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2、he European Standard EN 61165:2006 has the status of a British StandardICS 03.120.01; 03.120.30; 21.020; 29.020Application of Markov techniquesBRITISH STANDARDBS EN 61165:2006BS EN 61165:2006Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 14/05/2008 09:12, Uncontrolled Copy, (c) BSIThis Briti
3、sh Standard was published under the authority of the Standards Policy and Strategy Committee on 29 February 2008 BSI 2008ISBN 978 0 580 54072 1A list of organizations represented on DS/1/1 can be obtained on request to its secretary.This publication does not purport to include all the necessary prov
4、isions of a contract. Users are responsible for its correct application.Compliance with a British Standard cannot confer immunity from legal obligations.Amendments/corrigenda issued since publicationDate Commentsmethods for evaluating state transition diagrams without the need for more complicated m
5、athematical procedures or computer software programs. These methods were omitted from IEC 61165 during the latest revision.The importance of care when using modelling techniques cannot be overemphasized, particularly in the case of safety applications. An inaccurate model is destined to yield inaccu
6、rate results. Furthermore, it is important to appreciate that there may be unpredictable divergences between the results obtained by mathematical calculation and those obtained by simulation methods.National forewordThis British Standard is the UK implementation of EN 61165:2006, which is identical
7、with IEC 61165:2006. This standard supersedes BS 5760-15:1995, which is withdrawn. The UK participation in its preparation was entrusted by Technical Committee DS/1, Dependability and terotechnology, to Subcommittee DS/1/1, Dependability.National Annex NA is informative and provides some simple appr
8、oximation EUROPEAN STANDARD EN 61165 NORME EUROPENNE EUROPISCHE NORM July 2006 CENELEC European Committee for Electrotechnical Standardization Comit Europen de Normalisation Electrotechnique Europisches Komitee fr Elektrotechnische Normung Central Secretariat: rue de Stassart 35, B - 1050 Brussels 2
9、006 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members. Ref. No. EN 61165:2006 E ICS 03.120.01; 03.12.30; 21.020 English version Application of Markov techniques (IEC 61165:2006) Application des techniques de Markov (CEI 61165:2006) Anwendung des
10、 Markoff-Verfahrens (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.
11、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 translati
12、on 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,
13、 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. Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 14/05/2008 09:12, Uncontrolled C
14、opy, (c) BSIForeword 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 imp
15、lemented 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 Internatio
16、nal Standard IEC 61165:2006 was approved by CENELEC as a European Standard without any modification. _ EN 61165:2006 2 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 14/05/2008 09:12, Uncontrolled Copy, (c) BSICONTENTS INTRODUCTION.5 1 Scope.6 2 Normative references .6 3 Terms and definition
17、s .6 4 Symbols and abbreviations.8 4.1 Symbols for state transition diagrams8 4.2 Other symbols and abbreviations.9 4.3 Example 10 5 General description 10 6 Assumptions and limitations .11 7 Relationship with other analysis techniques12 7.1 General .12 7.2 Fault Tree Analysis (FTA)12 7.3 Reliabilit
18、y Block Diagram (RBD) 13 7.4 Petri nets.13 8 Development of state transition diagrams .13 8.1 Prerequisites .13 8.2 Rules for development and representation.14 9 Evaluation 15 9.1 General .15 9.2 Evaluation of reliability measures 16 9.3 Evaluation of availability and maintainability measures16 9.4
19、Evaluation of safety measures.17 10 Documentation of results17 Annex A (informative) Basic mathematical relationships for Markov techniques 18 Annex B (informative) Example: Development of state transition diagrams .21 Annex C (informative) Example: Numerical evaluation of some reliability, availabi
20、lity, maintainability and safety measures for a 1-out-of-2 active redundant system 26 Bibliography31 Figure 1 Diagram of transition probabilities in time interval (t,t+t), for arbitrary value of t and small t, for a non-restorable one-element system with constant failure rate .10 Figure 2 State tran
21、sition diagram of a non-restorable one-element system.10 Figure 3 - Interpretation of failure and restoration times in different contexts 16 Figure B.1 State transition diagram for a restorable one-element system .21 Figure B.2 State transition diagram with three states for a one-element system .21
22、Figure B.3 State transition diagram when restorations may be made from state 2 for a one-element system.21 Annex ZA (normative) Normative references to international publications with their corresponding European publications .34 EN 61165:2006 3 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS,
23、 14/05/2008 09:12, Uncontrolled Copy, (c) BSIFigure B.4 State transition diagram when direct transition is considered for a one-element system.22 Figure B.5 State transition diagram for the evaluation of reliability of a one-element system22 Figure B.6 State transition diagram for a 1-out-of-2 activ
24、e redundant system with no restorable elements 22 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 .23 Figure B.8 State transition diagram for a 1-out-of-2 active redundant system with restorab
25、le elements, two restoration teams and common cause for a system failure .23 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 .24 Figure B.10 Reliability block diagram for a 2-out-of-4 active re
26、dundant system 25 Figure B.11 Aggregated state transition diagram for reliability computation of the system in Figure B.10 .25 Figure C.1 State transition diagram for 1-out-of-2 active redundant system with different elements and two restoration teams26 Figure C.2 State transition diagram for a 1-ou
27、t-of-2 active redundant system with identical elements, two restoration teams and unlimited restoration resources26 Figure C.3 Numerical example for unavailability.28 Figure C.4 Numerical example for dangerous failure rate.30 EN 61165:2006 4 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 14/
28、05/2008 09:12, Uncontrolled Copy, (c) BSIINTRODUCTION Several distinct analytical methods for reliability, availability, maintainability and safety analysis are available of which the Markov technique is one. IEC 60300-3-1 gives an overview of available methods and their general characteristics. Thi
29、s standard defines the basic terminology and symbols for the application of Markov techniques. It describes ground rules for the development, representation and application of Markov techniques as well as assumptions and limitations of this approach. EN 61165:2006 5 Licensed Copy: Wang Bin, ISO/EXCH
30、ANGE CHINA STANDARDS, 14/05/2008 09:12, Uncontrolled Copy, (c) BSIAPPLICATION OF MARKOV TECHNIQUES 1 Scope 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.
31、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. 2 Normati
32、ve references 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. IEC 60050(191):1990, International
33、Electrotechnical Vocabulary (IEV) Chapter 191: Dependability and quality of service IEC 60300-3-1: Dependability management Part 3-1: Application guide Analysis techniques for dependability: Guide on methodology IEC 61508-4:1998, Functional safety of electrical/electronic/programmable electronic saf
34、ety-related systems Part 4: Definitions and abbreviations 3 Terms and definitions For the purposes of this document, the terms and definitions given in IEC 60050(191):1990 and the following apply. NOTE To facilitate the application of this standard for safety evaluations, the terminology from IEC 61
35、508 is used where appropriate. 3.1 system set of interrelated or interacting elements ISO 9000, 3.2.1 NOTE 1 In the context of dependability, a system will have a defined purpose expressed in terms of intended functions, stated conditions of operation/use, and defined boundaries. NOTE 2 The structur
36、e of a system may be hierarchical. 3.2 element component or set of components, which function as a single entity NOTE An element can usually assume only two states: up or down (see 3.4 and 3.5). For convenience the term element state will be used to denote the state of an element. EN 61165:2006 6 Li
37、censed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 14/05/2008 09:12, Uncontrolled Copy, (c) BSI3.3 system state X(t) particular combination of element states NOTE X(t) is the state of the system at time t. There are other factors that may have an effect on the system state (e. g. mode of operation
38、). 3.4 up state system (or element) state in which the system (or element) is capable of performing the required function NOTE A system can have several distinguishable up states (e.g. fully operational states and degraded states). 3.5 down state system (or element) state in which the system (or ele
39、ment) is not capable of performing the required function NOTE A system can have several distinguishable down states. 3.6 hazard potential source of physical injury or damage to the health of people or property IEC 61508-4, 3.1.2, modified 3.7 dangerous failure failure which has the potential to put
40、the safety-related system in a hazardous state or fail-to-function state IEC 61508-4, 3.6.7, modified NOTE 1 Whether or not the potential is realised may depend on the architecture of the system. NOTE 2 The term unsafe failure or hazardous failure is also commonly used in this context. 3.8 safe fail
41、ure failure which does not have the potential to put the safety-related system in a hazardous state or fail-to-function state IEC 61508, modified 3.9 transition change from one state to another state NOTE Transition takes place usually as a result of failure or restoration. A transition may also be
42、caused by other events such as human errors, external events, reconfiguration of software, etc. 3.10 transition probability Pij(t) conditional probability of transition from state i to state j in a given time interval (s, s+t) given that the system is in state i at the beginning of the time interval
43、 NOTE 1 Formally Pij(s, s+t) = P(X(s+t) = j | X(s) = i). When the Markov process is time-homogeneous, then Pij(s, s+t) does not depend on s and is designated as Pij(t). NOTE 2 For an irreducible Markov process (i.e. if every state can be reached from every other state) it holds that Pij()=Pj, where
44、Pjis the asymptotic and stationary or steady-state probability of state j. EN 61165:2006 7 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 14/05/2008 09:12, Uncontrolled Copy, (c) BSI3.11 transition rate qij limit, if it exists, of the ratio of the conditional probability that a transition ta
45、kes place from state i to state j within a given time interval (t, t+t) and the length of the interval t, when t tends to zero, given that the system is in state i at time t NOTE pijor cijare also used in this context. 3.12 initial state system state at time t = 0 NOTE Generally, a system starts its
46、 operation at t = 0 from an up state in which all elements of the system are functioning and transits towards the final system state, which is a down state, via other system up states having progressively fewer functioning elements. 3.13 absorbing state state which once entered, cannot be left (i. e
47、. no transitions out of the state are possible) 3.14 restorable system system containing elements which can fail and then be restored to their up state without necessarily causing system failure NOTE Repairable is also used in this context. 3.15 non-restorable system system the state transition diag
48、ram of which contains only transitions in the direction towards system failure states NOTE Non-repairable is also used in this context. 4 Symbols and abbreviations 4.1 Symbols for state transition diagrams Markov techniques are graphically represented by state transition diagrams or by transition ra
49、te diagrams, both terms being used as equivalents in this standard. The following symbols are used throughout this document. Other symbols may be applied as appropriate. 4.1.1 State symbol A state is represented by a circle or a rectangle. NOTE In order to increase readability, down states can be highlighted, e. g. by bold lines, colouring or hatching. 4.1.2 State description The state description is placed inside the state symbol and may take the form of words or alphanumeric characters defini
