1、Mathematical expressions for reliability, availability, maintainability and maintenance support termsBS EN 61703:2016BSI Standards PublicationWB11885_BSI_StandardCovs_2013_AW.indd 1 15/05/2013 15:06National forewordThis British Standard is the UK implementation of EN 61703:2016. It is identical to I
2、EC 61703:2016. It supersedes BS EN 61703:2002, which will bewithdrawn on 16 September 2019.The UK participation in its preparation was entrusted to TechnicalCommittee DS/1, Dependability.A list of organizations represented on this committee can be obtained onrequest to its secretary.This publication
3、 does not purport to include all the necessary provisions ofa contract. Users are responsible for its correct application. The British Standards Institution 2016.Published by BSI Standards Limited 2016ISBN 978 0 580 82730 3ICS 03.120.30; 21.020Compliance with a British Standard cannot confer immunit
4、y fromlegal obligations.This British Standard was published under the authority of theStandards Policy and Strategy Committee on 31 December 2016.Amendments/corrigenda issued since publicationDate Text affectedBRITISH STANDARDBS EN 61703:2016EUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN 61703
5、 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 mathmatiques pour les termes de fiabilit, de disponibilit, de maintenabilit et de logistiqu
6、e de maintenance (IEC 61703:2016) Mathematische Ausdrcke fr Begriffe der Zuverlssigkeit, Verfgbarkeit, Instandhaltbarkeit und Instandhaltungsbereitschaft (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 R
7、egulations 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 CENEL
8、EC 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
9、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
10、, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. European Committee for Electrotechnical Standardization Comit Europen de Normalisation Electrotechnique Europisches Komitee fr Elektrotechnische Normung CEN-CENELEC Ma
11、nagement 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 BS EN 61703:2016EN 61703:2016 2 European foreword The text of document 56/1682/FDIS, future edition 2 of IEC 61703,
12、 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: latest date by which the document has to be implemented at national level by publication of an identical national standard or by endorsement
13、(dop) 2017-06-16 latest date by which the national standards conflicting with the document have to be withdrawn (dow) 2019-09-16 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/o
14、r 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
15、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. BS EN 61703:2016EN 61703:2016 3 Annex Z
16、A (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. F
17、or 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 Eur
18、opean 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
19、in probability - - BS EN 61703:2016 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 .
20、 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 Assump
21、tion 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
22、 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 fail
23、ure intensity 192-05-08 . 44 6.1.7 Comparison of (t), V(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 Instantane
24、ous 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 Asymptoti
25、c 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 BS EN 61703:2016IEC 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 availab
26、ility 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 Asy
27、mptotic 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 Instanta
28、neous 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
29、-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
30、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 Cons
31、tituents 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 o
32、f 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 BS EN 617
33、03:2016 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 red
34、undant 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 Asti(0, t) related to the Ma
35、rkov 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 Illustratio
36、n of a system reliable behaviour over time interval t1, t2 37 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 Fi
37、gure 24 39 Figure 27 Evolution of Asti(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 (t) and V(t) related to the model in Figure 24 43 Figure 30 Comparison between z(t) and f(t) 46 Figure 31
38、Comparison of (t), V(t), z(t) and f(t) for high and small values of MTTRs . 47 Figure 32 Illustration of reliable behaviour over t1, t2 for a zero time to restoration individual item 55 Figure 33 Sample of possible number of failures at the renewal time t . 56 Figure 34 Illustration of reliable beha
39、viour over t1 ,t2 for a non-zero time to 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 +
40、 1/4) 69 Figure 39 Illustration of available behaviour at time tfor 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 tfor a non-zero time to restoration individual item . 73 Fig
41、ure 42 Evolution of the instantaneous unavailability U(t) . 74 Figure 43 Evolution of the mean availability ( )41/, +ttA 76 Figure 44 Evolution of the mean unavailability ( )41/, +ttU 77 Figure 45 Sample realization of the individual item state . 80 Figure 46 Plot of the up-time hazard rate function
42、 )(Ut 80 Figure 47 Evolution of the maintainability M(t, t+16h) 84 Figure 48 Evolution of the lognormal repair rate (t) . 86 BS EN 61703:2016IEC 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 opera
43、ting 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
44、continuously operating items with constant failure rate and restoration rate R95 BS EN 61703:2016 6 IEC 61703:2016 IEC 2016 INTERNATIONAL ELECTROTECHNICAL COMMISSION _ MATHEMATICAL EXPRESSIONS FOR RELIABILITY, AVAILABILITY, MAINTAINABILITY AND MAINTENANCE SUPPORT TERMS FOREWORD 1) The International
45、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 fie
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49、ation 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 respo
