IEC 61124:2012

IEC 61124 ®
Edition 3.0 2012-05
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Reliability testing – Compliance tests for constant failure rate and constant
failure intensity
Essais de fiabilité – Plan d’essais de conformité d’un taux de défaillance
constant et d’une intensité de défaillance constante

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IEC 61124 ®
Edition 3.0 2012-05
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Reliability testing – Compliance tests for constant failure rate and constant

failure intensity
Essais de fiabilité – Plan d’essais de conformité d’un taux de défaillance

constant et d’une intensité de défaillance constante

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
CODE PRIX XF
ICS 03.120.30; 19.020; 21.020 ISBN 978-2-88912-061-1

– 2 – 61124 © IEC:2012
CONTENTS
FOREWORD . 8
1 Scope . 10
2 Normative references . 10
3 Terms, definitions, abbreviations and symbols . 11
3.1 Terms and definitions . 11
3.2 Abbreviations and symbols . 11
3.2.1 Abbreviations . 11
3.2.2 Symbols . 11
4 General requirements and area of application . 13
4.1 Requirements . 13
4.2 Applicability to replaced and repaired items . 13
4.3 Types of test plans . 13
4.3.1 General . 13
4.3.2 Advantages and disadvantages of the different test plan types . 14
5 General test procedure . 14
5.1 Test conditions . 14
5.2 General characteristics of the test plans . 15
5.3 Data to be recorded . 15
*
5.4 Calculation of accumulated test time, T . 15
5.5 Number of failures . 16
6 Sequential test plans . 17
6.1 General . 17
6.2 Common test procedure . 17
6.3 Decision criteria . 17
6.4 Overview of test plans . 17
7 Fixed time/failure terminated test plans – Fixed duration test plans . 18
7.1 General . 18
7.2 Common test procedure . 18
7.3 Decision criteria . 19
7.4 Test plans . 19
8 Design of alternative time/failure terminated test plans . 20
8.1 General . 20
8.2 Design procedures . 20
8.3 Common test procedure . 20
8.4 Decision criteria . 21
9 Calendar time/failure terminated test plans for non-replaced items . 21
9.1 General . 21
9.2 Common test procedure . 21
9.3 Decision criteria . 21
9.4 Use of Table 2 of IEC 61123:1991 for fixed calendar time tests . 22
9.4.1 General . 22
9.4.2 Procedure when the test time is given . 22
9.4.3 Procedure when the number of items is given . 22
10 Combined test plans . 23

61124 © IEC:2012 – 3 –
10.1 General . 23
10.2 Common test procedure . 23
10.3 Decision criteria . 23
10.4 Test plans . 24
11 Performing the test . 24
12 Presentation of results . 24
Annex A (normative) Tables and graphs for sequential test plans . 25
Annex B (normative) Graphs for fixed time/failure terminated test plans . 44
Annex C (normative) Graphs for alternative time/failure terminated test plans . 53
Annex D (normative) Tables and graphs for combined test plans and additional
sequential test plans . 60
Annex E (informative) Examples and mathematical references for sequential test
plans . 78
Annex F (informative) Design of sequential test plans using a common spreadsheet
program . 86
Annex G (informative) Examples and mathematical references for fixed time/failure
terminated test plans – Fixed duration test plans . 97
Annex H (informative) Design of fixed duration time/failure terminated test plans using
a spreadsheet program . 99
Annex I (informative) Examples and mathematical references for the design of
alternative time/failure terminated test plans . 105
Annex J (informative) Examples and mathematical references for the calendar time
terminated test plans . 112
Annex K (informative) Derivation and mathematical reference for the optimized test
plans of GOST R 27 402 . 114
Bibliography . 122

Figure A.1 – Accept and reject lines for test plan A.1 . 25
Figure A.2 – Test plan A.1 – Operating characteristic curve . 26
Figure A.3 – Test plan A.1 – Expected accumulated test time to decision . 27
Figure A.4 – Accept and reject lines for test plan A.2 . 27
Figure A.5 – Test plan A.2 – Operating characteristic curve . 28
Figure A.6 – Test plan A.2 – Expected accumulated test time to decision . 29
Figure A.7 – Accept and reject lines for test plan A.3 . 29
Figure A.8 – Test plan A.3 – Operating characteristic curve . 30
Figure A.9 – Test plan A.3 – Expected accumulated test time to decision . 31
Figure A.10 – Accept and reject lines for test plan A.4 . 31
Figure A.11 – Test plan A.4 – Operating characteristic curve . 32
Figure A.12 – Test plan A.4 – Expected accumulated test time to decision . 33
Figure A.13 – Accept and reject lines for test plan A.5 . 33
Figure A.14 – Test plan A.5 – Operating characteristic curve . 34
Figure A.15 – Test plan A.5 – Expected accumulated test time to decision . 35
Figure A.16 – Accept and reject lines for test plan A.6 . 35
Figure A.17 – Test plan A.6 − Operating characteristic curve . 36
Figure A.18 – Test plan A.6 – Expected accumulated test time to decision . 37
Figure A.19 – Accept and reject lines for test plan A.7 . 37

– 4 – 61124 © IEC:2012
Figure A.20 – Test plan A.7 – Operating characteristic curve . 38
Figure A.21 – Test plan A.7 – Expected accumulated test time to decision . 39
Figure A.22 – Accept and reject lines for test plan A.8 . 40
Figure A.23 – Test plan A.8 – Operating characteristic curve . 41
Figure A.24 – Test plan A.8 – Expected accumulated test time to decision . 41
Figure A.25 – Accept and reject lines for test plan A.9 . 42
Figure A.26 – Test plan A.9 – Operating characteristic curve . 43
Figure A.27 – Test plan A.9 – Expected accumulated test time to decision . 43
Figure B.1 – Operating characteristic curves for test plans B.1, B.2, B.3 and B.4 . 44
Figure B.2 – Test plan B.1 – Expected test time to decision . 45
Figure B.3 – Test plan B.2 – Expected test time to decision . 45
Figure B.4 – Test plan B.3 – Expected test time to decision . 46
Figure B.5 – Test plan B.4 – Expected test time to decision . 46
Figure B.6 – Operating characteristic curves for test plans B.5, B.6, B.7 and B.8 . 47
Figure B.7 – Test plan B.5 – Expected test time to decision . 47
Figure B.8 – Test plan B.6 – Expected test time to decision . 48
Figure B.9 – Test plan B.7 – Expected test time to decision . 48
Figure B.10 – Test plan B.8 – Expected test time to decision . 49
Figure B.11 – Operating characteristic curves for test plans B.9, B.10 and B.11 . 49
Figure B.12 – Test plan B.9 – Expected test time to decision . 50
Figure B.13 – Test plan B.10 – Expected test time to decision . 50
Figure B.14 – Test plan B.11– Expected test time to decision . 51
Figure B.15 – Operating characteristic curves for test plans B.12 and B.13. 51
Figure B.16 – Test plan B.12 – Expected test time to decision . 52
Figure B.17 – Test plan B.13 – Expected test time to decision . 52
Figure C.1 – Discrimination ratio, D, and the acceptable number of failures, c = 0 to 8,
as a function of the expected number of failures, µ , for recommended values, 2,5 %,
5 %, 10 %, 20 %, and 30 % of α = β. 56
Figure C.2 – Operation characteristic curves for c = 0 to 8; probability of acceptance
P as a function of the (unknown) true expected number of failures, µ . 57
a 0
Figure C.3 – Discrimination ratio, D, as a function of the expected number of failures,
µ , for recommended values, 2,5 %, 5 %, 10 %, 15 %, 20 % and 30 % of α = β . 58
Figure C.4 – Acceptable number of failures, c, minus expected number of failures, µ
(Δµ = c – µ ) as a function of the expected number of failures µ for recommended
0 0 0
values 2,5 %, 5 %, 10 %, 20 %, and 30 % of α = β . 59
Figure D.1 – Accept and reject lines . 61
∗
Figure D.2 – Expected test time to decision T . 62
e
∗
Figure D.3 – Expected test time to decision of acceptance T (+) . 62
e
Figure D.4 – Operating characteristic P . 62
a
Figure D.5 – Accept and reject lines . 63
∗
T
Figure D.6 – Expected test time to decision . 64
e
∗
Figure D.7 – Expected test time to decision of acceptance T (+) . 64
e
Figure D.8 – Operating characteristic P . 64
a
61124 © IEC:2012 – 5 –
Figure D.9 – Accept and reject lines . 65
∗
Figure D.10 – Expected test time to decision T . 66
e
∗
Figure D.11 – Expected test time to decision of acceptance T (+) . 66
e
Figure D.12 – Operating characteristic P . 67
a
Figure D.13 – Accept and reject lines . 68
∗
Figure D.14 – Expected test time to decision T . 69
e
∗
Figure D.15 – Expected test time to decision of acceptance T (+) . 69
e
Figure D.16 – Operating characteristic P . 69
a
Figure D.17 – Accept and reject lines . 70
∗
Figure D.18 – Expected test time to decision T . 71
e
∗
T (+)
Figure D.19 – Expected test time to decision of acceptance . 71
e
Figure D.20 – Operating characteristic P . 71
a
Figure D.21 – Accept and reject lines . 72
∗
Figure D.22 – Expected test time to decision T . 73
e
∗
Figure D.23 – Expected test time to decision of acceptance T (+) . 73
e
Figure D.24 – Operating characteristic P . 73
a
Figure D.25 – Accept and reject lines . 74
∗
Figure D.26 – Expected test time to decision . 74
T
e
∗
Figure D.27 – Expected test time to decision of acceptance . 74
T (+)
e
Figure D.28 – Operating characteristic P . 75
a
Figure D.29 – Accept and reject lines . 75
*
Figure D.30 – Expected test time to decision T . 76
e
∗
Figure D.31 – Expected test time to decision of acceptance T (+) . 76
e
Figure D.32 – Operating characteristic P . 76
a
Figure E.1 – Example of a sequential test using test plan A.3 – α = β = 10 %, D = 3,
T *
= 1,11×10 h; r versus . 80
m
mo
Figure F.1 – SPRT spreadsheet graphing example . 92
Figure F.2 – OC curve for probability of acceptance, P . 95
a
Figure F.3 – Expected test time for making a decision . 95
Figure H.1 – OC curve plotted from the spreadsheet calculations . 104
Figure K.1 – Test plan types and terminology . 115
Figure K.2 – Principle of test plans . 117
Figure K.3 – Partitioning of the test plan graph . 117
Figure K.4 – Interior nodes and border nodes . 118
Figure K.5 – Paths to the accept line . 118
Figure K.6 – Paths to the reject line . 118
Figure K.7 – Probabilities of paths transfer between nodes . 119

– 6 – 61124 © IEC:2012
Figure K.8 – The recurrent element – Two cases . 121

Table 1 – Advantages and disadvantages for the different test plan types . 14
Table 2 – Overview of the sequential test plans given in Annex A and D . 18
Table 3 – Fixed time/failure terminated test plans . 19
Table 4 – Combined test plans in Annex D . 24
Table A.1 – Accept and reject lines for test plan A.1 . 26
Table A.2 – Accept and reject lines for test plan A.2 . 28
Table A.3 – Accept and reject lines for test plan A.3 . 30
Table A.4 – Accept and reject lines for test plan A.4 . 32
Table A.5 – Accept and reject lines for test plan A.5 . 34
Table A.6 – Accept and reject lines for test plan A.6 . 36
Table A.7 – Accept and reject lines for test plan A.7 . 38
Table A.8 – Accept and reject lines for test plan A.8 . 40
Table A.9 – Accept and reject lines for test plan A.9 . 42
Table D.1 – Sequential test plans in this annex . 60
Table D.2 – Combined test plans in this annex . 60
Table D.3 – Accept and reject lines . 61
Table D.4 – Expected test time to decision and operating characteristic P . 62
a
Table D.5 – Accept and reject lines . 63
Table D.6 – Expected test time to decision and operating characteristic P . 65
a
Table D.7 – Accept and reject lines . 66
Table D.8 – Expected test time to decision and operating characteristic P . 67
a
Table D.9 – Accept and reject lines . 68
Table D.10 – Expected test time to decision and operating characteristic P . 69
a
Table D.11 – Accept and reject lines . 70
Table D.12 – Expected test time to decision and operating characteristic P . 71
a
Table D.13 – Accept and reject lines . 72
Table D.14 – Expected test time to decision and operating characteristic P . 73
a
Table D.15 – Accept and reject lines . 74
Table D.16 – Expected test time to decision and operating characteristic P . 75
a
Table D.17 – Accept and reject lines . 76
Table D.18 – Expected test time to decision and operating characteristic P . 77
a
Table E.1 – Example for a sequential test using test plan A.3 (with example data) . 80
Table E.2 – Constants for border line formulae and their coordinates for sequential test
plans A.1 to A.9 . 85
Table F.1 – Beginning of the spreadsheet prepared to obtain a sequential test graph . 87
Table F.2 – Continuation of parameters calculation for the lines necessary for the
SPRT graph . 88
Table F.3 – Calculations of accept and reject line for the SPRT graph . 88
Table F.4 – Determination of the test termination time . 89
Table F.5 – Formulae for accept and reject line along with the test termination . 91
Table F.6 – Spreadsheet set-up for construction of the OC curves for the SPRT . 94

61124 © IEC:2012 – 7 –
Table H.1 – Set-up of the spreadsheet with embedded formulae – Example . 100
Table H.2 – Formulae embedded into the spreadsheet shown in Table H.1 . 101
Table H.3 – OC curve for the time/failure terminated fixed duration test . 103
Table I.1 – Cumulative normal distribution for fixed u values . 111
γ
Table I.2 – Inverse cumulative normal distribution for fixed 1–γ values . 111

– 8 – 61124 © IEC:2012
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
RELIABILITY TESTING –
COMPLIANCE TESTS FOR CONSTANT FAILURE RATE
AND CONSTANT FAILURE INTENSITY

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
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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 61124 has been prepared by IEC technical committee 56:
Dependability.
This third edition of IEC 61124 cancels and replaces the second edition, published in 2006,
and constitutes a technical revision.
The main changes with respect to the previous edition are as follows:
– A number of new test plans have been added based on the Russian standard GOST R
27.402 [1] , and it is intended to align the new edition of MIL-HDBK-781 [2] with this
edition. Algorithms for optimizing test plans using a spreadsheet program are given and a
number of optimized test plans are listed. Furthermore, emphasis is laid on the fact that
the test should be repeated following design changes.
———————
Figures in square brackets refer to the bibliography.

61124 © IEC:2012 – 9 –
– Discrepancies in test plans A, B as well as Annexes A and B that originated in IEC 60605-
7 [3], now withdrawn, have been corrected so these test plans differ from those given in
previous editions of IEC 61124. As requested by the National Committees, mathematical
background material and spreadsheet program information has been moved to informative
annexes. In addition, the symbol lists have been divided, so that some annexes have
separate lists of symbols.
– Guidance on how to choose test plans has been added as well as guidance on how to use
spreadsheet programs to create them. Test plans A.1 to A.9 and B.1 to B.13 have been
corrected.
– Subclauses 8.1, 8.2, 8.3, Clause 9, Annex C, Clauses G.2, I.2, I.3 and Annex J are
unchanged, except for updated terminology and references.
– Corrections to the second edition proposed by National Committees have been
implemented.
The text of this standard is based on the following documents:
FDIS Report on voting
56/1461/FDIS 56/1468/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
The committee has decided that the contents of this publication will remain unchanged until
the stability 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.
The contents of the corrigendum of January 2013 have been included in this copy.

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.
– 10 – 61124 © IEC:2012
RELIABILITY TESTING –
COMPLIANCE TESTS FOR CONSTANT FAILURE RATE
AND CONSTANT FAILURE INTENSITY

1 Scope
This International Standard gives a number of optimized test plans, the corresponding
operating characteristic curves and expected test times. In addition the algorithms for
designing test plans using a spreadsheet program are also given, together with guidance on
how to choose test plans.
This standard specifies procedures to test whether an observed value of
– failure rate,
– failure intensity,
– mean time to failure (MTTF),
– mean operating time between failures (MTBF),
conforms to a given requirement.
It is assumed, except where otherwise stated, that during the accumulated test time, the times
to failure or the operating times between failures are independent and identically
exponentially distributed. This assumption implies that the failure rate or failure intensity is
constant.
Four types of test plans are described as follows:
– truncated sequential tests;
– time/failure terminated tests;
– fixed calendar time terminated tests without replacement;
– combined test plans.
This standard does not cover guidance on how to plan, perform, analyse and report a test.
This information can be found in IEC 60300-3-5.
This standard does not describe test conditions. This information can be found in IEC 60605-2
and in IEC 60300-3-5.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and
are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 60050-191, International Electrotechnical Vocabulary (IEV) – Chapter 191: Dependability
and quality of service
IEC 60300-3-5:2001, Dependability management – Part 3-5: Application guide – Reliability
test conditions and statistical test principles

61124 © IEC:2012 – 11 –
IEC 60605-2, Equipment reliability testing – Part 2: Design of test cycles
IEC 60605-4:2001, Equipment reliability testing – Part 4: Statistical procedures for
exponential distribution – Point estimates, confidence intervals, prediction intervals and
tolerance intervals
IEC 60605-6, Equipment reliability testing – Part-6: Tests for the validity and estimation of the
constant failure rate and constant failure intensity
IEC 61123:1991, Reliability testing – Compliance test plans for success ratio
3 Terms, definitions, abbreviations and symbols
3.1 Terms and definitions
For the purposes of this document the terms and definitions given in IEC 60050-191 apply.
The terms "failure rate" and "failure intensity" are used as meaning constant failure rate and
constant failure intensity.
3.2 Abbreviations and symbols
3.2.1 Abbreviations
MTBF mean operating time between failures
MTTF mean time to failure
OC operating characteristic
SPRT sequential probability ratio test (in some literature called probability ratio sequential
test (PRST)).
3.2.2 Symbols
The generic symbol λ is used in the following for failure rate and failure intensity.
The symbol m is used to denote both the following reliability measures:
– mean operating time between failures, MTBF;
– mean time to failure, MTTF.
When used, the relationship between the above quantities, under the given assumptions, is:
λ =
m
Sequential test plans (see Clause 6) and fixed time/failure terminated test plans (see
Clause 7) are based on m as a reliability measure, thus in these cases:
m =
λ
c acceptable number of failures during the test
discrimination ratio; D = m m   or  D = λ λ
D
0 1 1 0
k summation variable for failures

– 12 – 61124 © IEC:2012
MTBF mean operating time between failures
MTTF mean time to failure
m true MTBF or MTTF
m specified MTTF or MTBF m = 1 λ (design goal)
0 0 0
m lower limit for MTTF or MTBF m = 1 λ
1 1 1
n number of test items at the beginning of the test
P
probability of acceptance
a
p
acceptable failure ratio
q acceptable success ratio, q = 1 – p
0 0 0
R(t) reliability at time t
observed number of failures during the test
r
r
test truncation failure number for sequential tests (SPRT)
*
T accumulated test time
*
accumulated test time stated as accept criterion
T
a
T * minimum test time for r = 0 stated as accept criterion
a, min
*
T expected accumulated test time to decision
e
∗
T (+) expected accumulated test time to acceptance
e
*
T accumulated test time stated as reject criterion
r
*
T accumulated test time stated as termination criterion
t
t test time
∗
test truncation time
t
∗
test time for each test item (assumed here to be the same for all test items)
t
t
t
life time of failed item i
i
*
t calendar test time stated as termination criterion
cal, t
P(r)
probability of r failures
∆µ auxiliary quantity for determination of c, ∆µ = c − µ
0 0 0
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)
λ true failure rate per item
λ
expected failure rate per item (design goal)
λ
upper limit for constant failure rate per item
61124 © IEC:2012 – 13 –
µ
expected number of failures during the test at the true λ

NOTE µ is not necessarily an integer.

µ expected number of failures during the test at the specified λ as parameter of the
0 0
∗ ∗
Poisson distribution µ = T / m = λ T
0 t 0 0 t
4 General requirements and area of application
4.1 Requirements
It is assumed, except where otherwise stated, that during the accumulated test time the times
to failure or the operating times between failures are independent, and identically
exponentially distributed. This assumption implies that the failure rate or failure intensity is
constant. Under this assumption there is no difference between failure rate and failure
intensity. Therefore they are both called λ and referred to in the following as failure rate.
It is assumed that the requirement is specified in one of the terms: the acceptable constant
failure rate λ , or the acceptable mean number of failures per time unit, λ or the acceptable
0 0
mean time to failure or mean operating time between failures, m .
If it is necessary to test the constant failure rate/constant failure intensity assumption, the
procedures given in IEC 60605-6 should be used.
4.2 Applicability to replaced and repaired items
The sequential test plans (see Clause 6), the time/failure terminated test plans (see Clause 7)
and the combined test plans (see Clause 10) are applicable to the following:
– replacement of failed items;
– without replacement of failed items;
under the assumption that
– an item can be replaced by repair of the item itself;
– the accumulated test time is calculated as elapsed operating item-time, in accordance
with 5.4;
– replaced items belong to the same population as the original items;
– repaired items can be considered to have the same failure intensity after repair as they
had before they failed.
The calendar time/failure terminated test plans in Clause 9, however, are applicable to c
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