EN 61703:2016
(Main)Mathematical expressions for reliability, availability, maintainability and maintenance support terms
Mathematical expressions for reliability, availability, maintainability and maintenance support terms
IEC 61703:2016 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. This standard is mainly applicable to hardware dependability, but many terms and their definitions may be applied to items containing software. 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: - standard made as self containing as possible; - item split between individual items and systems; - 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; - generalization of the availability to production availability]; - introduction of curves to illustrate the various concepts. Keywords: mathematical expressions for dependability
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
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-januar-2017
1DGRPHãþD
SIST EN 61703:2002
0DWHPDWLþQL]DSLVSRMPRY]DQHVOMLYRVWUD]SRORåOMLYRVWY]GUåHYDOQRVWLQ
Y]GUåHYDOQDSRGSRUD ,(&
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
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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
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
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.
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
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
– 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
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
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
...
SLOVENSKI STANDARD
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
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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
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
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.
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
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
– 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
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
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] .
...
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