Mathematical expressions for reliability, availability, maintainability and maintenance support terms (IEC 61703:2016)

This International Standard provides mathematical expressions for selected reliability, availability, maintainability and maintenance support measures defined in IEC 60050192:2015. In addition, it introduces some terms not covered in IEC 60050-192:2015. They are related to aspects of the system of item classes (see hereafter).
According to IEC 60050-192:2015, dependability [192-01-22] is the ability of an item to perform as and when required and an item [192-01-01] can be an individual part, component, device, functional unit, equipment, subsystem, or system.
To account for mathematical constraints, this standard splits the items between the individual items considered as a whole (e.g. individual components) and the systems made of several individual items. It provides general considerations for the mathematical expressions for systems as well as individual items but the individual items which are easier to model are analysed in more detail with regards to their repair aspects.
The following item classes are considered separately:
• Systems;
• Individual items:
– non-repairable [192-01-12];
– repairable [192-01-11]:
i) with zero (or negligible) time to restoration;
ii) with non-zero time to restoration.
In order to explain the dependability concepts which can be difficult to understand, keep the standard self-contained and the mathematical formulae as simple as possible, the following basic mathematical models are used in this standard to quantify dependability measures:
• Systems:
– state-transition models;
– Markovian models.
• Individual items:
– random variable (time to failure) for non-repairable items;
– simple (ordinary) renewal process for repairable items with zero time to restoration;
– simple (ordinary) alternating renewal process for repairable items with non-zero time to restoration.
The application of each dependability measure is illustrated by means of simple examples.
This standard is mainly applicable to hardware dependability, but many terms and their definitions may be applied to items containing software.

Mathematische Ausdrücke für Begriffe der Zuverlässigkeit, Verfügbarkeit, Instandhaltbarkeit und Instandhaltungsbereitschaft

Expressions mathématiques pour les termes de fiabilité, de disponibilité, de maintenabilité et de logistique de maintenance

L'IEC 61703:2016 fournit des expressions mathématiques pour les mesures sélectionnées liées à la fiabilité, à la disponibilité, à la maintenabilité et à la logistique de maintenance définies dans l'IEC 60050-192:2015. En outre, elle présente certains termes non couverts par l'IEC 60050-192:2015. Ces termes sont liés aux aspects relatifs aux items de la classe système (voir ci-après). Selon l'IEC 60050-192:2015, la sûreté de fonctionnement [192-01-22] est l'aptitude d'une entité à fonctionner quand et tel que requis; une entité [192-01-01] peut être une pièce isolée, un composant, un dispositif, une unité fonctionnelle, un équipement, un sous-système ou un système. Pour tenir compte des contraintes mathématiques, la présente norme effectue une distinction entre les entités individuelles considérées dans leur ensemble (par exemple, des composants individuels) et les systèmes composés de plusieurs entités individuelles. Elle fournit des considérations générales sur les expressions mathématiques liées aux systèmes et aux entités individuelles. Les entités individuelles plus facilement modélisables sont, quant à elles, analysées plus en détail pour ce qui concerne leurs aspects de réparation. La présente norme s'applique principalement à la sûreté de fonctionnement du matériel, mais de nombreux termes et leurs définitions peuvent être appliqués à des entités contenant du logiciel. Cette deuxième édition annule et remplace la première édition parue en 2001. Cette édition constitue une révision technique. Cette édition inclut les modifications techniques majeures suivantes par rapport à l'édition précédente: - norme aussi autonome que possible; - entité scindée entre entités individuelles et systèmes; - généralisation des concepts de sûreté de fonctionnement pour les systèmes constitués de plusieurs composants; - [introduction de l'intensité conditionnelle de défaillance (taux de défaillance de Vesely); - introduction des modèles états-transitions et des modèles de Markov; - généralisation de la disponibilité à la disponibilité de production]; - introduction de courbes pour représenter les différents concepts. Mots clés: des expressions mathématiques pour la fiabilité

Matematični zapis pojmov zanesljivost, razpoložljivost, vzdrževalnost in vzdrževalna podpora (IEC 61703:2016)

Ta mednarodni standard podaja matematične izraze za izbrane ukrepe zanesljivosti, razpoložljivosti, sposobnosti vzdrževanja in podpore vzdrževanja, ki so opredeljeni v standardu IEC 60050192:2015. Poleg tega uvaja nekatere pojme, ki niso zajeti v standardu IEC 60050-192:2015. Povezani so z vidiki sistema razredov elementov (glejte spodaj).
V skladu s standardom IEC 60050-192:2015 je zagotovljivost [192-01-22] zmožnost elementa, da deluje, kot in ko je to potrebno, pri čemer je element [192-01-01] lahko posamezen del, komponenta, naprava, funkcionalna enota, oprema, podsistem ali sistem.
Ta standard upošteva matematične omejitve tako, da deli elemente na posamezne elemente, ki se obravnavajo kot celota (npr. posamezne komponente) in sisteme, ki so sestavljeni iz več posameznih elementov. Zagotavlja splošne premisleke za matematične izraze za sisteme in posamezne elemente, pri čemer so posamezni elementi, ki jih je lažje modelirati, podrobneje analizirani glede na popravljivost.
Naslednji razredi elementov se obravnavajo posebej:
• sistemi;
• posamezni elementi:
– nepopravljivi [192-01-12];
– popravljivi [192-01-11]:
i) s takojšnjo obnovo ali zanemarljivim trajanjem obnove;
ii) z obnovo z določenim trajanjem.
Za obrazložitev načela zagotovljivosti, ki je lahko težko razumljiv, ter zagotavljanje samozadostnosti standarda in preprostosti matematičnih formul, so v tem standardu uporabljeni naslednji osnovni matematični modeli za kvantifikacijo ukrepov zagotovljivosti:
• sistemi:
– modeli prehajanja stanj;
– Markovski modeli.
• posamezni elementi:
– naključna spremenljivka (čas za odpoved) za nepopravljive elemente;
– preprost (navaden) postopek obnovitve za popravljive elemente s takojšnjo obnovo;
– preprost (navaden) izmenični postopek obnovitve za popravljive elemente, kjer takojšnja obnova ni mogoča.
Uporaba vsakega ukrepa zagotovljivosti je prikazana s preprostim primerom.
Ta standard se v glavnem uporablja za zagotovljivost strojne opreme, vendar se lahko številni pojmi in opredelitve uporabljajo za elemente, ki vsebujejo programsko opremo.

General Information

Status
Published
Publication Date
29-Nov-2016
Technical Committee
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
23-Nov-2016
Due Date
28-Jan-2017
Completion Date
30-Nov-2016

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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.
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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
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SIST EN 61703:2017
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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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SIST EN 61703:2017
– 2 – IEC 61703:2016 © IEC 2016
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

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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IEC 61703:2016 © IEC 2016 – 3 –

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

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

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

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

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

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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IEC 61703:2016 © IEC 2016 – 5 –

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

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SIST EN 61703:2017
– 6 – IEC 61703:2016 © IEC 2016
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

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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

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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

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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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SIST EN 61703:2017
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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SIST EN 61703:2017
– 8 – IEC 61703:2016 © IEC 2016
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

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].

____________
Numbers in brackets refer to the Bibliography.
---------------------- Page: 14 ----------------------
SIST EN 61703:2017
IEC 61703:2016 © IEC 2016 – 9 –
MATHEMATICAL EXPRESSIONS FOR RELIABILITY,
AVAILABILITY, MAIN
...

SLOVENSKI STANDARD
SIST EN 61703:2017
01-januar-2017
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SIST EN 61703:2002
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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 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
07.020 Matematika Mathematics
21.020 =QDþLOQRVWLLQQDþUWRYDQMH Characteristics and design of
VWURMHYDSDUDWRYRSUHPH machines, apparatus,
equipment
SIST EN 61703:2017 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
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
---------------------- Page: 2 ----------------------
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.
---------------------- Page: 3 ----------------------
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
---------------------- Page: 4 ----------------------
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
---------------------- Page: 5 ----------------------
– 2 – IEC 61703:2016 © IEC 2016
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

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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IEC 61703:2016 © IEC 2016 – 3 –

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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– 4 – IEC 61703:2016 © IEC 2016

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

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

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

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

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

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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IEC 61703:2016 © IEC 2016 – 5 –

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

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– 6 – IEC 61703:2016 © IEC 2016
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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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 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;
---------------------- Page: 10 ----------------------
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.
---------------------- Page: 11 ----------------------
– 8 – IEC 61703:2016 © IEC 2016
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

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].

____________
Numbers in brackets refer to the Bibliography.
---------------------- Page: 12 ----------------------
IEC 61703:2016 © IEC 2016 – 9 –
MATHEMATICAL EXPRESSIONS FOR RELIABILITY,
AVAILABILITY, MAINTAINABILITY AND
MAINTENANCE SUPPORT TERMS
1 Scope

This International Standard provides mathematical expressions for selected reliability,

availability, maintainability and maintenance support measures defined in

IEC 60050-192:2015. In addition, it introduces some terms not covered in IEC 60050-

192:2015. They are related to aspects of the system of item classes
...

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