EN IEC 61123:2020

SLOVENSKI STANDARD
01-maj-2020
Preskušanje zanesljivosti - Načrti za preverjanje skladnosti z določeno stopnjo
uspešnosti (IEC 61123:2019)
Reliability testing - Compliance test plans for success ratio (IEC 61123:2019)
Prüfung der Zuverlässigkeit - Konformitätsprüfpläne für den Erfolgsquotienten (IEC
61123:2019)
Essai de fiabilité - Plans d'essai de conformité pour une proportion de succès (IEC
61123:2019)
Ta slovenski standard je istoveten z: EN IEC 61123:2020
ICS:
03.120.01 Kakovost na splošno Quality in general
21.020 Značilnosti in načrtovanje Characteristics and design of
strojev, aparatov, opreme machines, apparatus,
equipment
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD EN IEC 61123

NORME EUROPÉENNE
EUROPÄISCHE NORM
February 2020
ICS 03.120.01; 03.120.30; 21.020

English Version
Reliability testing - Compliance test plans for success ratio
(IEC 61123:2019)
Essais de fiabilité - Plans d'essai de conformité pour une Prüfung der Zuverlässigkeit - Konformitätsprüfpläne für den
proportion de succès Erfolgsquotienten
(IEC 61123:2019) (IEC 61123:2019)
This European Standard was approved by CENELEC on 2019-12-27. CENELEC members are bound to comply with the CEN/CENELEC
Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration.
Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN-CENELEC
Management Centre or to any CENELEC member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CENELEC member into its own language and notified to the CEN-CENELEC Management Centre has the
same status as the official versions.
CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Croatia, Cyprus, the Czech Republic,
Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the
Netherlands, Norway, Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.

European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2020 CENELEC All rights of exploitation in any form and by any means reserved worldwide for CENELEC Members.
Ref. No. EN IEC 61123:2020 E
European foreword
The text of document 56/1852/FDIS, future edition 2 of IEC 61123, prepared by IEC/TC 56
"Dependability" was submitted to the IEC-CENELEC parallel vote and approved by CENELEC as
The following dates are fixed:
• latest date by which the document has to be implemented at national (dop) 2020-09-27
level by publication of an identical national standard or by endorsement
• latest date by which the national standards conflicting with the (dow) 2022-12-27
document have to be withdrawn
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CENELEC shall not be held responsible for identifying any or all such patent rights.

Endorsement notice
The text of the International Standard IEC 61123:2019 was approved by CENELEC as a European
Standard without any modification.
In the official version, for Bibliography, the following note has to be added for the standard indicated:
IEC 61124 NOTE Harmonized as EN 61124

Annex ZA
(normative)
Normative references to international publications
with their corresponding European publications
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.
NOTE 1  Where an International Publication has been modified by common modifications, indicated by (mod), the relevant
EN/HD applies.
NOTE 2  Up-to-date information on the latest versions of the European Standards listed in this annex is available here:
www.cenelec.eu.
Publication Year Title EN/HD Year
IEC 60050-192 2015 International electrotechnical vocabulary - - -
Part 192: Dependability
IEC 60300-3-5 2001 Dependability management - Part 3-5: - -
Application guide - Reliability test
conditions and statistical test principles

IEC 61123 ®
Edition 2.0 2019-11
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Reliability testing – Compliance test plans for success ratio

Essais de fiabilité – Plans d'essai de conformité pour une proportion de succès

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 03.120.01; 03.120.30; 21.020 ISBN 978-2-8322-7647-1

– 2 – IEC 61123:2019 © IEC 2019
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 8
2 Normative references . 8
3 Terms, definitions, abbreviated terms and symbols . 8
3.1 Terms and definitions . 8
3.2 Abbreviated terms and symbols . 9
3.2.1 Abbreviated terms . 9
3.2.2 Symbols . 9
4 General requirements and area of application . 10
4.1 Reliability requirement . 10
4.2 Repair and replacement . 10
4.3 Types of test plans . 10
4.3.1 General . 10
4.3.2 Features of the test plan types. 10
4.4 General test procedure . 11
4.5 General decision criteria . 11
5 Truncated sequential probability ratio test plans (SPRT) . 13
5.1 Characteristics . 13
5.2 Decision criteria . 13
5.3 Operating characteristic curve (OC) . 14
5.4 Expected number of trials to decision (ENT) . 15
6 Fixed trial/failure terminated test plans (FTFT) . 16
6.1 Characteristics . 16
6.2 Decision criteria . 16
7 Design of fixed trial/failure terminated test plans . 17
7.1 Characteristics . 17
7.2 Approach . 17
7.3 Common case . 18
7.4 Other cases . 18
7.5 Example of application . 18
7.6 Procedure to determine D and c or n and c . 18
7.6.1 Figure and table readings . 18
7.6.2 Use of figures and tables . 19
7.7 Decision criteria . 19
Annex A (informative) Additional information on sequential test plans . 20
A.1 Example. 20
A.2 Extension of the test set (through interpolation and extrapolation) . 21
A.2.1 General . 21
A.2.2 Extrapolation for p < 0,001 . 21
A.2.3 Interpolation . 21
Annex B (informative) Design of fixed trial/failure terminated test plans − Examples . 24
B.1 Use of figures and tables . 24
B.2 Case where number of events, n, is not known, but is predictable . 24
Annex C (informative) Design of fixed trial/failure terminated test plans – Mathematical
procedures and formulas . 26

IEC 61123:2019 © IEC 2019 – 3 –
C.1 General . 26
C.2 Symbols . 26
C.3 Computation . 26
C.3.1 Determination of D versus n . 26
C.3.2 Determination of n and c versus p , D, α, β . 27
C.3.3 Test without failures – Determination of n and D versus p , α, β . 27
C.3.4 Determination of OC curves . 28
C.3.5 Determination of inverse OC curves . 28
C.4 Accuracy . 29
C.5 Tables of cumulative normal distribution and its Inverse. 29
Annex D (normative) Truncated sequential test plans . 31
Annex E (informative) Design of fixed trial/failure terminated test plans – Figures and
tables to determine D and c or n and c . 40
Bibliography . 49

Figure 1 – Expected and maximal number of trials for SPRT and FTFT with the same risks . 11
Figure 2 – SPRT diagram. 14
Figure 3 – OC curve. 15
Figure 4 – SPRT – Curve of expected number of trials to decision (ENT) . 15
Figure 5 – Principal layout of Tables E.1 to E.3 . 19
Figure A.1 – Example of a truncated sequential test . 20
Figure E.1 – Discrimination ratio, D, versus number of events, n for p = 0,05 . 40
Figure E.2 – Discrimination ratio, D, versus number of events, n for p = 0,10 . 41
Figure E.3 – Discrimination ratio, D, versus number of events, n for p = 0,15 . 42
Table 1 – Overview – Maximal number of trials and expected number of trials at p for
SPRT and FTFT . 12
Table 2 – Range of the test parameters . 13
Table 3 – OC curve . 14
Table 4 – ENT (n ) versus true failure ratio (p) . 15
e
Table 5 – Fixed trial/failure terminated test plans . 16
Table A.1 – Example for interpolation by α and β . 23
Table C.1 – Cumulative normal distribution for fixed u values . 29
γ
Table C.2 – Inverse cumulative normal distribution for fixed 1 − γ values . 30
Table D.1 – Truncated sequential test plans . 31
Table E.1 – Acceptable number of failures, c, versus number of events, n for p = 0,05 . 43
Table E.2 – Acceptable number of failures, c, versus number of events, n for p = 0,10 . 45
Table E.3 – Acceptable number of failures, c, versus number of events, n for p = 0,15 . 47
– 4 – IEC 61123:2019 © IEC 2019
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
RELIABILITY TESTING –
COMPLIANCE TEST PLANS FOR SUCCESS RATIO

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
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
misinterpretation by any end user.
4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence between
any IEC Publication and the corresponding national or regional publication shall be clearly indicated in the latter.
5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any
services carried out by independent certification bodies.
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
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
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.
International Standard IEC 61123 has been prepared by IEC technical committee 56,
Dependability.
This second edition cancels and replaces the first edition published in 1991. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) The sequential probability ratio test (SPRT) [1, 2] has been significantly developed in
recent years [3, 4, 5]. This edition contains shorter and accurate tests, a wide range of test
plans, and significant additional characteristic data, as follows:
– the tests are significantly truncated (the maximum trial numbers are low) without
substantially increasing the expected number of trials to decision (ENT);
– the true producer’s and consumer’s risks (α', β') are given and very close to the nominal
(α, β);
______________
Numbers in square brackets refer to the bibliography.

IEC 61123:2019 © IEC 2019 – 5 –
– the range of the test parameters is wide (failure ratio, risks and discrimination ratio);
– the test plans include various risk ratios (not restricted to equal risks only);
– the values of ENT are accurate and given in the relevant region (for practical use);
– guidelines for extension of the test sets (interpolation and extrapolation) are included.
b) In Annex C, the use of the cumulative binomial distribution function of Excel that simplifies
the procedure of designing has been added (Clause C.3).
The text of this International Standard is based on the following documents:
FDIS Report on voting
56/1852/FDIS 56/1873/RVD
Full information on the voting for the approval of this International Standard can be found in the
report on voting indicated in the above table.
This document has been drafted in accordance with the ISO/IEC Directives, Part 2.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under "http://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 61123:2019 © IEC 2019
INTRODUCTION
A compliance test is an essential part of the reliability assurance system. Reliability is affected
by many random factors, so its prediction is not accurate. The direct way to check if the
item/system meets its reliability specifications is to perform a compliance test.
The test serves to verify the compliance with the specified probability that an item will perform
as required. The outcome of each trial of the test is either success or failure.
The probability of making the correct decision in the test depends on the sample size (number
of trials). The tests require a large sample size and, accordingly, a large consumption of funds
and time. The consumptions are especially high for reliability testing. For this reason, sampling
plans of the tests must be carefully planned in order to reduce the sample size.
This document is dedicated to sampling plans for the tests.
The procedures are based on the assumption that trials of the test are statistically independent
and the probability of success, q in them is constant. This document also applies the probability
of failure p = 1 – q.
The tests are characterized by operating characteristic (OC) and number of trials to decision.
OC is the probability of accepting an item as meeting the requirements. In this document, the
OC is represented by the coordinates of its two points (see ISO 3534-2):
– (p , 1 – α) are the coordinates of the producer’s risk point (PRP);
– (p , β) are the coordinates of the consumer’s risk point (CRP).
The number of trials to reaching a decision regarding the test is a random value and in this
document is usually characterized by its expected (ENT) and maximum (MaxNT) values.
This document contains two types of tests:
– truncated sequential probability ratio test (SPRT);
– fixed trial/failure terminated test (FTFT).
The FTFT is characterized by decision rules for accepting or rejecting compliance when the
termination trials number n (MaxNT) has been reached, or the acceptable number of failures c
f
has been exceeded. This test has the smallest n among all tests with specified PRP and CRP.
f
When testing objects with p ≤ p , ENT is close to n , and for p > p , ENT decreases significantly.
0 f 0
Another advantage of the FTFT is the ability to conduct all trials simultaneously, but ENT
increases and becomes equal to n .
f
In the SPRT, the decision is made after each trial: accept or reject compliance, or continue
testing. This document contains a truncated SPRT with MaxNT = n . This n is 1,1 to 1,2 times
t t
greater than n of the FTFT with the same PRP and CRP. However, the ENT of the SPRT is
f
significantly smaller than that of the corresponding FTFT, and for p ≤ p it can be 1,4 to 1,8
times smaller. This is a great advantage of the SPRT. If it is necessary to shorten the calendar
time of the SPRT, it is possible to run the trials by small portions of n , while the OC and ENT
t
will not change significantly.
The planning of the SPRT is quite complicated so this document contains extensive tables with
ready-to-use test plans and their characteristics. Tests are listed for α = β as well as for α ≠ β.
The tables also allow the design of additional tests by simple interpolation and, for small p , by
extrapolation.
IEC 61123:2019 © IEC 2019 – 7 –
Some of the tests have a very large sample size, which will probably be used rarely. However,
the data allow the user of this document to assess the economic benefit of the OC test
requirements and, in general, to assess the advisability of performing the test.
The test is used for reliability testing; for example, to check compliance of the reliability of a
non-repairable item for a given time interval (warranty period or designed lifetime). The test
makes no assumption on whether the failure rate is constant or non-constant. IEC 61124
assumes a constant failure rate and is more statistically efficient since it takes the accumulated
operating time into account.
Clause 4 presents the types of tests and recommendations for their selection. It also discusses
the ability to reuse items during the test. Clause 5 explains the parameters of the stopping
boundaries and the characteristics of the SPRT (their values are given in Annex D). Clause 6
is devoted to the FTFT, a table with parameters of stopping boundaries and characteristics is
given. Annex A is devoted to the SPRT and provides examples of choosing a test by cost-
benefit considerations, extension of the test set of Clause 5 by extra- and interpolation.

– 8 – IEC 61123:2019 © IEC 2019
RELIABILITY TESTING –
COMPLIANCE TEST PLANS FOR SUCCESS RATIO

1 Scope
This international standard is intended to define a procedure to verify if a reliability of an
item/system complies with the stated requirements. The requirement is assumed to be specified
as the percentage of success (success ratio) or the percentage of failures (failure ratio).
This document can be used where a number of items are tested (number of trials performed)
and classified as passed or failed. It can also be used where one or a number of items are
tested repeatedly. The procedures are based on the assumption that the probability of success
or failure is the same from trial to trial (statistically independent events). Plans for fixed
trial/failure terminated tests as well as truncated sequential probability ratio tests (SPRTs) are
included. This document contains extensive tables with ready-to-use SPRT plans and their
characteristics for equal and non-equal risks for supplier and customer.
In the case of the reliability compliance tests for constant failure rate/intensity, IEC 61124
applies.
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 60050-192:2015, International Electrotechnical Vocabulary – Part 192: Dependability
(available at http://www.electropedia.org)
IEC 60300-3-5:2001, Dependability management – Part 3-5: Application guide – Reliability test
conditions and statistical test principles
3 Terms, definitions, abbreviated terms and symbols
3.1 Terms and definitions
For the purposes of this document, the following terms and 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 http://www.iso.org/obp
3.1.1
success ratio
probability that an item will perform as required or that a trial will be successful under stated
conditions
Note 1 to entry: An observed success ratio is the ratio of the number of non-faulty items or of successful trials at
the completion of testing, to the total number of test items or number of trials.

IEC 61123:2019 © IEC 2019 – 9 –
3.1.2
failure ratio
probability that an item will fail or that a trial will be unsuccessful under stated conditions
Note 1 to entry: An observed failure ratio is the ratio of the number of faulty items or of unsuccessful trials at the
completion of testing, to the total number of test items or number of trials.
3.2 Abbreviated terms and symbols
3.2.1 Abbreviated terms
AQL acceptable quality level
CRP consumer’s risk point
ENT expected number of trials to decision
FTFT fixed trial/failure terminated test
LQ limiting quality
MaxNT maximal number of trials to decision
OC operating characteristic
PRP producer’s risk point
SPRT (truncated) sequential probability ratio test (in some literature called probability ratio
sequential test (PRST))
3.2.2 Symbols
α nominal producer's risk (type I risk)
α' true producer's risk (type I risk)
β nominal consumer's risk (type II risk)
β' true consumer's risk (type II risk)
c acceptable number of failures or unsuccessful events during the test
D nominal discrimination ratio, D = p / p = (1 – q ) / (1 – q )
1 0 1 0
D' true discrimination ratio
h intercept value of the accept line on the vertical axis of the SPRT diagram (Figure 2)
a
h intercept value of the reject line on the vertical axis of the SPRT diagram (Figure 2)
r
n number of items, number of trials, number of events, sample size
n ENT
e
indexed n , where j = L, 0, M, 1, H (which are related to five values of p as in Figure 4)
n
e,j e
n number of items, number of trials, number of events, sample size required for
f
acceptance in an FTFT
n accumulated number of trials in a sequential test plan
s
n number of items, number of trials, number of events, sample size at truncation in an
t
SPRT
p true failure ratio, p = 1 – q
p specified acceptable failure ratio, corresponding to acceptable quality level (AQL)
p unacceptable failure ratio, corresponding to limiting quality (LQ), p = p D
1 1 0
P probability of acceptance
a
q true success ratio, q = 1 – p
q specified acceptable success ratio, q = 1 – p
0 0 0
q unacceptable success ratio, q = 1 – p
1 1 1
– 10 – IEC 61123:2019 © IEC 2019
r number of relevant failures or relevant unsuccessful events
r number of relevant failures or relevant unsuccessful events at truncation
t
s slope of accept and reject lines in the sequential test diagram (see Figure 2)
4 General requirements and area of application
4.1 Reliability requirement
The requirement is assumed to be specified as:
– acceptable success ratio, q or
– acceptable failure ratio, p (p = 1 – q ).
0 0 0
In addition, a fixed time interval must be specified (see 3.1.1 and definition of reliability in
IEC 60050-192:2015, 192-05-05).
These test plans are based on the assumption that each trial is statistically independent and
that the probability of success (or failure) is constant (do not change from one trial to another),
i.e. the binomial distribution assumptions apply. The true producer's and consumer's risks for
the fixed trial/failure terminated test plans (Tables E.1 to E.3) differ from the nominal
characteristics, α and β, due to the necessary approximations to whole numbers. For the SPRT
(Table D.1), the true risks are equal to the nominal (exceptional case – see Note 1 of Table 2).
4.2 Repair and replacement
The test plans given in this document are applicable to reused as well as non-reused (one-shot)
items. Reused items may be repaired between successive trials, provided that the state and
performance are the same at the start of all trials. For non-reused items, a separate test item
(having the same performance) is used for each trial.
4.3 Types of test plans
4.3.1 General
Test plans are given for two types of tests:
– truncated sequential probability ratio test (SPRT);
– fixed trial/failure terminated test (FTFT).
For SPRT see Clause 5. Clause 6 includes ready-to-use FTFT plans. Clause 7 includes
guidelines for planning additional FTFTs which are not covered in Clause 6.
The detailed reliability test specification shall state which type of test and which test plan are
to be used. Guidance on the choice of type of test is similar to that given in IEC 60300-3-5 for
SPRTs and FTFTs for the case in which the failure rate/intensity is a function of time.
4.3.2 Features of the test plan types
In order to choose between the two types of test for a specified OC, it is necessary to make a
comparison between their MaxNT and ENT. A qualitative comparison between SPRT and FTFT
is given in the Introduction. In Figure 1 and Table 1, data is given for a quantitative comparison.
Table 1 shows some of the ready-to-use test plans available in this document. For each test,
two parameters of the number of trials to decision are listed: MaxNT (n for SPRT or n for FTFT)
t f
and point n of ENT (see Figure 1). For the SPRT, for p ≤ p or p ≥ p , there is a very small
e,0 0 1
probability that the number of trials to decision will reach n . ENT of the FTFT, shown
t
in Figure 1, is obtained when the FTFT is conducted sequentially and after each trial a decision
is made to stop/continue the test. When all FTFT trials are conducted simultaneously, the

IEC 61123:2019 © IEC 2019 – 11 –
calendar test time is shortened, but the number of trials increases and becomes equal to
MaxNT.
In addition to choosing either SPRT or FTFT, Table 1 helps the users choose the relevant area
of the desired test characteristics (OC and the number of trials). Table 1 contains only part of
the ready-to-use test plans available in this document. Information about all these plans is given
in Clause 5 (for SPRT) and in Clause 6 (for FTFT).

NOTE This figure is drawn for p = 0,01, D = 3 (p = 0,03), α’ = β’ = 0,094.
0 1
Figure 1 – Expected and maximal number of trials for SPRT and FTFT
with the same risks
4.4 General test procedure
The test items should be subjected to the number of trials according to the relevant test plan.
For reused, replaced or repaired items, the detailed reliability test specifications should
preferably state the number of test items as well as the maximum number of trials for each test
item.
A trial is defined as the operation or cycle as described in the detailed reliability test
specification.
4.5 General decision criteria
All test plans and decision criteria are based on either:
– an acceptable number of relevant failures for a specified number of trials; or
– an acceptable number of trials for a specified number of relevant failures.
The numbers of trials and relevant failures (see IEC 60300-3-5) are counted and compared with
the decision criteria of the test plan.
The detailed decision criteria for the two types of test plans are given in 5.2, 6.2 and 7.7,
respectively.
– 12 – IEC 61123:2019 © IEC 2019
Table 1 – Overview – Maximal number of trials and expected number
of trials at p for SPRT and FTFT
p = 0,001 p = 0,01 p = 0,1
0 0 0
Test Para-
α β
type meter
D =1,5 D = 2 D = 3 D = 5 D =1,5 D = 2 D = 3 D = 5 D =1,5 D = 2 D = 3
n
t
63 969 18 687 6 015 2 407 6 316 1 866 601 199 558 158 51
SPRT
n
e,0
30 397 9 268 3 106 1 129 3 004 910 303 112 264 78 25
0,05 0,05
n
f
53 998 15 703 5 232 – 5 320 1 567 521 – 474 135 41
FTFT
n
e,0
53 848 15 624 5 197 – 5 293 1 553 513 – 460 127 36
n
t
38 019 11 007 3 814 1 590 3 719 1 103 382 116 331 96 33
SPRT
n
e,0
20 464 6 266 2 038 744 2 035 612 199 75 179 52 18
0,1 0,1
n
f
32 922 10 061 3 090 – 3 215 945 308 – 288 86 25
FTFT
n
e,0
32 675 9 948 3 029 – 3 183 928 299 – 277 80 22
n
t
16 092 4 790 1 611 782 1 610 479 162 53 146 43 18*
SPRT
n
e,0
9 786 2 936 963 353 961 288 94 39 83 27 8*
0,2 0,2
n
f
14 291 4 537 1 426 – 1 428 453 142 – 134 39 14
FTFT
n
e,0
13 927 4 374 1 348 – 1 389 435 133 – 127 35 12
n
t
6 449 2 050 1 075 388* 643 203 105 34* 31* 13 –
SPRT
n
e,0
3 906 1 159 383 234* 383 114 38 23* 23* 9 –
0,3 0,3
n
f
5 407 1 807 813 – 540 180 81 – 53 18 8
FTFT
n
e,0
5 041 1 645 751 – 502 163 74 – 48 15 6
n
t
48 380 13 979 4 667 1 864 4 758 1 401 465 188 461 119 40
0,05 0,1 SPRT
n
e,0
23 649 7 238 2 356 853 2 344 705 231 82 197 61 18
n
t
48 776 14 295 4 599 1 727 4 803 1 428 461 169 430 121 38
0,1 0,05 SPRT
n
e,0
27 707 6 225 2 826 1 026 2 732 829 275 99 239 71 22
n
t
36 138 10 819 3 321 1 345 3 545 1 015 335 139 316 89 28
0,05 0,2 SPRT
n
e,0
15 876 4 740 1 602 574 1 565 476 155 55 137 40 12
n
t
36 660 11 232 3 714 1 437 3 655 1 126 364 150 322 97 40
0,2 0,05 SPRT
n
e,0
21 997 6 642 2 220 820 2 173 650 218 79 192 56 17
NOTE For FTFT, the values of α and β are approximate. For SPRT, the values of α and β are insignificantly different
from nominal, except those marked with asterisks, for which the exact values are indicated in Table D.1.

IEC 61123:2019 © IEC 2019 – 13 –
5 Truncated sequential probability ratio test plans (SPRT)
5.1 Characteristics
Sequential test plans are characterized by decision rules for accepting or rejecting compliance,
or for continuing testing, after any number of trials. They are determined by selected values of
risks and discrimination ratio. In order to choose a test plan, the acceptable failure ratio, p has
to be specified (or derived).
Associated operating characteristic curves and values of the expected relevant number of trials
to decision are included.
Table D.1 presents the appropriate test plans for various p , D, α' and β'. The table contains
parameter values of h , h , s, n , r (Figure 2) and n (on 5 points, Figure 4) for each test plan.
a r t t e
NOTE n and r (that determine the truncation) were chosen as small as possible without significantly increasing
t t
the ENT [3, 4].
The range of the test parameters in Table D.1 are as in Table 2:
Table 2 – Range of the test parameters
p 0,001 0,002 0,005 0,01 0,02 0,05 0,1 0,2
D 1,5 1,75 2 3 5
α 0,025 0,05 0,1 0,2 0,3 0,4
0,025 0,05 0,1 0,025 0,05 0,1 0,2 0,025 0,05 0,1 0,2 0,4 0,05 0,1 0,2 0,3 0,1
β
NOTE 1 For a few short tests, mainly for D = 5 and α and β = 0,3, the deviation from the nominal risks is significant
because of the discreteness of the tests, and no suitable test is available.
NOTE 2 Extension of test sets is available, see Clause A.2 and [3, 4, 5].

5.2 Decision criteria
The decision criteria are as follows:
– accept if sn – h ≥ r;
s a
– continue if sn – h < r < sn + h ;
s a s r
– reject if r ≥ sn + h .
s r
The SPRT shall be truncated at lines based on the values n , r given in Table D.1 .
t t
The truncation gives rise to the following additional criteria:
– accept if n = n – r + r and r < r ;
s t t t
– reject if r > r .
t
The accumulated results are checked against the criteria after each trial and a decision is made
whether to accept, continue or reject.

– 14 – IEC 61123:2019 © IEC 2019

NOTE This figure is drawn for p = 0,01, D = 3 (p = 0,03), α' = β' = 0,100.
0 1
Figure 2 – SPRT diagram
5.3 Operating characteristic curve (OC)
For any of the truncated sequential tests, the following approximate points on the operating
characteristic curve are given in Table 3 and Figure 3:
Table 3 – OC curve
P
p
a
pD ~ 1
p
1 – α
ln(1−β )− lnα
s
ln(1−β )− lnαβ− ln + ln 1−α
( )
p
β
pD ~ 0
NOTE For α = β case, P (s) = 0,5.
a
In addition, the methodology for detailed calculation of the OC by Wald [1] is described in [3,
Subsection 2.2] and in [4, Appendix A].

IEC 61123:2019 © IEC 2019 – 15 –

NOTE This figure is drawn for p = 0,01, D = 3 (p = 0,03), α' = β' = 0,100.
0 1
Figure 3 – OC curve
5.4 Expected number of trials to decision (ENT)
For any of the truncated sequential test plans in Table D.1 the ENT curve is defined via 5 points
(n ) versus the true failure ratio (p), and according to Table 4 and Figure 4:
e,j
Table 4 – ENT (n ) versus true failure ratio (p)
e
p p p = pD
pD pD pD
0 0 0 10 1
n
n n n n n
e,j
e,L e,0 e,M e,1 e,H
NOTE j = L, 0, M, 1, H (see Figure 4).

NOTE This figure is drawn for p = 0,01, D = 3 (p = 0,03), α' = β' = 0,100.
0 1
Figure 4 – SPRT – Curve of expected number of trials to decision (ENT)

– 16 – IEC 61123:2019 © IEC 2019
6 Fixed trial/failure terminated test plans (FTFT)
6.1 Characteristics
Trial/failure terminated test plans are characterized by decision rules for accepting or rejecting
compliance when the termination number of trial has been reached or the acceptable number
of relevant failures has been exceeded. The test plans are determined by selected values of
risks and discrimination ratio. To implement a test plan, the acceptable failure ratio, p has to
be specified (or derived).
Table 5 presents appropriate test plans for various values of the specified p , D, α and β.
Associated OC curves and the exact values of α' and β' can be calculated using the methodology
given in C.3.4.
6.2 Decision criteria
The decision criteria are as follows:
– accept if r ≤ c at n = n ;
f
– reject if r > c at n ≤ n .
f
EXAMPLE:
p = 0,01; D = 3,0 (p = 0,03); α = β = 10 %. From Table 5 a number of trials n = 308 would be required and an accept
0 1 f
decision is made if r ≤ 5.
NOTE The curves of Annex E (Figures E.1 to E.3) are useful in giving an overview of the characteristics of the
different test plans.
Table 5 – Fixed trial/failure terminated test plans
α = β = 5 % α = β = 10 % α = β = 20 % α = β = 30 %
q p
D
0 0
n n n n
f c f c f c f c
0,999 5 0,000 5 1,5 108 002 66 65 849 40 28 584 17 10 814 6
1,75 51 726 34 32 207 21 14 306 9 5 442 3

2 31 410 22 20 125 14 9 074 6 3 615 2

3 10 467 9 6 181 5 2 852 2 1 626 1

0,999 0,001 1,5 53 998 66 32 922 40 14 291 17 5 407 6
1,75 25 861 34 16 102 21 7 152 9 2 721 3

2 15 703 22 10 061 14 4 537 6 1 807 2

3 5 232 9 3 090 5 1 426 2 813 1

0,995 0,005 1,5 10 647 65 6 581 40 2 857 17 1 081 6
1,75 5 168 34 3 218 21 1 429 9 544 3

2 3 137 22 1 893 13 906 6 361 2

3 1 044 9 617 5 285 2 162 1
0,99 0,01 1,5 5 320 65 3 215 39 1 428 17 540 6
1,75 2 581 34 1 607 21 714 9 272 3

2 1 567 22 945 13 453 6 180 2
3 521 9 308 5 142 2 81 1
0,98 0,02 1,5 2 620 64 1 605 39 713 17 270 6
1,75 1 288 34 770 20 356 9 136 3

2 781 22 471 13 226 6 90 2
3 259 9 153 5 71 2 40 1
0,97 0,03 1,5 1 720 63 1 044 38 450 16 180 6
1,75 835 33 512 20 237 9 90 3
2 519 22 313 13 150 6 60 2
3 158 8 101 5 47 2 27 1
0,96 0,04 1,5 1 288 63 782 38 337 16 135 6
1,75 625 33 383 20 161 8 68 3
2 374 21 234 13 98 5 45 2
3 117 8 76 5 35 2 20 1
IEC 61123:2019 © IEC 2019 – 17 –
α = β = 5 % α = β = 10 % α = β = 20 % α = β = 30 %
q p
D
0 0
n n n n
f c f c f c f c
0,95 0,05 1,5 1 014 62 610 37 269 16 108 6
1,75 486 32 306 20 129 8 54 3
2 298 21 187 1
...