CISPR TR 16-4-3:2004

CISPR TR 16-4-3 ®
Edition 2.1 2007-01
CONSOLIDATED VERSION
TECHNICAL
REPORT
INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE

Specification for radio disturbance and immunity measuring apparatus and
methods –
Part 4-3: Uncertainties, statistics and limit modelling – Statistical considerations
in the determination of EMC compliance of mass-produced products

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CISPR TR 16-4-3 ®
Edition 2.1 2007-01
CONSOLIDATED VERSION
TECHNICAL
REPORT
INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE

Specification for radio disturbance and immunity measuring apparatus and

methods –
Part 4-3: Uncertainties, statistics and limit modelling – Statistical considerations

in the determination of EMC compliance of mass-produced products

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 33.100.10; 33.100.20 ISBN 2-8318-8915-4

– 2 – TR CISPR 16-4-3 © IEC:2004
+A1:2006(E)
CONTENTS
FOREWORD.3

1 Scope.5
2 Normative references.5
3 Terms, definitions and symbols .6
4 General requirements .6
4.1 Limits.6
4.2 Type testing approaches .6
5 Emission measurements.6
5.1 Test based on the non-central t-distribution.6
5.2 Test based on the binomial distribution .9
5.3 Test based on an additional acceptance limit .9
5.4 Additional sampling in case of non-compliance.10
5.5 Properties of the different methods that can be used .11
5.6 Compliance criteria and measurement instrumentation uncertainty.12
6 Immunity tests.12
6.1 Application of the CISPR 80 %/80 % rule to immunity tests .12
6.2 Application guidelines.12

Annex A (informative) Statistical considerations in the determination of limits of radio
interference .14
Annex B (informative) An analytical assessment of statistical parameters of radio
disturbance in the case of an incompletely defined sample .22
Annex C (informative) Test based on an additional acceptance limit .27
Annex D (informative) Estimation of the acceptance probability of a sample .31

Bibliography.36

TR CISPR 16-4-3 © IEC:2004 – 3 –
+A1:2006(E)
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SPECIFICATION FOR RADIO DISTURBANCE
AND IMMUNITY MEASURING APPARATUS AND METHODS –
Part 4-3: Uncertainties, statistics and limit modelling –
Statistical considerations in the determination
of EMC compliance of mass-produced products
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
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
this end and in addition to other activities, IEC publishes International Standards, Technical Specifications,
Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC
Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested
in the subject dealt with may participate in this preparatory work. International, governmental and non-
governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely
with the International Organization for Standardization (ISO) in accordance with conditions determined by
agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
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4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
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between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
the latter.
5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with an IEC Publication.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
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Publications.
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.
This consolidated version of the official IEC Standard and its amendment has been
prepared for user convenience.
CISPR 16-4-3 edition 2.1 contains the second edition (2004) [documents CISPR/A/491/
DTR and CISPR/A/492/DTR and CISPR/A/507/RVC and CISPR/A/508/RVC] and its
amendment 1 (2006) [documents CISPR/A/666/DTR and CISPR/A/691/RVC].
A vertical line in the margin shows where the base publication has been modified by
amendment 1.
The main task of IEC technical committees is to prepare International Standards. However, a
technical committee may propose the publication of a technical report when it has collected
data of a different kind from that which is normally published as an International Standard,
for example "state of the art".

– 4 – TR CISPR 16-4-3 © IEC:2004
+A1:2006(E)
CISPR 16-4-3, which is a technical report, has been prepared by CISPR subcommittee A:
Radio interference measurements and statistical methods.
This second edition of CISPR 16-4-3 cancels and replaces the first edition published in 2003
and constitutes a technical revision. It includes a new mathematical approach for the
application of the 80%/80% rule, based on a method involving an additional acceptance limit.
The mathematical basis for this new method is also provided. Furthermore, an additional test
approach, based on the non-central t distribution and using frequency sub-ranges has been
added as well, along with a description of the properties of all methods which are available at
this point in time.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
The committee has decided that the contents of the base publication and its amendments will
remain unchanged until the maintenance result date indicated on the IEC web site
under "http://webstore.iec.ch" in the data related to the specific publication. At this
date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
A bilingual version of this publication may be issued at a later date.

TR CISPR 16-4-3 © IEC:2004 – 5 –
+A1:2006(E)
SPECIFICATION FOR RADIO DISTURBANCE
AND IMMUNITY MEASURING APPARATUS AND METHODS –

Part 4-3: Uncertainties, statistics and limit modelling –
Statistical considerations in the determination
of EMC compliance of mass-produced products

1 Scope
This part of CISPR 16 deals with statistical considerations in the determination of EMC
compliance of mass-produced products.
The reasons for such statistical considerations are:
a) that the abatement of interference aims that the majority of the appliances to be approved
shall not cause interference;
b) that the CISPR limits should be suitable for the purpose of type approval of mass-
produced appliances as well as approval of single-produced appliances;
c) that to ensure compliance of mass-produced appliances with the CISPR limits, statistical
techniques have to be applied;
d) that it is important for international trade that the limits shall be interpreted in the same
way in every country;
e) that the National Committees of the IEC which collaborate in the work of the CISPR should
seek to secure the agreement of the competent authorities in their countries.
Therefore, this part of CISPR 16 specifies requirements and provides guidance based on
statistical techniques. EMC compliance of mass-produced appliances should be based on the
application of statistical techniques that must reassure the consumer, with an 80 % degree of
confidence, that 80 % of the appliances of a type being investigated comply with the emission
or immunity requirements. Clause 4 gives some general requirements for this so-called
80 %/80 % rule. Clause 5 gives more specific requirements for the application of the
80 %/80 % rule to emission tests. Clause 6 gives guidance on the application of the CISPR
80 %/80 % rule to immunity tests. The 80 %/80 % rule protects the consumer from non-
compliant appliances, but it says hardly anything about the probability that a batch of
appliances from which the sample has been taken will be accepted. This acceptance
probability is very important to the manufacturer. In Annex A, more information is given on
acceptance probability (manufacturer’s risk).
2 Normative references
The following referenced documents are indispensable for the application of this document.
For dated references, only the edition cited applies. For undated references, the latest edition
of the referenced document (including any amendments) applies.
IEC 60050-161:1990, International Electrotechnical Vocabulary (IEV) – Chapter 161:
Electromagnetic compatibility
Amendment 1 (1997)
Amendment 2 (1998)
CISPR 16-4-2, Specification for radio disturbance and immunity measuring apparatus
and methods – Part 4-2: Uncertainties, statistics and limit modelling – Uncertainty in EMC
measurements
– 6 – TR CISPR 16-4-3 © IEC:2004
+A1:2006(E)
3 Terms, definitions and symbols
For the purpose of this document, the terms, definitions and symbols given in IEC 60050-161
apply.
4 General requirements
The following interpretation of CISPR limits and of methods of statistical sampling for
compliance of mass-produced appliances with these limits should be applied.
4.1 Limits
4.1.1 A CISPR limit is a limit that is recommended to national authorities for incorporation in
national standards, relevant legal regulations and official specifications. It is also
recommended that international organizations use these limits.
4.1.2 The significance of the limits for type-approved appliances shall be that, on a
statistical basis, at least 80 % of the mass-produced appliances comply with the limits with at
least 80 % confidence.
4.2 Type testing approaches
Type tests can be made using the following two approaches.
4.2.1 Use of a sample of appliances of the same type
When using this approach, the sample of appliances of the same type shall be evaluated
statistically in accordance with the methods described in Clause 5 (emission tests) and
Clause 6 (immunity tests).
Statistical assessment of compliance with limits shall be made according to the methods
described in Clauses 5 and 6 or in accordance with some other method that ensures
compliance with the requirements of clause 4.1.2.
4.2.2 Use of a single device with subsequent quality assurance testing
For simplicity, a type test can be performed initially on one item only. However, subsequent
tests from time to time on items taken at random from the production are necessary.
4.2.3 Withdrawal of the type approval
In the case of controversy involving the possible withdrawal of a type approval, withdrawal
shall be considered only after tests on an adequate sample in accordance with 4.2.1 above.
5 Emission measurements
Statistical assessment of compliance with emission limits shall be made according to one of
the three tests described below or to some other test that ensures compliance with the
requirements of 4.1.2.
5.1 Test based on the non-central t-distribution.
This test should be performed on a sample of not less than five items of the type, but if, in
exceptional circumstances, five items are not available, then a sample of three shall be used.
Compliance is judged from the following relationship:
x + kS ≤ L (1)
n n
TR CISPR 16-4-3 © IEC:2004 – 7 –
+A1:2006(E)
where
x = arithmetic mean value of the levels of n items in the sample;
n
S = ()x − x ()n −1; (2)
∑
n n
x = level of individual item;
k = the factor derived from tables of the non-central t-distribution with 80 % confidence that
80 % of the type is below the limit; the value of k depends on the sample size n and is
stated below:
N 3 4 5 6 7 8 9 10 11 12
k 2,04 1,69 1,52 1,42 1,35 1,30 1,27 1,24 1,21 1,20

L = the permissible limit;
the quantities x, x , S and L are expressed logarithmically dB(μV), dB(μV/m) or dB(pW);
n n
If one or some appliance of the sample can not be measured due to the insufficient sensitivity
of the test equipment, Annex B describes an approach to solve this situation.
5.1.1 Tests using sub-ranges
5.1.1.1 Introduction
The 80 %/80 % rule shall be used for the specific emission at a specific frequency or
frequency range at each EUT of the sample. Modern computer-controlled measurement
equipment usually scans the frequency range and measures a limited number of the highest
disturbances at certain frequencies of the whole emission spectrum. Because the level of the
disturbance at the same frequency or the frequency at the highest emission varies from EUT
to EUT, the measured frequencies of the highest disturbance levels usually vary from one
EUT to another in a sample. These measurement results cannot be used for the
80 %/80 % rule because one does not obtain measurement levels at approximately the same
frequency for each EUT to calculate the average and standard deviation of the EUT’s level.
For this reason, it is useful to divide the whole frequency range into defined sub-ranges,
which allow a statistical analysis of the emission spectrum in the whole frequency range by
taking the highest measured level in each sub-range.
For the application of the non-central t-distribution in the 80 %/80 % rule, it is necessary to
normalise the measured values. These normalised values allow the use of the 80 %/80 % rule
in the sub-ranges independently of variations of the limit in a sub-range.
The whole frequency range shall be divided on a logarithmic frequency axis into sub-ranges.
The border of the sub-ranges may correspond to changes in limits, if a product committee so
requires.
NOTE The division of the frequency range into sub-ranges is applicable only to the test based on the non-central
t-distribution.
5.1.1.2 Number of sub-ranges
It is suggested that the frequency range of the disturbance measurement method in question
is divided into a number of frequency sub-ranges. The span of each frequency sub-range
should decrease in a logarithmic way as a function of the frequency. For the different
disturbance measurement methods, the following number of sub-ranges is suggested:
– at least 8 sub-ranges in the frequency range of up to 30 MHz for the measurement of the
disturbance voltage;
– at least 4 sub-ranges in the frequency range from 30 MHz to 300 MHz for the
measurement of the disturbance power, and

– 8 – TR CISPR 16-4-3 © IEC:2004
+A1:2006(E)
– about 8 sub-ranges in the frequency range from 30 MHz to 1000 MHz for the
measurement of disturbance field strength.
NOTE 1 The number of sub-ranges shall be determined such that the frequency dependence of the
disturbance’s characteristic can be estimated. This condition is fulfilled if the ratio of limit to average plus
standard deviation of the emission in the sub-ranges does not decrease when the number of sub-ranges is
reduced.
NOTE 2 The product committees should determine the number of sub-ranges depending on the disturbance
characteristics of the different products.
NOTE 3 The recommended number of sub-ranges is based on the investigations of samples of CISPR 14 and
CISPR 22 devices.
NOTE 4 The sub-range transition frequency can be calculated as follows:
⎛ f ⎞
i
upp
⎜ ⎟
log
⎜ ⎟
N f
⎝ low ⎠
f = f ×10
low
where
i = 1 … N is the index of the i-th sub-range transition frequency;
f , f are the lower and upper frequency of the frequency range;
low upp
N= is the number of frequency sub-ranges.
NOTE 5 For predominantly narrow band emission it is possible to select single narrow band emission by
preexamination for the use of the non-central t-distribution without using sub-ranges.
5.1.1.3 Normalization of the measured disturbance levels
The average value and the standard deviation of the measured values in a frequency sub-
range shall be compared to the limit. Because the limit may not be constant over the
frequency sub-range, it is necessary to normalize the measured values.
For normalization, the difference, d , between the measured level, x , and the limit level, L , shall
f f f
be determined at the specific frequency f that has the largest difference, using Equation (3).
The difference is negative as long as the measured value is below the limit.
d = x – L (3)
f f f
where
d = the gap to the limit at the specific frequency in dB;
f
x = the measured level in dB(μV or pW or μV/m);
f
L = the limit at the specific frequency in dB(μV or pW or μV/m).
f
5.1.1.4 Tests based on the non-central t-distribution with frequency sub-ranges
As a result of the measurement of all pieces of the sample for each sub-frequency range, the
average and the standard deviation of the gap d shall be calculated. The average of the gap
f
is
d = d (4)
∑
f f
n n
where
n = the number of items in the sample
d = the average gap in the sub-range
f
TR CISPR 16-4-3 © IEC:2004 – 9 –
+A1:2006(E)
and the standard deviation is
S = (d − d ) (5)
df ∑ f f
n −1
n
where S = the standard deviation in the sub-range.
df
Compliance is judged from the following relationship:
d + k ⋅ S ≤ 0
f df
(6)
k: see 5.1 above.
5.2 Test based on the binomial distribution
This test should be performed on a sample of not less than seven items. Compliance is
judged from the condition that the number of appliances with an interference level above the
permissible limit may not exceed c in a sample of size n.
n 7 14 20 26 32
c 0 1 2 3 4
5.3 Test based on an additional acceptance limit
This test should be performed on a sample of not less than five items of a particular type, but
if, in exceptional circumstances, five items are not available, then a sample of at least three
shall be used. Details on this method are described in 5.5. Compliance is judged if every
measured disturbance level x satisfies the following relation:
i
x ≤ AL = L – σ ·k (7)
i max E
where
AL is the acceptance limit
L is the permissible limit
σ is the expected maximum standard deviation of the product, which is 2 times the
max
expected standard deviation, and which is determined by the product committee
using the procedure of 5.3.1 or alternatively the following conservative values for the
different types of disturbance measurements can be used:
disturbance voltage: σ = 6 dB*)
max
disturbance power: σ = 6 dB**)
max
disturbance field strength: σ = xx dB
max
NOTE 1 The values of 6 dB were determined by measurements of 130*) and 40**) different EUT types
(3 or 5 samples each). The value of 6 dB was estimated by comparing the tests using the non-central
t-distribution with the tests using the additional margin. Both tests give about the same percentage of
approvals.
NOTE 2 The disturbance field strength value is under consideration.
———————
Under consideration
– 10 – TR CISPR 16-4-3 © IEC:2004
+A1:2006(E)
k is the factor derived from tables of the normal distribution with 80 % confidence that
E
80 % of the type is below the limit; the value of k depends on the sample size n and
E
is stated below (see Annex C.1):
n 3 4 5 6
k 0,63 0,41 0,24 0,12
E
The quantities x, L, k and σ are expressed logarithmically as dB(μV), dB(μV/m)
E max
or dB(pW).
NOTE With σ = 6 dB the following additional acceptance limit will be calculated:
max
Sample size 3 4 5 6
additional acceptance limit [dB] 3,8 2,5 1,5 0,7

5.3.1 Estimation of the maximum expected standard deviation
The expected standard deviation of disturbance emission shall be determined by an efficient
number of samples of the product concerned. The following procedure is recommended:
On each investigated frequency or in each frequency sub-range in the sample being
investigated, the difference x between the measured maximum emission x and the limit L
min i
shall be determined
x = (x – L) (8)
min i max
The standard deviation S of the differences in a sub-range or investigated frequency of a
sub
sample shall be calculated
S = (x − x ) (9)
∑
sub min min
n −1 n
where n is the number of appliances in the sample.
The average standard deviation S over the sub-ranges shall be determined for each
sample
sample. The expected standard deviation S is the average over S of all samples.
sample
expect
The maximum expected standard deviation is two times the expected standard deviation.
NOTE The factor of two is chosen by comparison of the test methods using the additional margin and the non-
central t-distribution. Both test methods have, with the factor two, approximately the same rejection rate of
samples.
Product committees may verify the expected standard deviation of their products.
5.4 Additional sampling in case of non-compliance
Should the test on the sample result in non-compliance with the requirements in 5.1, 5.2 or
5.3, then a second sample may be tested and the results combined with those from the first
sample and compliance checked for the larger sample. For 5.3 this method is only applicable
to samples of 7 or less appliances.

TR CISPR 16-4-3 © IEC:2004 – 11 –
+A1:2006(E)
5.5 Properties of the different methods that can be used
The possible four test methods for compliance evaluation of mass products are:
• using a single device,
• non-central t-distribution (see 5.1),
• binomial distribution (see 5.2) and
• the additional margin (see 5.3)
Each of these methods are based on different statistical methodologies, and therefore each of
the methods have different properties (advantages or disadvantages) when applied in practice
by manufacturers or authorities.
a) Using a single device
A test on a single device is used by manufacturers. The method requires that repetitive
testing of the product over time has to occur.
b) Non-central t-distribution:
The test is based on the non-central t-distribution and contains the condition of normal
distribution for the totality. As long as this condition is fulfilled, the test gives correct
results for the approval of a sample. But disapproval may be indicated without reason if
one or two measurements are far below the limit and the other measurement results are
near (but below) the limit.
If the failure is caused by measurement results far below the limit due to the large
standard deviation, alternatively the test with the additional margin may be used for the
failed sample. If the sample passes, the product is o.k.
In case of disapproval, it is possible to select further devices from the same product batch
and to combine all the failed and newly selected devices in a larger sample.
An advantage of this test method is that the sample can be relatively small.
c) Binomial distribution:
The test is based on the binomial distribution and contains no further condition of
distribution for the totality. The test gives correct results for the approval and disapproval
of a sample.
In case of disapproval, it is possible to select further devices from the same product batch
and to combine all the failed and newly selected devices in a larger sample.
The disadvantage of this test method is that the sample must have at least 7 devices.
d) Additional acceptance limit:
The test is based on the condition of normal distribution for the totality and the estimation
of the expected standard deviation. The test gives correct results for the approval of a
sample.
If the failure is caused by measurement results which are close to the limit, an additional
test on the sample based on the non-central t-distribution may be used for the failed
sample. If the sample passes the test, the product is o.k.
In case of disapproval, it is possible to select further devices from the same product batch
and to combine all the failed and newly selected devices in a larger sample. This method
is only applicable to samples with less than 7 devices.

– 12 – TR CISPR 16-4-3 © IEC:2004
+A1:2006(E)
5.6 Compliance criteria and measurement instrumentation uncertainty
The requirement for product compliance contains two parts: one is the requirement of the
80 %/80 % rule and the other is the measurement instrumentation uncertainty as specified in
CISPR 16-4-2.
Therefore the outcome of the 80 %/80 % test indicates compliance with the limit as long as
the requirement of CISPR 16-4-2 is fulfilled. This means U is lower than or equal to
Lab
U .
CISPR
In cases where U is higher than U , the measurement results which are used for the
Lab CISPR
80 %/80 % rule have to be increased by the value Δ.
Δ =[]U − U (10)
Lab CISPR
U < U
CISPR Lab
6 Immunity tests
6.1 Application of the CISPR 80 %/80 % rule to immunity tests
In the assessment of the immunity of appliances and equipment in large-scale production,
consideration should be given to the specification of the statistical method to be used in the
CISPR sampling scheme. Two methods have been standardized: one using the binomial
distribution and the other using the non-central t-distribution.
The binomial distribution method is essentially sampling by attributes. Hence, this method
should be used in an immunity test in which the immunity level cannot be determined, with the
result that it is only possible to verify whether an appliance or equipment complies with the
immunity limit or not, i.e. only a pass or fail test at a specified immunity level is possible.
The non-central t-distribution method is essentially sampling by variables. Hence, this method
is suitable for an immunity test in which the immunity level or the level of a signal that is a
measure of the degradation of operation, can be determined. The latter level shall be
expressed in logarithmic units before applying the non-central t-distribution method.
6.2 Application guidelines
Subclause 6.1 only gives conditions related to the choice of statistical test method to be used
in the assessment of the immunity of appliances and equipment in large-scale production
after it has been decided by the relevant Product Committee that a statistical evaluation is
needed. A Product Committee may also decide that a type-test alone is adequate.
6.2.1 Sampling by attributes
When testing the immunity of an equipment under test (EUT), the combination of type of
disturbance signal and type of susceptible part in the EUT might result in damage to the EUT
if the immunity level is exceeded. In such a case, only an immunity test on a Pass/Fail or
Go/No Go basis will be possible, i.e. a test which verifies only whether the EUT complies or
does not comply with the immunity limit. Consequently, only two test results are possible: the
EUT passes or the EUT fails. The properties "pass" and "fail" are attributes of the EUT, so the
method based on the binomial distribution has to be used.
An immunity test on a Pass/Fail basis is not necessarily associated with damage to the EUT.
If the test is to be carried out with a fixed-level electromagnetic disturbance, it may also be
possible to use only the Pass/Fail criterion. Also in this case the sampling method based on
the binomial distribution has to be used.

TR CISPR 16-4-3 © IEC:2004 – 13 –
+A1:2006(E)
An example of an immunity test on a Pass/Fail basis in view of the possibility of damaging the
EUT is the testing of telecommunication equipment for immunity to transients caused by
lightning. An example of such a test in view of the fixed-level disturbance is the electrostatic
discharge test on (digital) information technology equipment.
6.2.2 Sampling by variables
If the EUT and the chosen immunity test allow the determination of the immunity level or the
level of a signal that is a measure of the degradation of operation, these levels will be
variables and, hence, a Product Committee may decide to opt for sampling by variables. In
that case, the sampling method based on the non-central t-distribution has to be used.
Note the above formulation "may decide", as a Product Committee can always decide to opt
for a test on a Pass/Fail basis. In addition, note that if the EUT is sufficiently immune, it might
not be possible to determine the levels mentioned. This does not exclude, however, the
possibility of sampling by variables. Such a situation is completely comparable with
the situation in an emission test when the emission level is lower than the noise level of the
CISPR receiver.
The determination of the immunity level in an immunity test is, generally speaking, not very
practical. It always causes over-exposure of the EUT to the applied disturbance signal, and
may easily lead to unforeseen effects during immunity testing. Nevertheless, there is no need
to exclude this determination beforehand.
A signal which is a measure of the degradation of operation of the EUT may be available for
sampling by variables: for example, the demodulated signal when testing several samples of
EUT, say an audio equipment, for their immunity to amplitude-modulated RF signals of
constant level and frequency. The level of the demodulated signal is then a measure of the
degradation of the EUT. Another example is the bit-error rate when performing immunity tests
on digital communication equipment.

– 14 – TR CISPR 16-4-3 © IEC:2004
+A1:2006(E)
Annex A
(informative)
Statistical considerations in the determination
of limits of radio interference

NOTE This annex was previously published as CISPR Report 48. Its content is identical to the text taken from the
earlier publication CISPR 8B.
A.1 Introduction
Compliance of mass-produced appliances with radio interference limits should be based on
the application of statistical techniques that have to ensure the consumer, with an 80 %
degree of confidence, that 80 % of the appliances of a type being investigated are below the
specified radio interference limit. This so-called 80 % /80 % rule protects the consumer from
appliances with too high a radio interference level, but it says hardly anything about the
probability that a batch of appliances from which the sample has been taken will be accepted.
This acceptance probability is very important to the manufacturer. The manufacturer knows
only that if 20 % of the items of the batch are above the relevant limit, the acceptance
probability is 20 % and knowledge is necessary about the dependence of the acceptance
probability on the sample size and the fraction of items in the batch that are above the
relevant limit. The curves representing the acceptance probability versus fraction items above
the limit and the sample size as a parameter are called the operating characteristic curves.
These curves can be calculated using either the non-central t-distribution (sampling by
variables) or the binomial distribution (sampling by attributes).
The Poisson distribution cannot be used since the fraction appliances above the limit should
be very small (<1 %) and the sample size large (more than 20 items). Besides sampling of
batches, it is also possible to ensure conformity of the production by means of control chart
techniques. These methods provide a continuous recording of the wanted information – for
example, the radio interference level of the appliances being produced.
A.2 Tests based on the non-central t-distribution (sampling by variables)
The following condition must be fulfilled:
X +k S ≤ L (A.1)
n
and has to ensure, with an 80 % degree of confidence, that 80 % of the appliances produced
on a large scale are below a specified radio interference limit L.
Meaning of the symbols used in this expression:
X = mean value of the interference level of the sample with size n of the appliances to be
tested; X is known;
S = standard deviation of the interference level of the sample with size n of the appliances
n
to be tested; S is known;
n
n
X = X (A.2)
∑
i
n
i=1
()X − X
∑
i
S = (A.3)
n
n −1
k = constant to be determined in such a way that the above-stated rule is satisfied;
L = the permissible radio interference limit; L is an upper limit.

TR CISPR 16-4-3 © IEC:2004 – 15 –
+A1:2006(E)
A.2.1 Determination of the constant k
It is assumed that the production being investigated has a normal distribution with the
following parameters:
μ = mean value of the radio interference level of all appliances; μ is unknown;
σ = standard deviation of the radio interference level of all appliances; σ is unknown.
Assume: p fraction that is above the limit L (fraction defective) and (1 – p) fraction of the lot
below the specified limit L.
Define a constant K :
p
y
∞
−
p = e dy (A.4)
∫
2π
K
p
y
−
in which f(y) = e is the standardized normal density function.
2π
K can be determined from appropriate tables of the normal distribution function.
p
f (y)
Fraction defective p
K
p
L − μ x − μ
y
σ
σ
IEC  539/04
Figure A.1 – Determination of the faction p
From the definition of K as well as the figure drawn above it follows that:
p
L = μ + K σ  (A.5)
p
with K > 0
p
since L is an upper limit.
– 16 – TR CISPR 16-4-3 © IEC:2004
+A1:2006(E)
According to the CISPR, if p = 0,2, then K = 0,84. The test instruction can now be read as
p
follows:
( )
p X +kS ≥ L / L = μ + K σ = 1−α (A.6)
n p
The probability α of a batch with a fraction defective p being accepted gives the consumer's risk.
For CISPR, α = 0,2 (1 – α = 0,8 → 80 %) and K = 0, 84.
p
To determine the constant k, the expression should be rewritten as follows:
( )
p X +kS ≥ L / L = μ + K σ = 1−α (A.7)
n p
⎛ ⎞
X − μ L − μ kS
n
⎜ ⎟
= p − ≥ − L = μ + K σ (A.8)
p
⎟
⎜
σ n σ n σ n
⎝ ⎠
⎛ ⎞
X − μ L − μ
⎜ − + ⎟
⎜ σ n σ n ⎟
= p ≤ k n L = μ + K σ (A.9)
p
⎜ ⎟
S σ
n
⎜ ⎟
⎜ ⎟
⎝ ⎠
By definition:
X − μ L − μ
− +
σ n σ n
t =
n.c.
S σ
n
t is a non-central t-distribution with non-centrality parameter
n.c.
(L − μ) σ n = K n (A.10)
p
and (n – 1) degrees of freedom.
The non-centrality parameter follows from the condition that not more than a fraction p of the
lot being investigated is above the permissible limit.
p()t ≤ k n = 1−α (A.11)
n.c.
⎛ ⎞
t n
n.c.
⎜ ⎟
p ≤ k = 1−α (A.12)
⎜ ⎟
n −1
n −1
⎝ ⎠
This probability function has been tabulated in [1] and [2]. Some figures are given below.
With α = 0,2, p = 0,1 (1 – α = 80 %, 1 – p = 80 %), the following values for k will be obtained
for different sample sizes:
n 4 5 6 7 8 9 10 11 12
k 1,68 1,51 1,42 1,35 1,30 1,27 1,24 1,21 1,20

TR CISPR 16-4-3 © IEC:2004 – 17 –
+A1:2006(E)
A.2.2 Determination of the sample size n
The producer wants to know the probability of the appliances being accepted and has to know:
( )
p X +kS ≤ L / L = μ + K σ (A.13)
n p
By definition, this expression is equal to β(p), the acceptance probability. The probability
1 – β(p) of a batch with a fraction defective p being rejected gives the producer's risk.
This can be rewritten as follows:
⎛ ⎞
t n
n.c.
⎜ ⎟
p ≥ k = β ( p) (A.14)
⎜ ⎟
n −1
n −1
⎝ ⎠
For a lot with the same fraction defective p as in A.2.1, β(p) equals α. With p = 0,2, α = 0,2
(CISPR values), β(0,2) is 0,2. From the producer's point of view, β(p) should be maximized by
improving the production (a smaller percentage of defectives) since β(p) depends on the
defective fraction.
Generally, the manufacturer needs an acceptance probability as high as 95 %. The function
representing the dependence of the acceptable probability β(p) on the fraction defective p is
called the operating characteristic of the test and 1 – β(p) the power curve of the test. The
mathematical representation for the O.C. curve is
⎛ ⎞
t n
n.c.
⎜ ⎟
β ( p) = p ≥ k (A.15)
⎜ ⎟
n −1
n −1
⎝ ⎠
for fixed n.
In Figure A.1, a few curves are given for α = 0,2. From these curves, it can be seen that in
order to ensure the same acceptance probability β(p), the percentage of defectives will
increase with the sample size. The so-called discriminatory power of the operating
characteristic curve increases as the sample size increases and is ideal if n equals the total
number of appliances to be approved.
A.2.3 Example (see Figure A.1)
A batch of appliances has to be checked. According to the 80 %/80 % rule with a sample size
n = 6, we have k = 1,42. The consumer has an 80 % degree of confidence that 80 % of the
batch lies below the limit.
The acceptance probability β(p) is 20 % at p = 0,2 (80 % below the limit). To obtain a greater
acceptance probability, the percentage defective p should be decreased. At p = 0,035 (96,5 %
below the limit), the acceptance probability is 80 %. From every 10 samples consisting of six
units taken from lots with p = 0,035, eight samples will on average yield a positive result. At
p = 0,009 (99,1 % below the limit), the acceptance probability is 95 %. In the latter case, the
manufacturer has to apply a μ and σ which fulfil the expression μ + 2,4 σ ≤ L.
A.3 Tests based on the binomial distribution (sampling by attributes)
The number of defective units c that occur in a sample of size n has to ensure with an 80 %
degree of confidence that 80 % of the appliances produced on a large scale are below a
specified radio interference limit L. An item has to be considered defective as soon as its
radio interference level is above the specified value L.

– 18 – TR CISPR 16-4-3 © IEC:2004
+A1:2006(E)
A.3.1 Determination of constant c
The occurrence of defective units by sampling a batch of appliances should satisfy the
requirement that the occurrences are statistically independent and not more than one
occurrence takes place at the same moment.
The binomial distribution is characterized by the fraction defective p of the batch of appliances
being tested and the sample size n.
The probability that a sample of size n has exactly c defective items is given by:
⎛ n⎞
c n−c
p(x = c) = p (1− p) n,
...