC 60216-3:2021

Electrical insulating materials - Thermal endurance properties - Part 3: Instructions for calculating thermal endurance characteristics

IEC 60216-3:2021 specifies the calculation procedures used for deriving thermal endurance characteristics from experimental data obtained in accordance with the instructions of IEC 60216-1 and IEC 60216-2, using fixed ageing temperatures and variable ageing times. The experimental data can be obtained using non-destructive, destructive or proof tests. Data obtained from non-destructive or proof tests can be incomplete, in that it is possible that measurement of times taken to reach the end-point will have been terminated at some point after the median time but before all specimens have reached end-point. The procedures are illustrated by worked examples, and suitable computer programs are recommended to facilitate the calculations.
This edition includes the following significant technical changes with respect to the previous edition:
- a new computer program has been included;
- Annex E " has been completely reworked.

Matériaux isolants électriques - Propriétés d’endurance thermique - Partie 3: Instructions pour le calcul des caractéristiques d’endurance thermique

L'IEC 60216-3:2021 spécifie les méthodes de calcul utilisées pour obtenir les caractéristiques d'endurance thermique à partir des données expérimentales obtenues conformément aux instructions de l'IEC 60216-1 et de l'IEC 60216-2, en utilisant des températures de vieillissement fixes et des temps de vieillissement variables.
Les données expérimentales peuvent être obtenues en utilisant des essais non destructifs, des essais destructifs ou des essais d'épreuve. Les données obtenues à partir d'essais non destructifs ou d'essais d'épreuve peuvent être incomplètes, en ce sens que le mesurage des temps mis pour atteindre le point limite peut avoir été interrompu à un moment situé après le temps médian, mais avant que toutes les éprouvettes n'aient atteint le point limite. Les méthodes sont illustrées par des exemples pratiques, et des programmes informatiques adaptés sont recommandés pour faciliter les calculs.
Cette édition inclut les modifications techniques majeures suivantes par rapport à l'édition précédente:
- un nouveau programme informatique est inclus;
- l'Annexe E a été complètement remaniée.

General Information

• Status: Published
• Publication Date: 15-Mar-2021
• ICS: 17.220.99 - Other standards related to electricity and magnetism
• ICS: 19.020 - Test conditions and procedures in general
• Technical Committee: TC 112 - Evaluation and qualification of electrical insulating materials and systems
• Drafting Committee: WG 1 - TC 112/WG 1
• Current Stage: PPUB - Publication issued
• Start Date: 16-Mar-2021
• Completion Date: 26-Feb-2021

Relations

• Revises: IEC 60216-3:2006/COR1:2009 - Corrigendum 1 - Electrical insulating materials - Thermal endurance properties - Part 3: Instructions for calculating thermal endurance characteristics
• Effective Date: 05-Sep-2023
• Revises: IEC 60216-3:2006 - Electrical insulating materials - Thermal endurance properties - Part 3: Instructions for calculating thermal endurance characteristics
• Effective Date: 05-Sep-2023

Overview

IEC 60216-3:2021 - part of the IEC 60216 series - provides standardized calculation procedures for deriving thermal endurance characteristics of electrical insulating materials from experimental ageing data. It applies when tests use fixed ageing temperatures and variable ageing times, and supports data from non‑destructive, destructive or proof tests. The standard explains how to handle incomplete (censored) data, illustrates procedures with worked examples, and recommends a computer program (Annex E) to facilitate calculations. This third edition includes a new program and a reworked Annex E.

Key topics and technical requirements

• Input data types: Procedures accept non‑destructive, proof and destructive test results, including incomplete (censored) data sets.
• Preliminary processing: Group selection, temperature-to‑x conversions and handling of incomplete measurements.
• Statistical methods: Calculation of group means and variances, regression analysis, variance equality tests, linearity (F‑test), and confidence limits for X and Y estimates.
• Censored data handling: Specific coefficients and methods for proof/non‑destructive tests where end‑point observations may be terminated early.
• Results and reporting: Generation of thermal endurance graphs, calculation of characteristic times/temperatures, precision/uncertainty assessments and required content for the test report.
• Decision aids and examples: Decision flow chart and table (Annex A/B), statistical tables (Annex C), and worked examples (Annex D) to guide practical calculations.
• Software support: Annex E details a recommended computer program, file formats and example data to streamline implementation.

Practical applications and users

IEC 60216-3:2021 is intended for professionals and organizations involved in the evaluation and qualification of insulating materials and systems:

• Materials and reliability engineers using accelerated ageing data to predict service life and temperature limits.
• Testing laboratories performing thermal endurance measurements and producing compliant test reports.
• R&D teams comparing formulations or processing routes under controlled thermal stress.
• Manufacturers establishing material specifications, design margins and quality assurance procedures.
• Certification bodies and compliance assessors that require standardized, traceable calculation methods.

Practical uses include lifetime estimation, material selection for high‑temperature applications, validation of insulation systems and generation of standardized thermal endurance graphs for specifications.

Related standards

• IEC 60216-1 - General instructions for aging tests (referenced for experimental data).
• IEC 60216-2 - Instructions for performing ageing tests (data acquisition methods referenced by Part 3).

Keywords: IEC 60216-3:2021, thermal endurance, electrical insulating materials, calculation procedures, accelerated ageing, non‑destructive tests, proof tests, destructive tests, statistical analysis, insulation lifetime.

Standards Content (Sample)

IEC 60216-3 ®
Edition 3.0 2021-03
REDLINE VERSION
INTERNATIONAL
STANDARD
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Electrical insulating materials – Thermal endurance properties –
Part 3: Instructions for calculating thermal endurance characteristics

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IEC 60216-3 ®
Edition 3.0 2021-03
REDLINE VERSION
INTERNATIONAL
STANDARD
colour
inside
Electrical insulating materials – Thermal endurance properties –

Part 3: Instructions for calculating thermal endurance characteristics

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 17.220.99; 19.020 ISBN 978-2-8322-9583-0

– 2 – IEC 60216-3:2021 RLV © IEC 2021
CONTENTS
FOREWORD . 4
1 Scope . 6
2 Normative references . 6
3 Terms, definitions, symbols and abbreviated terms . 6
3.1 Terms and definitions . 6
3.2 Symbols and abbreviated terms . 8
4 Principles of calculations . 10
4.1 General principles . 10
4.2 Preliminary calculations . 11
4.2.1 General . 11
4.2.2 Non-destructive tests . 11
4.2.3 Proof tests . 11
4.2.4 Destructive tests . 11
4.3 Variance calculations . 12
4.4 Statistical tests . 12
4.5 Results . 13
5 Requirements and recommendations for valid calculations . 13
5.1 Requirements for experimental data . 13
5.1.1 General . 13
5.1.2 Non-destructive tests . 13
5.1.3 Proof tests . 13
5.1.4 Destructive tests . 13
5.2 Precision of calculations . 14
6 Calculation procedures . 14
6.1 Preliminary calculations . 14
6.1.1 Temperatures and x-values . 14
6.1.2 Non-destructive tests . 14
6.1.3 Proof tests . 14
6.1.4 Destructive tests . 14
6.1.5 Incomplete data . 18
6.2 Main calculations . 18
6.2.1 Calculation of group means and variances . 18
6.2.2 General means and variances . 19
6.2.3 Regression calculations . 20
6.3 Statistical tests . 21
6.3.1 Variance equality test . 21
6.3.2 Linearity test (F-test) . 21
6.3.3 Confidence limits of X and Y estimates . 22
6.4 Thermal endurance graph . 23
7 Calculation and requirements for results . 23
7.1 Calculation of thermal endurance characteristics . 23
7.2 Summary of statistical tests and reporting . 24
7.3 Reporting of results . 24
8 Test report . 24
Annex A (normative) Decision flow chart . 26

Annex B (normative) Decision table . 28
Annex C (informative) Statistical tables . 29
Annex D (informative) Worked examples. 39
Annex E (informative)  Computer program . 48
E.1 General . 55
E.1.1 Overview . 55
E.1.2 Convenience program execution . 56
E.2 Structure of data files used by the program . 58
E.2.1 Text file formats . 58
E.2.2 Office Open XML formats. 59
E.3 Data files for computer program . 60
E.4 Output files and graph . 65
Bibliography . 66

Figure 1 – Example of groups selection . 15
Figure A.1 – Decision flow chart . 27
Figure D.1 – Thermal endurance graph . 44
Figure D.2 – Example 3: Property-time graph (destructive-test data) . 46
Figure E.1 – Shortcut property dialog for program launch . 57
Figure E.2 – Thermal endurance graph of example N3 . 65

Table B.1 – Decisions and actions according to tests . 28
Table C.1 – Coefficients for censored data calculations . 29
Table C.2 – Fractiles of the F-distribution, F(0,95, f , f ) . 35
n d
Table C.3 – Fractiles of the F-distribution, F(0,995, f , f ) . 36
n d
Table C.4 – Fractiles of the t-distribution, t . 38
0,95
Table C.5 – Fractiles of the χ -distribution . 38
Table D.1 – Worked example 1 – Censored data (proof tests: file CENEX3.DTA) . 39
Table D.2 – Worked example 2 – Complete data (non-destructive tests: file
TEST2.DTA) . 41
Table D.3 – Worked example 3 – Destructive tests . 45
Table D.4 – Worked example 3 – Selection of groups . 47
Table E.1 – Non-destructive test data . 58
Table E.2 – Destructive test data . 58
Table E.3 – Non-destructive test data . 59
Table E.4 – Destructive test data . 59

– 4 – IEC 60216-3:2021 RLV © IEC 2021
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ELECTRICAL INSULATING MATERIALS –
THERMAL ENDURANCE PROPERTIES –

Part 3: Instructions for calculating
thermal endurance characteristics

FOREWORD
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This redline version of the official IEC Standard allows the user to identify the changes
made to the previous edition IEC 60216-3:2006. A vertical bar appears in the margin
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strikethrough red text.
IEC 60216-3 has been prepared by IEC technical committee 112: Evaluation and qualification
of electrical insulating materials and systems. It is an International Standard.
This third edition cancels and replaces the second edition published in 2006. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) a new computer program has been included;
b) Annex E " has been completely reworked.
The text of this International Standard is based on the following documents:
Draft Report on voting
112/475/CDV 112/495/RVC
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this International Standard is English.
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement,
available at www.iec.ch/members_experts/refdocs. The main document types developed by
IEC are described in greater detail at www.iec.ch/standardsdev/publications.
A list of all parts in the IEC 60216 series, published under the general title Electrical insulating
materials – Thermal endurance properties, can be found on the IEC website.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under webstore.iec.ch in the data related to the
specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
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– 6 – IEC 60216-3:2021 RLV © IEC 2021
ELECTRICAL INSULATING MATERIALS –
THERMAL ENDURANCE PROPERTIES –

Part 3: Instructions for calculating
thermal endurance characteristics

1 Scope
This part of IEC 60216 specifies the calculation procedures to be used for deriving thermal
endurance characteristics from experimental data obtained in accordance with the instructions
of IEC 60216-1 and IEC 60216-2 [1] , using fixed ageing temperatures and variable ageing
times.
The experimental data may can be obtained using non-destructive, destructive or proof tests.
Data obtained from non-destructive or proof tests may can be incomplete, in that it is possible
that measurement of times taken to reach the end-point may will have been terminated at
some point after the median time but before all specimens have reached end-point.
The procedures are illustrated by worked examples, and suitable computer programs are
recommended to facilitate the calculations.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their
content constitutes requirements 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 60216-1:20012013, Electrical insulating materials – Thermal endurance properties – Part
1: Ageing procedures and evaluation of test results
IEC 60216-2:2005, Electrical insulating materials – Properties of thermal endurance – Part 2:
Determination of thermal endurance properties of electrical insulating materials – Choice of
test criteria
IEC 60493-1:1974, Guide for the statistical analysis of ageing test data – Part 1: Methods
based on mean values of normally distributed test results
3 Terms, definitions, symbols and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the following definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at https://www.iso.org/obp
___________
Numbers in square brackets refer to the bibliography.

3.1.1
ordered data
group of data arranged in sequence so that in the appropriate direction through the sequence
each member is greater than, or equal to, its predecessor
Note 1 to entry: In this document, ascending order implies that the data is ordered in this way, the first being the
smallest.
Note 2 to entry: It has been established that the term "group" is used in the theoretical statistics literature to
represent a subset of the whole data set. The group comprises those data having the same value of one of the
parameters of the set (e.g. ageing temperature). A group may itself comprise a number of sub-groups
characterized by another parameter (e.g. time in the case of destructive tests).
3.1.2
order-statistic
each individual value in a group of ordered data is referred to as an order-statistic identified
by its numerical position in the sequence
assigned numerical position in the sequence of individual values in a group of ordered data
3.1.3
incomplete data
ordered data, where the values above and/or below defined points are not known
3.1.4
censored data
incomplete data, where the number of unknown values is known
Note 1 to entry: If the censoring is begun above/below a specified numerical value, the censoring is Type I.
If above/below a specified order-statistic it is Type II. This document is concerned only with Type II.
3.1.5
degrees of freedom
number of data values minus the number of parameter values
3.1.6
variance of a data group
sum of the squares of the deviations of the data from a reference level
Note 1 to entry: The reference level may be defined by one or more parameters, for example a mean value (one
parameter) or a line (two parameters, slope and intercept), divided by the number of degrees of freedom.
3.1.7
central second moment of a data group
sum of the squares of the differences between the data values and the value of the group
mean, divided by the number of data in the group
3.1.8
covariance of data groups
for two groups of data with equal numbers of elements where each element in one group
corresponds to one in the other, the sum of the products of the deviations of the
corresponding members from their group means, divided by the number of degrees of
freedom
3.1.9
regression analysis
process of deducing the best-fit line expressing the relation of corresponding members of two
data groups by minimizing the sum of squares of deviations of members of one of the groups
from the line
Note 1 to entry: The parameters are referred to as the regression coefficients.

– 8 – IEC 60216-3:2021 RLV © IEC 2021
3.1.10
correlation coefficient
number expressing the completeness of the relation between members of two data groups,
equal to the covariance divided by the square root of the product of the variances of the
groups
Note 1 to entry: The value of its square is between 0 (no correlation) and 1 (complete correlation).
3.1.11
end-point line
line parallel to the time axis intercepting the property axis at the end-point value
Note 1 to entry: For guidance on the choice of end-point value, refer to IEC 60216-2.
3.2 Symbols and abbreviated terms
Subclause
a Regression coefficient (y-intercept) 4.3, 6.2
a Regression coefficient for destructive test calculations 6.1
p
b Regression coefficient (slope) 4.3, 6.2
b Regression coefficient for destructive test calculations 6.1
p
b 6.3
ˆ
r
X
Intermediate constant (calculation of )
c
c 6.3
Intermediate constant (calculation of χ )
f Number of degrees of freedom Table C.2 to
Table C.5
F Fisher distributed stochastic variable 4.2, 6.1, 6.3
F Tabulated value of F (linearity of thermal endurance graph) 4.4, 6.3
F Tabulated value of F (linearity of property graph – significance 6.1
0,05)
F Tabulated value of F (linearity of property graph – significance 6.1
0,005)
g Order number of ageing time for destructive tests 6.1
h Order number of property value for destructive tests 6.1
HIC Halving interval at temperature equal to TI 4.3, Clause 7
HIC Halving interval corresponding to TI 7.3
g g
i Order number of exposure temperature 4.1, 6.2
j Order number of time to end-point 4.1, 6.2
k Number of ageing temperatures 4.1, 6.2
m Number of specimens aged at temperature ϑ 4.1, 6.1
i i
N Total number of times to end-point 6.2
n Number of property values in group aged for time τ 6.1
g g
n Number of values of y at temperature ϑ 4.1, 6.1
i i
p
Mean value of property values in selected groups 6.1
p Value of diagnostic property 6.1
P 4.4, 6.3.1
Significance level of χ distribution
p Value of diagnostic property at end-point for destructive tests 6.1
e
6.1
Mean of property values in group aged for time τ
p
g
g
p Individual property value 6.1
gh
Subclause
q Base of logarithms 6.3
r Number of ageing times selected for inclusion in calculation 6.1
(destructive tests)
r Square of correlation coefficient 6.2.3
s 2 2 6.3
s s
Weighted mean of and
1 2
2 2 4.3, 6.1 to 6.3
s Weighted mean of s , pooled variance within selected groups
1 1i
2 4.4, 6.3
s
Adjusted value of
s
( 1 )
a
6.1
Variance of property values in group aged for time τ
s g
1g
2 4.3, 6.2
Variance of y values at temperature ϑ
ij
i
s
1i
2 Variance about regression line 6.1 to 6.3
s
2 Adjusted value of s 6.3
s
a
Intermediate constant 6.3
s
r
2 Variance of Y 6.3
s
Y
t Student distributed stochastic variable 6.3
t Adjusted value of t (incomplete data) 6.3
c
TC Lower 95 % confidence limit of TI 4.4, 7
TC Adjusted value of TC 7.1
a
TI Temperature index 4.3, Clause 7
TI Temperature index at 10 kh 7.1
TI Adjusted value of TI 7.3
a
TI Temperature index obtained by graphical means or without 7.3
g
defined confidence limits
x Independent variable: reciprocal of thermodynamic
temperature
x Weighted mean value of x 6.2
X Specified value of x for estimation of y 6.3
ˆ
Estimated value of x at specified value of y 6.3
X
ˆ
6.3
ˆ Upper 95 % confidence limit of
X
X
c
x Reciprocal of thermodynamic temperature corresponding to ϑ 4.1, 6.1
i i
y
Weighted mean value of y 6.2
y Dependent variable: logarithm of time to end-point
ˆ
Estimated value of y at specified value of x 6.3

Y
Y Specified value of y for estimation of x 6.3
ˆ
6.3
ˆ
Lower 95 % confidence limit of Y
Y
c
y
4.3, 6.2
i Mean values of y at temperature ϑ
ij i
y Value of y corresponding to τ 4.1, 6.1
ij ij
– 10 – IEC 60216-3:2021 RLV © IEC 2021
Subclause
Mean value of z 6.1
z
g
z Logarithm of ageing time for destructive tests – group g 6.1
g
α Censored data coefficient for variance 4.3, 6.2
β Censored data coefficient for variance 4.3, 6.2
ε Censored data coefficient for variance of mean 4.3, 6.2
Temperature 0 °C on the thermodynamic scale (273,15 K) 4.1, 6.1
Θ
ˆ
Estimate of temperature for temperature index 6.3.3
ϑ
ˆ
Confidence limit of 6.3.3
ˆ ϑ
ϑ
c
ϑ Ageing temperature for group i 4.1, 6.1
i
μ Censored data coefficient for mean 4.3, 6.2
μ (x) Central second moment of x values 6.2, 6.3
ν Total number of property values selected at one ageing 6.1
temperature
τ Time selected for estimate of temperature 6.3
f
Time of ageing for selected group g 6.1
τ
g
Times to end-point 6.4
τ
ij
2 2
χ χ -distributed stochastic variable 6.3
4 Principles of calculations
4.1 General principles
The general calculation procedures and instructions given in Clause 6 are based on the
principles set out in IEC 60493-1 [2]. These may be simplified as follows (see 3.7.1 of
IEC 60493-1:1974):
a) the relation between the mean of the logarithms of the times taken to reach the specified
end-point (times to end-point) and the reciprocal of the thermodynamic (absolute)
temperature is linear;
b) the values of the deviations of the logarithms of the times to end-point from the linear
relation are normally distributed with a variance which is independent of the ageing
temperature.
The data used in the general calculation procedures are obtained from the experimental data
by a preliminary calculation. The details of this calculation are dependent on the character of
the diagnostic test: non-destructive, proof or destructive (see 4.2). In all cases the data
comprise values of x, y, m, n and k
where
x = 1/(ϑ + Θ ) is the reciprocal of thermodynamic value of ageing temperature ϑ in °C;
i i 0 i
y = log τ is the logarithm of the value of time (j) to end-point at temperature ϑ ;
ij ij i
n is the number of y values in group number i aged at temperature ϑ ;
i i
m is the number of samples in group number i aged at temperature ϑ
i i
(different from n for censored data);
i
k is the number of ageing temperatures or groups of y values.
NOTE Any number may can be used as the base for logarithms, provided consistency is observed throughout
calculations. The use of natural logarithms (base e) is recommended beneficial, since most computer programming
languages and scientific calculators have this facility.

4.2 Preliminary calculations
4.2.1 General
In all cases, the reciprocals of the thermodynamic values of the ageing temperatures are
calculated as the values of x .
i
The values of y are calculated as the values of the logarithms of the individual times to end-
ij
point τ obtained as described below.
ij
In many cases of non-destructive and proof tests, it is advisable for economic reasons, (for
example, when the scatter of the data is high) to stop ageing before all specimens have
reached the end-point, at least for some temperature groups. In such cases, the procedure for
calculation on censored data (see 6.2.1.3) shall be carried out on the (x, y) data available.
Groups of complete and incomplete data or groups censored at a different point for each
ageing temperature may be used together in one calculation in 6.2.1.3.
4.2.2 Non-destructive tests
Non-destructive tests (for example, loss of mass on ageing) give directly the value of the
diagnostic property of each specimen each time it is measured, at the end of an ageing
period. The time to end-point τ is therefore available, either directly or by linear interpolation
ij
between consecutive measurements.
4.2.3 Proof tests
The time to end-point τ for an individual specimen is taken as the mid-point of the ageing
ij
period immediately prior to reaching the end-point (6.3.2 of IEC 60216-1:2001).
4.2.4 Destructive tests
When destructive test criteria are employed, each test specimen is destroyed in obtaining a
property value and its time to end-point cannot therefore be measured directly.
To enable estimates of the times to end-point to be obtained, the assumptions are made that
in the vicinity of the end-point:
a) the relation between the mean property values and the logarithm of the ageing time is
approximately linear;
b) the values of the deviations of the individual property values from this linear relation are
normally distributed with a variance which is independent of the ageing time;
c) the curves of property versus logarithm of time for the individual test specimens are
straight lines parallel to the line representing the relation of a) above.
For the application of these assumptions, an ageing curve is drawn for the data obtained at
each of the ageing times. The curve is obtained by plotting the mean value of property for
each specimen group against the logarithm of its ageing time. If possible, ageing is continued
at each temperature until at least one group mean is beyond the end-point level. An
approximately linear region of this curve is drawn in the vicinity of the end-point line (see
Figure D.2).
A statistical test (F-test) is carried out to decide whether deviations from linearity of the
selected region are acceptable (see 6.1.4, step 4). If acceptable, then, on the same graph,
points representing the properties of the individual specimens are drawn. A line parallel to the
ageing line is drawn through each individual specimen data point. The estimate of
the logarithm of the time to end-point for that specimen (y ) is then the value of the logarithm
ij
of time corresponding to the intersection of the line with the end-point line (Figure D.2).

– 12 – IEC 60216-3:2021 RLV © IEC 2021
With some limitations, an extrapolation of the linear mean value graph to the end-point level is
permitted.
The above operations are executed numerically in the calculations detailed in 6.1.4.
4.3 Variance calculations
Commencing with the values of x and y obtained in 4.2, the following calculations are made:
s
For each group of y values, the mean y and variance are calculated, and from the latter
1i
ij i
the pooled variance within the groups, s , is derived, weighting the groups according to size.
For incomplete data, the calculations have been developed from those originated by Saw [3]
and given in 6.2.1.3. For the coefficients required (µ for mean, α, β for variance and ε for
deriving the variance of mean from the group variance) see Annex C, Table C.1. For multiple
groups, the variances are pooled, weighting according to the group size. The mean value of
the group values of ε is obtained without weighting, and multiplied by the pooled variance.
NOTE The weighting according to the group size is implicit in the definition of ε, which here is equal to that
originally proposed by Saw, multiplied by the group size. This makes for simpler representation in equations.
From the means and the values of x , the coefficients a and b (the coefficients of the best
y
i i
fit linear representation of the relationship between x and y) are calculated by linear
regression analysis.
From the regression coefficients, the values of TI and HIC are calculated. The variance of
the deviations from the regression line is calculated from the regression coefficients and the
group means.
4.4 Statistical tests
The following statistical tests are made:
a) Fisher test for linearity (Fisher test, F-test) on destructive test data prior to the calculation
of estimated times to end-point (see 4.2.4);
b) variance equality (Bartlett's χ -test) to establish whether the variances within the groups of
y values differ significantly;
c) F-test to establish whether the ratio of the deviations from the regression line to the
pooled variance within the data groups is greater than the reference value F , i.e. to test
the validity of the Arrhenius hypothesis as applied to the test data.
In the case of data of very small dispersion, it is possible for a non-linearity to be detected as
statistically significant which is of little practical importance.
In order that a result may be obtained even where the requirements of the F-test are not met
for this reason, a procedure is included as follows:
s
1) increase the value of the pooled variance within the groups by the factor F/F so that
( 1 )
the F-test gives a result which is just acceptable (see 6.3.2);
s
2) use this adjusted value to calculate the lower confidence limit TC of the result;
( 1 )
a
a
3) if the lower confidence interval (TI – TC ) is found acceptable, the non-linearity is deemed
a
to be of no practical importance (see 6.3.2);

2 2
s s
4) from the components of the data dispersion, and the confidence interval of an
( 1 ) ( 2 )
estimate is calculated using the regression equation.
When the temperature index (TI), its lower confidence limit (TC) and the halving interval (HIC)
have been calculated, (see 7.1), the result is considered acceptable if
TI – TC ≤ 0,6 HIC (1)
When the lower confidence interval (TI – TC) exceeds 0,6 HIC by a small margin, a usable
result may still be obtained, provided F ≤ F , by substituting (TC + 0,6 HIC) for the value of TI
(see Clause 7).
4.5 Results
The temperature index (TI), its halving interval (HIC) and its lower 95 % confidence limit (TC)
are calculated from the regression equation, making allowance as described above for minor
deviations from the prescribed specified results of the statistical tests.
The mode of reporting of the temperature index and halving interval is determined by the
results of the statistical tests (see 7.2).
It is necessary to emphasize the need to present the thermal endurance graph as part of the
report, since a single numerical result, TI (HIC), cannot present an overall qualitative view of
the test data, and appraisal of the data cannot be complete without this.
5 Requirements and recommendations for valid calculations
5.1 Requirements for experimental data
5.1.1 General
The data submitted to the procedures of this document shall conform to the requirements of
IEC 60216-1:2001.
5.1.2 Non-destructive tests
For most diagnostic properties in this category, groups of five specimens will be adequate.
However, if the data dispersion (confidence interval, see 6.3.3) is found to be too great, more
satisfactory results are likely to be obtained by using a greater number of specimens. This is
particularly true if it is necessary to terminate ageing before all specimens have reached end-
point.
5.1.3 Proof tests
Not more than one specimen in any group shall reach end-point during the first ageing period:
if more than one group contains such a specimen, the experimental procedure should be
carefully examined (see 6.1.3) and the occurrence included in the test report.
The number of specimens in each group shall be at least five, and for practical reasons the
maximum number treatable is restricted to 31 (Table C.1). The recommended number for
most purposes is 21.
5.1.4 Destructive tests
At each temperature, ageing should be continued until the property value mean of at least one
group is above and at least one below the end-point level. In some circumstances, and with
appropriate limitations, a small extrapolation of the property value mean past the end-point

– 14 – IEC 60216-3:2021 RLV © IEC 2021
level may be permitted (see 6.1.4, step 4). This shall not be permitted for more than one
temperature group.
5.2 Precision of calculations
Many of the calculation steps involve summing of the differences of numbers or the squares of
these differences, where the differences may be small by comparison with the numbers. In
these circumstances it is necessary that the calculations be made with an internal precision of
at least six significant digits, and preferably more, to achieve a result precision of three
significant digits. In view of the repetitive and tedious nature of the calculations, it is strongly
recommended that they be performed using a programmable calculator or microcomputer, in
which case internal precision of ten or more significant digits is easily available.
6 Calculation procedures
6.1 Preliminary calculations
6.1.1 Temperatures and x-values
For all types of test, express each ageing temperature in K on the thermodynamic
temperature scale, and calculate its reciprocal for use as x :
i
x = 1/(ϑ + Θ ) (2)
i i 0
where Θ = 273,15 K.
6.1.2 Non-destructive tests
For specimen number j of group number i, a property value after each ageing period is
obtained. From these values, if necessary by linear interpolation, obtain the time to end-point
and calculate its logarithm as y .
ij
6.1.3 Proof tests
For specimen number j of group number i, calculate the mid-point of the ageing period
immediately prior to reaching the end-point and take the logarithm of this time as y .
ij
A time to end-point within the first ageing period shall be treated as invalid. Either:
a) start again with a new group of specimens, or
b) ignore the specimen and reduce the value ascribed to the number of specimens in the
group (m ) by one in the calculation for group means and variances (see 6.2.1.3).
i
If the end-point is reached for more than one specimen during the first period, discard the
group and test a further group, paying particular attention to any critical points of experimental
procedure.
6.1.4 Destructive tests
Within the groups of specimens aged at each temperature ϑ, carry out the following
i
procedure in five steps:
NOTE The subscript i is omitted from the expressions in step 2 to step 4 in order to avoid confusing multiple
subscript combinations in print. The calculations of these subclauses shall be step 2 to step 4 are carried out
separately on the data from each ageing temperature.
Step 1 Calculate the mean property value for the data group obtained at each ageing time
and the logarithm of the ageing time. Plot these values on a graph with the property value p

as ordinate and the logarithm of the ageing time z as abscissa (see Figure D.2). Fit by visual
means a smooth curve through the mean property points (see Figure 1).
Step 2 Select a time range within which the curve so fitted is approximately linear
(see step 4). Ensure that this time range includes at least three mean property values with at
least one point on each side of the end-point line p = p . If this is not the case, and further
e
measurements at greater times cannot be made (for example, because no specimens
remain), a small extrapolation is permitted, subject to the conditions of step 4.

Key
Value of diagnostic property at end-point p
e
Time range with selected groups, following an approximate linear
– - – - – - – - – - – - – - – - – - – - – - – -
trend (common slope)
NOTE Example destructive test data N3 (arbitrary units) from Clause E.3, temperature 150 °C with small
extrapolation.
Figure 1 – Example of groups selection
Let the number of selected mean values (and corresponding value groups) be r, the
logarithms of the individual ageing times be z and the individual property values be p ,
g gh
where
g = 1 . r is the order number of the selected group tested at time τ ;
g
h = 1 . n is the order number of the property value within group number g;
g
n is the number of property values in group number g.
g
In most cases, the number n of specimens tested at each test time is identical, but this is not
g
a necessary condition, and the calculation can be carried out with different values of n for
g
different groups.
p
Calculate the mean value and the variance s for each selected property value group.
g
1g
– 16 – IEC 60216-3:2021 RLV © IEC 2021
n
g
p = p / n
(3)
g ∑ gh g
h=1
n
 g 
2 22
 
s= p− n p n−1
(4)
( )
1g ∑ gh g g g
 
h=1
 
Calculate the logarithms of τ :
g
z = log τ (5)
g g
Step 3 Calculate the values
r
vn=
(6)
∑ g
g=1
r
z = z n /v
(7)
∑ gg
g=1
r
(8)
p = p n /ν
∑
g g
g=1
p a+ bz
Calculate the coefficients of the regression equation
pp
r

n z p − vz p
gg g
∑

g=1

(9)
b =
p
r


n z − vz
gg
∑

g=1

a p− bz
(10)
pp
Calculate the pooled variance within the property groups
r
s= n−−1 s /v r
( )
( ) (11)
11∑ gg
g=1
Calculate the weighted variance of the deviations of the property group means from the
regression li
...

IEC 60216-3 ®
Edition 3.0 2021-03
INTERNATIONAL
STANDARD
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INTERNATIONALE
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Electrical insulating materials – Thermal endurance properties –
Part 3: Instructions for calculating thermal endurance characteristics

Matériaux isolants électriques – Propriétés d'endurance thermique –
Partie 3: Instructions pour le calcul des caractéristiques d'endurance thermique

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IEC 60216-3 ®
Edition 3.0 2021-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Electrical insulating materials – Thermal endurance properties –

Part 3: Instructions for calculating thermal endurance characteristics

Matériaux isolants électriques – Propriétés d'endurance thermique –

Partie 3: Instructions pour le calcul des caractéristiques d'endurance thermique

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 17.220.99; 19.020 ISBN 978-2-8322-9440-6

– 2 – IEC 60216-3:2021 © IEC 2021
CONTENTS
FOREWORD . 4
1 Scope . 6
2 Normative references . 6
3 Terms, definitions, symbols and abbreviated terms . 6
3.1 Terms and definitions . 6
3.2 Symbols and abbreviated terms . 8
4 Principles of calculations . 10
4.1 General principles . 10
4.2 Preliminary calculations . 10
4.2.1 General . 10
4.2.2 Non-destructive tests . 11
4.2.3 Proof tests . 11
4.2.4 Destructive tests . 11
4.3 Variance calculations . 12
4.4 Statistical tests . 12
4.5 Results . 13
5 Requirements and recommendations for valid calculations . 13
5.1 Requirements for experimental data . 13
5.1.1 General . 13
5.1.2 Non-destructive tests . 13
5.1.3 Proof tests . 13
5.1.4 Destructive tests . 13
5.2 Precision of calculations . 14
6 Calculation procedures . 14
6.1 Preliminary calculations . 14
6.1.1 Temperatures and x-values . 14
6.1.2 Non-destructive tests . 14
6.1.3 Proof tests . 14
6.1.4 Destructive tests . 14
6.1.5 Incomplete data . 18
6.2 Main calculations . 18
6.2.1 Calculation of group means and variances . 18
6.2.2 General means and variances . 19
6.2.3 Regression calculations . 20
6.3 Statistical tests . 21
6.3.1 Variance equality test . 21
6.3.2 Linearity test (F-test) . 21
6.3.3 Confidence limits of X and Y estimates . 22
6.4 Thermal endurance graph . 23
7 Calculation and requirements for results . 23
7.1 Calculation of thermal endurance characteristics . 23
7.2 Summary of statistical tests and reporting . 24
7.3 Reporting of results . 24
8 Test report . 24
Annex A (normative) Decision flow chart . 26

Annex B (normative) Decision table . 27
Annex C (informative) Statistical tables . 28
Annex D (informative) Worked examples. 38
Annex E (informative) Computer program . 46
E.1 General . 46
E.1.1 Overview . 46
E.1.2 Convenience program execution . 47
E.2 Structure of data files used by the program . 48
E.2.1 Text file formats . 48
E.2.2 Office Open XML formats. 50
E.3 Data files for computer program . 51
E.4 Output files and graph . 56
Bibliography . 57

Figure 1 – Example of groups selection . 15
Figure A.1 – Decision flow chart . 26
Figure D.1 – Thermal endurance graph . 42
Figure D.2 – Example 3: Property-time graph. 44
Figure E.1 – Shortcut property dialog for program launch . 47
Figure E.2 – Thermal endurance graph of example N3 . 56

Table B.1 – Decisions and actions according to tests . 27
Table C.1 – Coefficients for censored data calculations . 28
Table C.2 – Fractiles of the F-distribution, F(0,95, f , f ) . 34
n d
Table C.3 – Fractiles of the F-distribution, F(0,995, f , f ) . 35
n d
Table C.4 – Fractiles of the t-distribution, t . 37
0,95
Table C.5 – Fractiles of the χ -distribution . 37
Table D.1 – Worked example 1 – Censored data (proof tests: file CENEX3.DTA) . 38
Table D.2 – Worked example 2 – Complete data (non-destructive tests: file
TEST2.DTA) . 40
Table D.3 – Worked example 3 – Destructive tests . 43
Table D.4 – Worked example 3 – Selection of groups . 44
Table E.1 – Non-destructive test data . 49
Table E.2 – Destructive test data . 49
Table E.3 – Non-destructive test data . 50
Table E.4 – Destructive test data . 50

– 4 – IEC 60216-3:2021 © IEC 2021
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ELECTRICAL INSULATING MATERIALS –
THERMAL ENDURANCE PROPERTIES –

Part 3: Instructions for calculating
thermal endurance characteristics

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
indispensable for the correct application of this publication.
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.
IEC 60216-3 has been prepared by IEC technical committee 112: Evaluation and qualification
of electrical insulating materials and systems. It is an International Standard.
This third edition cancels and replaces the second edition published in 2006. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) a new computer program has been included;
b) Annex E " has been completely reworked.

The text of this International Standard is based on the following documents:
Draft Report on voting
112/475/CDV 112/495/RVC
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this International Standard is English.
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement,
available at www.iec.ch/members_experts/refdocs. The main document types developed by
IEC are described in greater detail at www.iec.ch/standardsdev/publications.
A list of all parts in the IEC 60216 series, published under the general title Electrical insulating
materials – Thermal endurance properties, can be found on the IEC website.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under webstore.iec.ch in the data related to the
specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct
understanding of its contents. Users should therefore print this document using a
colour printer.
– 6 – IEC 60216-3:2021 © IEC 2021
ELECTRICAL INSULATING MATERIALS –
THERMAL ENDURANCE PROPERTIES –

Part 3: Instructions for calculating
thermal endurance characteristics

1 Scope
This part of IEC 60216 specifies the calculation procedures used for deriving thermal
endurance characteristics from experimental data obtained in accordance with the instructions
of IEC 60216-1 and IEC 60216-2 [1] , using fixed ageing temperatures and variable ageing
times.
The experimental data can be obtained using non-destructive, destructive or proof tests. Data
obtained from non-destructive or proof tests can be incomplete, in that it is possible that
measurement of times taken to reach the end-point will have been terminated at some point
after the median time but before all specimens have reached end-point.
The procedures are illustrated by worked examples, and suitable computer programs are
recommended to facilitate the calculations.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their
content constitutes requirements 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 60216-1:2013, Electrical insulating materials – Thermal endurance properties – Part 1:
Ageing procedures and evaluation of test results
3 Terms, definitions, symbols and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the following definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at https://www.iso.org/obp
3.1.1
ordered data
group of data arranged in sequence so that in the appropriate direction through the sequence
each member is greater than, or equal to, its predecessor
Note 1 to entry: In this document, ascending order implies that the data is ordered in this way, the first being the
smallest.
___________
Numbers in square brackets refer to the bibliography.

Note 2 to entry: It has been established that the term "group" is used in the theoretical statistics literature to
represent a subset of the whole data set. The group comprises those data having the same value of one of the
parameters of the set (e.g. ageing temperature). A group may itself comprise a number of sub-groups
characterized by another parameter (e.g. time in the case of destructive tests).
3.1.2
order-statistic
assigned numerical position in the sequence of individual values in a group of ordered data
3.1.3
incomplete data
ordered data, where the values above and/or below defined points are not known
3.1.4
censored data
incomplete data, where the number of unknown values is known
Note 1 to entry: If the censoring is begun above/below a specified numerical value, the censoring is Type I.
If above/below a specified order-statistic it is Type II. This document is concerned only with Type II.
3.1.5
degrees of freedom
number of data values minus the number of parameter values
3.1.6
variance of a data group
sum of the squares of the deviations of the data from a reference level
Note 1 to entry: The reference level may be defined by one or more parameters, for example a mean value (one
parameter) or a line (two parameters, slope and intercept), divided by the number of degrees of freedom.
3.1.7
central second moment of a data group
sum of the squares of the differences between the data values and the value of the group
mean, divided by the number of data in the group
3.1.8
covariance of data groups
for two groups of data with equal numbers of elements where each element in one group
corresponds to one in the other, the sum of the products of the deviations of the
corresponding members from their group means, divided by the number of degrees of
freedom
3.1.9
regression analysis
process of deducing the best-fit line expressing the relation of corresponding members of two
data groups by minimizing the sum of squares of deviations of members of one of the groups
from the line
Note 1 to entry: The parameters are referred to as the regression coefficients.
3.1.10
correlation coefficient
number expressing the completeness of the relation between members of two data groups,
equal to the covariance divided by the square root of the product of the variances of the
groups
Note 1 to entry: The value of its square is between 0 (no correlation) and 1 (complete correlation).

– 8 – IEC 60216-3:2021 © IEC 2021
3.1.11
end-point line
line parallel to the time axis intercepting the property axis at the end-point value
Note 1 to entry: For guidance on the choice of end-point value, refer to IEC 60216-2.
3.2 Symbols and abbreviated terms
Subclause
a Regression coefficient (y-intercept) 4.3, 6.2
a Regression coefficient for destructive test calculations 6.1
p
b Regression coefficient (slope) 4.3, 6.2
b Regression coefficient for destructive test calculations 6.1
p
b 6.3
ˆ
r
X
Intermediate constant (calculation of )
c
c 6.3
Intermediate constant (calculation of χ )
f Number of degrees of freedom Table C.2 to
Table C.5
F Fisher distributed stochastic variable 4.2, 6.1, 6.3
F Tabulated value of F (linearity of thermal endurance graph) 4.4, 6.3
F Tabulated value of F (linearity of property graph – significance 6.1
0,05)
F Tabulated value of F (linearity of property graph – significance 6.1
0,005)
g Order number of ageing time for destructive tests 6.1
h Order number of property value for destructive tests 6.1
HIC Halving interval at temperature equal to TI 4.3, Clause 7
HIC Halving interval corresponding to TI 7.3
g g
i Order number of exposure temperature 4.1, 6.2
j Order number of time to end-point 4.1, 6.2
k Number of ageing temperatures 4.1, 6.2
m 4.1, 6.1
Number of specimens aged at temperature ϑ
i
i
N Total number of times to end-point 6.2
n Number of property values in group aged for time τ 6.1
g g
n 4.1, 6.1
Number of values of y at temperature ϑ
i
i
p
Mean value of property values in selected groups 6.1
p Value of diagnostic property 6.1
P Significance level of χ distribution 4.4, 6.3.1
p Value of diagnostic property at end-point for destructive tests 6.1
e
6.1
Mean of property values in group aged for time τ
p
g
g
p Individual property value 6.1
gh
q Base of logarithms 6.3
r Number of ageing times selected for inclusion in calculation 6.1
(destructive tests)
r Square of correlation coefficient 6.2.3
s 2 2 6.3
Weighted mean of s and s
1 2
Subclause
2 2
4.3, 6.1 to 6.3
s s
Weighted mean of , pooled variance within selected groups
1 1i
2 4.4, 6.3
Adjusted value of s
s
( 1 )
a
Variance of property values in group aged for time τ 6.1
s g
1g
2 4.3, 6.2
Variance of y values at temperature ϑ
ij
i
s
1i
2 Variance about regression line 6.1 to 6.3
s
2 Adjusted value of s 6.3
s
a
2 Intermediate constant 6.3
s
r
2 Variance of Y 6.3
s
Y
t Student distributed stochastic variable 6.3
t Adjusted value of t (incomplete data) 6.3
c
TC Lower 95 % confidence limit of TI 4.4, 7
TC Adjusted value of TC 7.1
a
TI Temperature index 4.3, Clause 7
TI Temperature index at 10 kh 7.1
TI Adjusted value of TI 7.3
a
TI Temperature index obtained by graphical means or without 7.3
g
defined confidence limits
x Independent variable: reciprocal of thermodynamic
temperature
Weighted mean value of x 6.2
x
X Specified value of x for estimation of y 6.3
ˆ
Estimated value of x at specified value of y 6.3

X
ˆ
6.3
ˆ Upper 95 % confidence limit of X
X
c
x 4.1, 6.1
Reciprocal of thermodynamic temperature corresponding to ϑ
i
i
y
Weighted mean value of y 6.2
y Dependent variable: logarithm of time to end-point
ˆ
Estimated value of y at specified value of x 6.3

Y
Y Specified value of y for estimation of x 6.3
ˆ
6.3
ˆ
Lower 95 % confidence limit of Y
Y
c
y 4.3, 6.2
Mean values of y at temperature ϑ
i
ij i
y 4.1, 6.1
Value of y corresponding to τ
ij
ij
Mean value of z 6.1
z
g
z Logarithm of ageing time for destructive tests – group g 6.1
g
Censored data coefficient for variance 4.3, 6.2
α
β Censored data coefficient for variance 4.3, 6.2
ε Censored data coefficient for variance of mean 4.3, 6.2

– 10 – IEC 60216-3:2021 © IEC 2021
Subclause
Θ Temperature 0 °C on the thermodynamic scale (273,15 K) 4.1, 6.1
ˆ
Estimate of temperature for temperature index 6.3.3
ϑ
ˆ
Confidence limit of 6.3.3
ˆ ϑ
ϑ
c
Ageing temperature for group i 4.1, 6.1
ϑ
i
μ Censored data coefficient for mean 4.3, 6.2
μ (x) Central second moment of x values 6.2, 6.3
ν Total number of property values selected at one ageing 6.1
temperature
Time selected for estimate of temperature 6.3
τ
f
τ Time of ageing for selected group g 6.1
g
τ Times to end-point 6.4
ij
2 2
6.3
χ χ -distributed stochastic variable

4 Principles of calculations
4.1 General principles
The general calculation procedures and instructions given in Clause 6 are based on the
principles set out in IEC 60493-1 [2]. These may be simplified as follows:
a) the relation between the mean of the logarithms of the times taken to reach the specified
end-point (times to end-point) and the reciprocal of the thermodynamic (absolute)
temperature is linear;
b) the values of the deviations of the logarithms of the times to end-point from the linear
relation are normally distributed with a variance which is independent of the ageing
temperature.
The data used in the general calculation procedures are obtained from the experimental data
by a preliminary calculation. The details of this calculation are dependent on the character of
the diagnostic test: non-destructive, proof or destructive (see 4.2). In all cases the data
comprise values of x, y, m, n and k
where
x = 1/(ϑ + Θ ) is the reciprocal of thermodynamic value of ageing temperature ϑ in °C;
i i 0 i
y = log τ is the logarithm of the value of time (j) to end-point at temperature ϑ ;
ij ij i
n is the number of y values in group number i aged at temperature ϑ ;
i i
m is the number of samples in group number i aged at temperature ϑ
i i
(different from n for censored data);
i
k is the number of ageing temperatures or groups of y values.
NOTE Any number can be used as the base for logarithms, provided consistency is observed throughout
calculations. The use of natural logarithms (base e) is beneficial, since most computer programming languages and
scientific calculators have this facility.
4.2 Preliminary calculations
4.2.1 General
In all cases, the reciprocals of the thermodynamic values of the ageing temperatures are
.
calculated as the values of x
i
The values of y are calculated as the values of the logarithms of the individual times to end-
ij
point τ obtained as described below.
ij
In many cases of non-destructive and proof tests, it is advisable for economic reasons, (for
example, when the scatter of the data is high) to stop ageing before all specimens have
reached the end-point, at least for some temperature groups. In such cases, the procedure for
calculation on censored data (see 6.2.1.3) shall be carried out on the (x, y) data available.
Groups of complete and incomplete data or groups censored at a different point for each
ageing temperature may be used together in one calculation in 6.2.1.3.
4.2.2 Non-destructive tests
Non-destructive tests (for example, loss of mass on ageing) give directly the value of the
diagnostic property of each specimen each time it is measured, at the end of an ageing
period. The time to end-point τ is therefore available, either directly or by linear interpolation
ij
between consecutive measurements.
4.2.3 Proof tests
The time to end-point τ for an individual specimen is taken as the mid-point of the ageing
ij
period immediately prior to reaching the end-point.
4.2.4 Destructive tests
When destructive test criteria are employed, each test specimen is destroyed in obtaining a
property value and its time to end-point cannot therefore be measured directly.
To enable estimates of the times to end-point to be obtained, the assumptions are made that
in the vicinity of the end-point:
a) the relation between the mean property values and the logarithm of the ageing time is
approximately linear;
b) the values of the deviations of the individual property values from this linear relation are
normally distributed with a variance which is independent of the ageing time;
c) the curves of property versus logarithm of time for the individual test specimens are
straight lines parallel to the line representing the relation of a) above.
For the application of these assumptions, an ageing curve is drawn for the data obtained at
each of the ageing times. The curve is obtained by plotting the mean value of property for
each specimen group against the logarithm of its ageing time. If possible, ageing is continued
at each temperature until at least one group mean is beyond the end-point level. An
approximately linear region of this curve is drawn in the vicinity of the end-point line (see
Figure D.2).
A statistical test (F-test) is carried out to decide whether deviations from linearity of the
selected region are acceptable (see 6.1.4, step 4). If acceptable, then, on the same graph,
points representing the properties of the individual specimens are drawn. A line parallel to the
ageing line is drawn through each individual specimen data point. The estimate of
the logarithm of the time to end-point for that specimen (y ) is then the value of the logarithm
ij
of time corresponding to the intersection of the line with the end-point line (Figure D.2).
With some limitations, an extrapolation of the linear mean value graph to the end-point level is
permitted.
The above operations are executed numerically in the calculations detailed in 6.1.4.

– 12 – IEC 60216-3:2021 © IEC 2021
4.3 Variance calculations
Commencing with the values of x and y obtained in 4.2, the following calculations are made:
For each group of y values, the mean and variance s are calculated, and from the latter
y
1i
ij i
the pooled variance within the groups, s , is derived, weighting the groups according to size.
For incomplete data, the calculations have been developed from those originated by Saw [3]
and given in 6.2.1.3. For the coefficients required (µ for mean, α, β for variance and ε for
deriving the variance of mean from the group variance) see Annex C, Table C.1. For multiple
groups, the variances are pooled, weighting according to the group size. The mean value of
the group values of ε is obtained without weighting, and multiplied by the pooled variance.
NOTE The weighting according to the group size is implicit in the definition of ε, which here is equal to that
originally proposed by Saw, multiplied by the group size. This makes for simpler representation in equations.
From the means y and the values of x , the coefficients a and b (the coefficients of the best
i i
fit linear representation of the relationship between x and y) are calculated by linear
regression analysis.
From the regression coefficients, the values of TI and HIC are calculated. The variance of
the deviations from the regression line is calculated from the regression coefficients and the
group means.
4.4 Statistical tests
The following statistical tests are made:
a) Fisher test for linearity (Fisher test, F-test) on destructive test data prior to the calculation
of estimated times to end-point (see 4.2.4);
b) variance equality (Bartlett's χ -test) to establish whether the variances within the groups of
y values differ significantly;
c) F-test to establish whether the ratio of the deviations from the regression line to the
pooled variance within the data groups is greater than the reference value F , i.e. to test
the validity of the Arrhenius hypothesis as applied to the test data.
In the case of data of very small dispersion, it is possible for a non-linearity to be detected as
statistically significant which is of little practical importance.
In order that a result may be obtained even where the requirements of the F-test are not met,
a procedure is included as follows:
s
1) increase the value of the pooled variance within the groups by the factor F/F so that
( 1 )
the F-test gives a result which is just acceptable (see 6.3.2);
s
2) use this adjusted value to calculate the lower confidence limit TC of the result;
( )
a
a
3) if the lower confidence interval (TI – TC ) is found acceptable, the non-linearity is deemed
a
to be of no practical importance (see 6.3.2);
2 2
s s
4) from the components of the data dispersion, and the confidence interval of an
( 1 ) ( 2 )
estimate is calculated using the regression equation.
When the temperature index (TI), its lower confidence limit (TC) and the halving interval (HIC)
have been calculated, (see 7.1), the result is considered acceptable if

TI – TC ≤ 0,6 HIC (1)
When the lower confidence interval (TI – TC) exceeds 0,6 HIC by a small margin, a usable
result may still be obtained, provided F ≤ F , by substituting (TC + 0,6 HIC) for the value of TI
(see Clause 7).
4.5 Results
The temperature index (TI), its halving interval (HIC) and its lower 95 % confidence limit (TC)
are calculated from the regression equation, making allowance as described above for minor
deviations from the specified results of the statistical tests.
The mode of reporting of the temperature index and halving interval is determined by the
results of the statistical tests (see 7.2).
It is necessary to emphasize the need to present the thermal endurance graph as part of the
report, since a single numerical result, TI (HIC), cannot present an overall qualitative view of
the test data, and appraisal of the data cannot be complete without this.
5 Requirements and recommendations for valid calculations
5.1 Requirements for experimental data
5.1.1 General
The data submitted to the procedures of this document shall conform to the requirements of
IEC 60216-1.
5.1.2 Non-destructive tests
For most diagnostic properties in this category, groups of five specimens will be adequate.
However, if the data dispersion (confidence interval, see 6.3.3) is found to be too great, more
satisfactory results are likely to be obtained by using a greater number of specimens. This is
particularly true if it is necessary to terminate ageing before all specimens have reached end-
point.
5.1.3 Proof tests
Not more than one specimen in any group shall reach end-point during the first ageing period:
if more than one group contains such a specimen, the experimental procedure should be
carefully examined (see 6.1.3) and the occurrence included in the test report.
The number of specimens in each group shall be at least five, and for practical reasons the
maximum number treatable is restricted to 31 (Table C.1). The recommended number for
most purposes is 21.
5.1.4 Destructive tests
At each temperature, ageing should be continued until the property value mean of at least one
group is above and at least one below the end-point level. In some circumstances, and with
appropriate limitations, a small extrapolation of the property value mean past the end-point
level may be permitted (see 6.1.4, step 4). This shall not be permitted for more than one
temperature group.
– 14 – IEC 60216-3:2021 © IEC 2021
5.2 Precision of calculations
Many of the calculation steps involve summing of the differences of numbers or the squares of
these differences, where the differences may be small by comparison with the numbers. In
these circumstances it is necessary that the calculations be made with an internal precision of
at least six significant digits, and preferably more, to achieve a result precision of three
significant digits. In view of the repetitive and tedious nature of the calculations, it is strongly
recommended that they be performed using a programmable calculator or microcomputer, in
which case internal precision of ten or more significant digits is easily available.
6 Calculation procedures
6.1 Preliminary calculations
6.1.1 Temperatures and x-values
For all types of test, express each ageing temperature in K on the thermodynamic
temperature scale, and calculate its reciprocal for use as x :
i
x = 1/(ϑ + Θ ) (2)
i i 0
where Θ = 273,15 K.
6.1.2 Non-destructive tests
For specimen number j of group number i, a property value after each ageing period is
obtained. From these values, if necessary by linear interpolation, obtain the time to end-point
and calculate its logarithm as y .
ij
6.1.3 Proof tests
For specimen number j of group number i, calculate the mid-point of the ageing period
immediately prior to reaching the end-point and take the logarithm of this time as y .
ij
A time to end-point within the first ageing period shall be treated as invalid. Either:
a) start again with a new group of specimens, or
b) ignore the specimen and reduce the value ascribed to the number of specimens in the
group (m ) by one in the calculation for group means and variances (see 6.2.1.3).
i
If the end-point is reached for more than one specimen during the first period, discard the
group and test a further group, paying particular attention to any critical points of experimental
procedure.
6.1.4 Destructive tests
Within the groups of specimens aged at each temperature ϑ, carry out the following
i
procedure in five steps:
NOTE The subscript i is omitted from the expressions in step 2 to step 4 in order to avoid confusing multiple
subscript combinations in print. The calculations of step 2 to step 4 are carried out separately on the data from
each ageing temperature.
Step 1 Calculate the mean property value for the data group obtained at each ageing time
and the logarithm of the ageing time. Plot these values on a graph with the property value p
as ordinate and the logarithm of the ageing time z as abscissa. Fit by visual means a smooth
curve through the mean property points (see Figure 1).

Step 2 Select a time range within which the curve so fitted is approximately linear
(see step 4). Ensure that this time range includes at least three mean property values with at
least one point on each side of the end-point line p = p . If this is not the case, and further
e
measurements at greater times cannot be made (for example, because no specimens
remain), a small extrapolation is permitted, subject to the conditions
...