1、BRITISH STANDARDBS EN 61165:2006Application of Markov techniquesThe European Standard EN 61165:2006 has the status of a British StandardICS 03.120.01; 03.120.30; 21.020; 29.020g49g50g3g38g50g51g60g44g49g42g3g58g44g55g43g50g56g55g3g37g54g44g3g51g40g53g48g44g54g54g44g50g49g3g40g59g38g40g51g55g3g36g54g
2、3g51g40g53g48g44g55g55g40g39g3g37g60g3g38g50g51g60g53g44g42g43g55g3g47g36g58BS EN 61165:2006This British Standard was published under the authority of the Standards Policy and Strategy Committee on 29 February 2008 BSI 2008ISBN 978 0 580 54072 1National forewordThis British Standard is the UK implem
3、entation of EN 61165:2006, which is identical 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 This standard supersedes BS 5760-15:1995, which is withdrawn.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 N
4、A is informative and provides some simple approximation methods for evaluating state transition diagrams without the need for more complicated mathematical procedures or computer software programs. These methods were omitted from IEC 61165 during the latest revision.The importance of care when using
5、 modelling techniques cannot be overemphasized, particularly in the case of safety applications. An inaccurate model is destined to yield inaccurate results. Furthermore, it is important to appreciate that there may be unpredictable divergences between the results obtained by mathematical calculatio
6、n and those obtained by simulation methods.A 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 provisions of a contract. Users are responsible for its correct application.Compliance with a British St
7、andard cannot confer immunity from legal obligations.Amendments/corrigenda issued since publicationDate CommentsEUROPEAN STANDARD EN 61165 NORME EUROPENNE EUROPISCHE NORM July 2006 CENELEC European Committee for Electrotechnical Standardization Comit Europen de Normalisation Electrotechnique Europis
8、ches Komitee fr 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 ICS 03.120.01; 03.12.30; 21.020 English version Application of
9、Markov techniques (IEC 61165:2006) Application des techniques de Markov (CEI 61165:2006) Anwendung des 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 c
10、onditions 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 i
11、n 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 electrote
12、chnical 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 U
13、nited Kingdom. 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
14、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 Interna
15、tional Standard IEC 61165:2006 was approved by CENELEC as a European Standard without any modification. _ EN 61165:2006 2 CONTENTS INTRODUCTION.5 1 Scope.6 2 Normative references .6 3 Terms and definitions .6 4 Symbols and abbreviations.8 4.1 Symbols for state transition diagrams8 4.2 Other symbols
16、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 Reliability Block Diagram (RBD) 13 7.4 Petri nets.13 8 Development of state transition diagrams .13 8.1 Pr
17、erequisites .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 Evaluation of safety measures.17 10 Documentation of results17 Annex A (informative) Basic mathe
18、matical relationships for Markov techniques 18 Annex B (informative) Example: Development of state transition diagrams .21 Annex C (informative) Example: Numerical evaluation of some reliability, availability, maintainability and safety measures for a 1-out-of-2 active redundant system 26 Bibliograp
19、hy31 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 transition diagram of a non-restorable one-element system.10 Figure 3 - Interpretation of failure an
20、d 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 Figure B.3 State transition diagram when restorations may be made from state 2 for a one-element
21、 system.21 Annex ZA (normative) Normative references to international publications with their corresponding European publications .34 EN 61165:2006 3 Figure B.4 State transition diagram when direct transition is considered for a one-element system.22 Figure B.5 State transition diagram for the evalu
22、ation of reliability of a one-element system22 Figure B.6 State transition diagram for a 1-out-of-2 active 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 l
23、imitations .23 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 .23 Figure B.9 State transition diagram for a 1-out-of-2 active redundant system with only one restoration team and restor
24、ation priority as first-in/first-out .24 Figure B.10 Reliability block diagram for a 2-out-of-4 active redundant 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
25、system with different elements and two restoration teams26 Figure C.2 State transition diagram for a 1-out-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
26、 for dangerous failure rate.30 EN 61165:2006 4 INTRODUCTION 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 characteristic
27、s. This 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 APPLICATION OF MARKOV TECHN
28、IQUES 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. This standard is applicable to all industries where systems, which exhibit state-dependent be
29、haviour, 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 Normative references The following referenced documents are indispensable for the application of thi
30、s 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 Electrotechnical Vocabulary (IEV) Chapter 191: Dependability and quality of service IEC 60300
31、-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 safety-related systems Part 4: Definitions and abbreviations 3 Terms and definitions For the pur
32、poses 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 61508 is used where appropriate. 3.1 system set of interrelated or interacting elements ISO 900
33、0, 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 structure of a system may be hierarchical. 3.2 element component or set of components, which function
34、 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 3.3 system state X(t) particular combination of element states NOTE X(t) is the state of the sy
35、stem at time t. There are other factors that may have an effect on the system state (e. g. mode of operation). 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 o
36、perational states and degraded states). 3.5 down state system (or element) state in which the system (or element) 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 p
37、eople or property IEC 61508-4, 3.1.2, modified 3.7 dangerous failure failure which has the potential to put 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 syst
38、em. NOTE 2 The term unsafe failure or hazardous failure is also commonly used in this context. 3.8 safe failure 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 anothe
39、r state NOTE Transition takes place usually as a result of failure or restoration. A transition may also be 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
40、 in a given time interval (s, s+t) given that the system is in state i at the beginning of the time interval 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 irreducib
41、le Markov process (i.e. if every state can be reached from every other state) it holds that Pij()=Pj, where Pjis the asymptotic and stationary or steady-state probability of state j. EN 61165:2006 7 3.11 transition rate qij limit, if it exists, of the ratio of the conditional probability that a tran
42、sition takes 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 s
43、tarts its 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 l
44、eft (i. e. 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 transi
45、tion diagram 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 tran
46、sition rate 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
47、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 defining those combinations of failed and functioning elements which characterise the state. EN 61
48、165:2006 8 4.1.3 State label A state label is a number or a letter in a circle, placed adjacent to the state symbol, or in the absence of a state description, within the state symbol itself. NOTE The state can often be adequately represented by a circle with the state number or letter. 4.1.4 Transit
49、ion arrow The transition arrow indicates the direction of a transition (e. g. as a result of failure or restoration). Transition rates are written near the transition arrow. 4.2 Other symbols and abbreviations Symbols for reliability, availability, maintainability and safety measures follow those of IEC 60050(191), where available. The references below with a prefix 191 are from IEC 60050(191). In this standard the following symbols are used: Symbol/ Abbreviation Term Reference ()tR reliabili
