EN 61165:2006
(Main)Application of Markov techniques
Application of Markov techniques
This International Standard provides guidance on the application of Markov techniques to model and analyze a system and estimate reliability, availability, maintainability and safety measures. This standard is applicable to all industries where systems, which exhibit state-dependent behaviour, have to be analyzed. The Markov techniques covered by this standard assume constant time-independent state transition rates. Such techniques are often called homogeneous Markov techniques.
Anwendung des Markoff-Verfahrens
Application des techniques de Markov
Cette Norme internationale fournit un guide sur l'application des techniques de Markov pour analyser et modéliser un système, et estimer la fiabilité, la disponibilité, la maintenabilité et les mesures de sécurité. Cette norme est applicable à toutes les industries où les systèmes, qui présentent un comportement dépendant de leur état, doivent être analysés. Les techniques de Markov couvertes par cette norme supposent des fréquences de changement d'état constantes, indépendantes du temps. De telles techniques sont souvent appelées globalement 'techniques de Markov'.
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EUROPEAN STANDARD
EN 61165
NORME EUROPÉENNE
July 2006
EUROPÄISCHE NORM
ICS 03.120.01; 03.12.30; 21.020
English version
Application of Markov techniques
(IEC 61165:2006)
Application des techniques de Markov Anwendung des Markoff-Verfahrens
(CEI 61165:2006) (IEC 61165:2006)
This European Standard was approved by CENELEC on 2006-07-01. 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 Central Secretariat 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 Central Secretariat has the same status as the official versions.
CENELEC members are the national electrotechnical committees of Austria, Belgium, Cyprus, the Czech
Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.
CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung
Central Secretariat: rue de Stassart 35, B - 1050 Brussels
© 2006 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.
Ref. No. EN 61165:2006 E
Foreword
The text of document 56/1096/FDIS, future edition 2 of IEC 61165, prepared by IEC TC 56,
Dependability, was submitted to the IEC-CENELEC parallel vote and was approved by CENELEC as
EN 61165 on 2006-07-01.
The following dates were fixed:
– latest date by which the EN has to be implemented
at national level by publication of an identical
national standard or by endorsement (dop) 2007-04-01
– latest date by which the national standards conflicting
with the EN have to be withdrawn (dow) 2009-07-01
Annex ZA has been added by CENELEC.
__________
Endorsement notice
The text of the International Standard IEC 61165:2006 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 60812 NOTE Harmonized as EN 60812:2006 (not modified).
IEC 61078 NOTE Harmonized as EN 61078:2006 (not modified).
__________
- 3 - EN 61165:2006
Annex ZA
(normative)
Normative references to international publications
with their corresponding European publications
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
NOTE When an international publication has been modified by common modifications, indicated by (mod), the relevant EN/HD
applies.
Publication Year Title EN/HD Year
IEC 60050-191 1990 International Electrotechnical Vocabulary - -
(IEV)
Chapter 191: Dependability and quality of
service
1) 2)
IEC 60300-3-1 - Dependability management EN 60300-3-1 2004
Part 3-1: Application guide - Analysis
techniques for dependability - Guide on
methodology
IEC 61508-4 1998 Functional safety of EN 61508-4 2001
+ corr. April 1999 electrical/electronic/programmable electronic
safety-related systems
Part 4: Definitions and abbreviations
1)
Undated reference.
2)
Valid edition at date of issue.
NORME CEI
INTERNATIONALE
IEC
INTERNATIONAL
Deuxième édition
STANDARD
Second edition
2006-05
Application des techniques de Markov
Application of Markov techniques
IEC 2006 Droits de reproduction réservés Copyright - all rights reserved
Aucune partie de cette publication ne peut être reproduite ni No part of this publication may be reproduced or utilized in any
utilisée sous quelque forme que ce soit et par aucun procédé, form or by any means, electronic or mechanical, including
électronique ou mécanique, y compris la photocopie et les photocopying and microfilm, without permission in writing from
microfilms, sans l'accord écrit de l'éditeur. the publisher.
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Telephone: +41 22 919 02 11 Telefax: +41 22 919 03 00 E-mail: inmail@iec.ch Web: www.iec.ch
CODE PRIX
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PRICE CODE
Commission Electrotechnique Internationale
International Electrotechnical Commission
МеждународнаяЭлектротехническаяКомиссия
Pour prix, voir catalogue en vigueur
For price, see current catalogue
61165 IEC:2006 – 3 –
CONTENTS
FOREWORD.7
INTRODUCTION.11
1 Scope.13
2 Normative references .13
3 Terms and definitions .13
4 Symbols and abbreviations.17
4.1 Symbols for state transition diagrams.17
4.2 Other symbols and abbreviations.19
4.3 Example .21
5 General description .21
6 Assumptions and limitations .23
7 Relationship with other analysis techniques.25
7.1 General .25
7.2 Fault Tree Analysis (FTA).25
7.3 Reliability Block Diagram (RBD) .27
7.4 Petri nets.27
8 Development of state transition diagrams .27
8.1 Prerequisites .27
8.2 Rules for development and representation.29
9 Evaluation .31
9.1 General .31
9.2 Evaluation of reliability measures .33
9.3 Evaluation of availability and maintainability measures.33
9.4 Evaluation of safety measures.35
10 Documentation of results .35
Annex A (informative) Basic mathematical relationships for Markov techniques .37
Annex B (informative) Example: Development of state transition diagrams .43
Annex C (informative) Example: Numerical evaluation of some reliability, availability,
maintainability and safety measures for a 1-out-of-2 active redundant system .53
Bibliography.63
Figure 1 – Diagram of transition probabilities in time interval (t,t+Δt), for arbitrary value
of t and small Δt, for a non-restorable one-element system with constant failure rate λ .21
Figure 2 – State transition diagram of a non-restorable one-element system.21
Figure 3 - Interpretation of failure and restoration times in different contexts .33
Figure B.1 – State transition diagram for a restorable one-element system .43
Figure B.2 – State transition diagram with three states for a one-element system .43
Figure B.3 – State transition diagram when restorations may be made from state 2 for
a one-element system.43
61165 IEC:2006 – 5 –
Figure B.4 – State transition diagram when direct transition is considered for a one-
element system.45
Figure B.5 – State transition diagram for the evaluation of reliability of a one-element
system .45
Figure B.6 – State transition diagram for a 1-out-of-2 active redundant system with no
restorable elements .45
Figure B.7 – State transition diagram for a 1-out-of-2 active redundant system with
restorable elements, two restoration teams and no restoration limitations .47
Figure B.8 – State transition diagram for a 1-out-of-2 active redundant system with
restorable elements, two restoration teams and common cause for a system failure .47
Figure B.9 – State transition diagram for a 1-out-of-2 active redundant system with
only one restoration team and restoration priority as first-in/first-out .49
Figure B.10 – Reliability block diagram for a 2-out-of-4 active redundant system .51
Figure B.11 – Aggregated state transition diagram for reliability computation of the
system in Figure B.10 .51
Figure C.1 – State transition diagram for 1-out-of-2 active redundant system with
different elements and two restoration teams .53
Figure C.2 – State transition diagram for a 1-out-of-2 active redundant system with
identical elements, two restoration teams and unlimited restoration resources .53
Figure C.3 – Numerical example for unavailability.57
Figure C.4 – Numerical example for dangerous failure rate.61
61165 IEC:2006 – 7 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
___________
APPLICATION OF MARKOV TECHNIQUES
FOREWORD
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