SIST EN 61703:2017

SLOVENSKI STANDARD
SIST EN 61703:2017
01-januar-2017
Nadomešča:
SIST EN 61703:2002
Matematični zapis pojmov zanesljivost, razpoložljivost, vzdrževalnost in
vzdrževalna podpora (IEC 61703:2016)
Mathematical expressions for reliability, availability, maintainability and maintenance
support terms (IEC 61703:2016)
Ta slovenski standard je istoveten z: EN 61703:2016
ICS:
03.120.30 Uporaba statističnih metod Application of statistical
methods
07.020 Matematika Mathematics
21.020 Značilnosti in načrtovanje Characteristics and design of
strojev, aparatov, opreme machines, apparatus,
equipment
SIST EN 61703:2017 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN 61703:2017

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SIST EN 61703:2017


EUROPEAN STANDARD EN 61703

NORME EUROPÉENNE

EUROPÄISCHE NORM
November 2016
ICS 03.120.30; 21.020 Supersedes EN 61703:2002
English Version
Mathematical expressions for reliability, availability,
maintainability and maintenance support terms
(IEC 61703:2016)
Expressions mathématiques pour les termes de fiabilité, de Mathematische Ausdrücke für Begriffe der Zuverlässigkeit,
disponibilité, de maintenabilité et de logistique de Verfügbarkeit, Instandhaltbarkeit und
maintenance Instandhaltungsbereitschaft
(IEC 61703:2016) (IEC 61703:2016)
This European Standard was approved by CENELEC on 2016-09-16. 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, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, 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: Avenue Marnix 17, B-1000 Brussels
© 2016 CENELEC All rights of exploitation in any form and by any means reserved worldwide for CENELEC Members.
 Ref. No. EN 61703:2016 E

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SIST EN 61703:2017
EN 61703:2016
European foreword
The text of document 56/1682/FDIS, future edition 2 of IEC 61703, prepared by IEC/TC 56
"Dependability" was submitted to the IEC-CENELEC parallel vote and approved by CENELEC as
EN 61703:2016.

The following dates are fixed:
(dop) 2017-06-16
• latest date by which the document has to be
implemented at national level by
publication of an identical national
standard or by endorsement
• latest date by which the national (dow) 2019-09-16
standards conflicting with the
document have to be withdrawn

This document supersedes EN 61703:2002.

Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CENELEC [and/or CEN] shall not be held responsible for identifying any or all such
patent rights.

Endorsement notice
The text of the International Standard IEC 61703:2016 was approved by CENELEC as a European
Standard without any modification.
In the official version, for Bibliography, the following notes have to be added for the standards indicated:

IEC 61508 Series NOTE Harmonized as EN 61508 Series.
IEC 61511 Series NOTE Harmonized as EN 61511 Series.
IEC 61025 NOTE Harmonized as EN 61025.
IEC 61078 NOTE Harmonized as EN 61078.
IEC 61165 NOTE Harmonized as EN 61165.
2

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SIST EN 61703:2017
EN 61703:2016
Annex ZA
(normative)

Normative references to international publications
with their corresponding European publications

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.

NOTE 1 When 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
ISO 3534-1 2006 Statistics - Vocabulary and symbols - - -
Part -1: General statistical terms and terms
used in probability

3

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SIST EN 61703:2017



IEC 61703

®


Edition 2.0 2016-08




INTERNATIONAL



STANDARD




NORME



INTERNATIONALE











Mathematical expressions for reliability, availability, maintainability and

maintenance support terms




Expressions mathématiques pour les termes de fiabilité, de disponibilité, de

maintenabilité et de logistique de maintenance
















INTERNATIONAL

ELECTROTECHNICAL

COMMISSION


COMMISSION

ELECTROTECHNIQUE


INTERNATIONALE




ICS 03.120.30; 21.020 ISBN 978-2-8322-3558-4



Warning! Make sure that you obtained this publication from an authorized distributor.

Attention! Veuillez vous assurer que vous avez obtenu cette publication via un distributeur agréé.

® Registered trademark of the International Electrotechnical Commission
Marque déposée de la Commission Electrotechnique Internationale

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CONTENTS
FOREWORD . 6
INTRODUCTION . 8
1 Scope . 9
2 Normative references. 10
3 Terms and definitions . 10
4 Glossary of symbols and abbreviations . 13
4.1 General . 13
4.2 Acronyms used in this standard . 13
4.3 Symbols used in this standard . 15
5 General models and assumptions . 18
5.1 Constituents of up and down times . 18
5.2 Introduction to models and assumptions . 19
5.3 State-transition approach . 20
5.4 Model and assumptions for non-repairable individual items . 22
5.5 Assumptions and model for repairable individual items . 23
5.5.1 Assumption for repairable individual items . 23
5.5.2 Instantaneous repair . 24
5.5.3 Non-instantaneous repair . 25
5.6 Continuously operating items (COI) versus intermittently operating individual
items (IOI) . 26
6 Mathematical models and expressions . 27
6.1 Systems . 27
6.1.1 General . 27
6.1.2 Availability related expressions . 29
6.1.3 Reliability related expressions . 36
6.1.4 Mean operating time between failures [192-05-13] and mean time
between failures . 40
6.1.5 Instantaneous failure rate [192-05-06] and conditional failure intensity
(Vesely failure rate) . 41
6.1.6 Failure density and unconditional failure intensity [192-05-08] . 44
6.1.7 Comparison of λ(t), λ (t), z(t) and f(t) for high and small MTTRs . 47
V
6.1.8 Restoration related expressions . 47
6.2 Non-repairable individual items . 49
6.2.1 General . 49
6.2.2 Instantaneous availability [192-08-01] . 50
6.2.3 Reliability [192-05-05] . 50
6.2.4 Instantaneous failure rate [192-05-06] . 51
6.2.5 Mean failure rate [192-05-07] . 52
6.2.6 Mean operating time to failure [192-05-11] . 53
6.3 Repairable individual items with zero time to restoration . 54
6.3.1 General . 54
6.3.2 Reliability [192-05-05] . 54
6.3.3 Instantaneous failure intensity [192-05-08]. 56
6.3.4 Asymptotic failure intensity [192-05-10] . 58
6.3.5 Mean failure intensity [192-05-09] . 59
6.3.6 Mean time between failures (see 3.3) . 60

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6.3.7 Mean operating time to failure [192-05-11] . 60
6.3.8 Mean operating time between failures [192-05-13] . 61
6.3.9 Instantaneous availability [192-08-01], mean availability [192-08-05]
and asymptotic availability [192-08-07] . 61
6.3.10 Mean up time [192-08-09] . 61
6.4 Repairable individual items with non-zero time to restoration . 62
6.4.1 General . 62
6.4.2 Reliability [192-05-05] . 62
6.4.3 Instantaneous failure intensity [192-05-08]. 64
6.4.4 Asymptotic failure intensity [192-05-10] . 67
6.4.5 Mean failure intensity [192-05-09] . 68
6.4.6 Mean operating time to failure [192-05-11] . 69
6.4.7 Mean time between failures (see 3.3) . 70
6.4.8 Mean operating time between failures [192-05-13] . 71
6.4.9 Instantaneous availability [192-08-01] . 71
6.4.10 Instantaneous unavailability [192-08-04] . 73
6.4.11 Mean availability [192-08-05] . 74
6.4.12 Mean unavailability [192-08-06] . 76
6.4.13 Asymptotic availability [192-08-07] . 78
6.4.14 Asymptotic unavailability [192-08-08] . 78
6.4.15 Mean up time [192-08-09] . 79
6.4.16 Mean down time [192-08-10] . 81
6.4.17 Maintainability [192-07-01] . 82
6.4.18 Instantaneous repair rate [192-07-20] . 84
6.4.19 Mean repair time [192-07-21] . 86
6.4.20 Mean active corrective maintenance time [192-07-22] . 87
6.4.21 Mean time to restoration [192-07-23] . 88
6.4.22 Mean administrative delay [192-07-26] . 89
6.4.23 Mean logistic delay [192-07-27] . 90
Annex A (informative) Performance aspects and descriptors . 91
Annex B (informative) Summary of measures related to time to failure . 92
Annex C (informative) Comparison of some dependability measures for continuously
operating items . 95
Bibliography . 97

Figure 1 – Constituents of up time . 18
Figure 2 – Constituents of down time. 19
Figure 3 – Acronyms related to failure times . 19
Figure 4 – Simple state-transition diagram . 21
Figure 5 – Sample realization (chronogram) related to the system in Figure 4 . 22
Figure 6 – State-transition diagram of a non-repairable individual item . 22
Figure 7 – Sample realization of a non-repairable individual item . 23
Figure 8 – State-transition diagram of an instantaneously repairable individual item . 24
Figure 9 – Sample realization of a repairable individual item with zero time to
restoration . 25
Figure 10 – State-transition diagram of a repairable individual item . 25

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Figure 11 – Sample realization of a repairable individual item with non-zero time to
restoration . 26
Figure 12 – Comparison of an enabled time for a COI and an IOI . 26
Figure 13 – Equivalent operating time for IOI items . 27
Figure 14 – State-transition graph for a simple redundant system . 27
Figure 15 – Markov graph for a simple redundant system . 28
Figure 16 – Evolution of the state probabilities related to the Markov model in Figure 15 . 28
Figure 17 – Evolution of A(t) and U(t) related to the Markov model in Figure 15 . 29
Figure 18 – Evolution of the Ast (0, t) related to the Markov model in Figure 15 . 31
i
Figure 19 – Instantaneous availability and mean availability of a periodically tested item . 33
Figure 20 – Example of a simple production system . 34
Figure 21 – Evolution of A(t) and K(t) . 35
Figure 22 – Illustration of a system reliable behaviour over [0, t] . 36
Figure 23 – Illustration of a system reliable behaviour over time interval [t , t ] . 37
1 2
Figure 24 – State-transition and Markov graphs for reliability calculations . 37
Figure 25 – Evolution of the state probabilities related to the Markov model in Figure 24 . 38
Figure 26 – Evolution of R(t) and F(t) related to the Markov model in Figure 24 . 39
Figure 27 – Evolution of Ast (0, t) related to the Markov model in Figure 24 . 40
i
Figure 28 – Time between failures versus operating time between failures . 40
Figure 29 – Comparison between λ(t) and λ (t) related to the model in Figure 24 . 43
V
Figure 30 – Comparison between z(t) and f(t) . 46
Figure 31 – Comparison of λ(t), λ (t), z(t) and f(t) for high and small values of MTTRs . 47
V
Figure 32 – Illustration of reliable behaviour over [t , t ] for a zero time to restoration
1 2
individual item . 55
Figure 33 – Sample of possible number of failures at the renewal time t . 56
Figure 34 – Illustration of reliable behaviour over [t t ] for a non-zero time to
1 , 2
restoration individual item . 62
Figure 35 – Evolution of R(t, t + 1/4) . 64
Figure 36 – Sample of possible number of failures at the renewal time t . 64
Figure 37 – Evolution of the failure intensity z(t) . 66
Figure 38 – Evolution of the mean failure intensity z(t, t + 1/4) . 69
Figure 39 – Illustration of available behaviour at time t for a non-zero time to

restoration individual item . 71
Figure 40 – Evolution of the instantaneous availability A(t) . 73
Figure 41 – Illustration of unavailable behaviour at time t for a non-zero time to

restoration individual item . 73
Figure 42 – Evolution of the instantaneous unavailability U(t) . 74
Figure 43 – Evolution of the mean availability A (t, t + 1/ 4) . 76
Figure 44 – Evolution of the mean unavailability U (t, t +1/ 4) . 77
Figure 45 – Sample realization of the individual item state . 80
Figure 46 – Plot of the up-time hazard rate function λ (t) . 80
U
Figure 47 – Evolution of the maintainability M(t, t+16h) . 84
Figure 48 – Evolution of the lognormal repair rate µ(t) . 86

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Figure A.1 – Performance aspects and descriptors . 91

Table B.1 – Relations among measures related to time to failure of continuously
operating items . 92
Table B.2 – Summary of characteristics for some continuous probability distributions of
time to failure of continuously operating items . 93
Table B.3 – Summary of characteristics for some probability distributions of repair time . 94
Table C.1 – Comparison of some dependability measures of continuously operating
items with constant failure rate λ and restoration rate µ . 95
R

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INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________

MATHEMATICAL EXPRESSIONS FOR RELIABILITY,
AVAILABILITY, MAINTAINABILITY AND
MAINTENANCE SUPPORT TERMS

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,
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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-
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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 61703 has been prepared by IEC technical committee 56:
Dependability.
This second edition cancels and replaces the first edition published in 2001. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) standard made as self containing as possible;
b) item split between individual items and systems;
c) generalization of the dependability concepts for systems made of several components;
– introduction of the conditional failure intensity (Vesely failure rate);
– introduction of the state-transition and the Markovian models;

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IEC 61703:2016 © IEC 2016 – 7 –
– generalization of the availability to production availability;
d) introduction of curves to illustrate the various concepts.
The text of this standard is based on the following documents:
FDIS Report on voting
56/1682/FDIS 56/1693/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.
This International Standard is to be used in conjunction with IEC 60050-192:2015.
The committee has decided that the contents of this publication will remain unchanged until
the stability date indicated on the IEC website 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.

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INTRODUCTION
IEC 60050-192 provides definitions for dependability and its influencing factors, reliability,
availability, maintainability and maintenance support, together with definitions of other related
terms commonly used in this field. Some of these terms are measures of specific
dependability characteristics, which can be expressed mathematically.
It is important for the users to understand the mathematical meaning of those expressions and
how they are established. This is the purpose of the present International Standard which,
used in conjunction with IEC 60050-192, provides practical guidance essential for the
quantification of those measures. For those requiring further information, for example on
1
detailed statistical methods, reference should be made to the IEC 60605 series [23] .
Annex A provides a diagrammatic explanation of the relationships between some basic
dependability terms, related random variables, probabilistic descriptors and modifiers.
Annex B provides a summary of measures related to time to failure.
Annex C compares some dependability measures for continuously operating items.
The bibliography gives references for the mathematical basis of this standard, in particular,
the mathematical material is based on references [2], [6], [8], [9], [13], [14] and [18]; the
renewal theory (renewal and alternating renewal processes) can be found in [6], [8], [9], [10],
[11], [13], [15], and [17]; and more advanced treatment of renewal theory can be found in
references [1], [3], [12], [16], [19] and [20]. More information on the theory and applications of
Markov processes can be found in references [3], [9], [10], [15], [16], [17] and [19].

____________
1
 Numbers in brackets refer to the Bibliography.

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MATHEMATICAL EXPRESSIONS FOR RELIABILITY,
AVAILABILITY, MAIN
...