1、EIASTANDARDMathematical Expressions for Reliability, Availability, Maintainability and Maintenance Support TermsEIA-61703 (IEC 61703:2016, IDT) September 2017 Electronic Components Industry Association ANSI/EIA-61703-2017 Approved: September 21, 2017 EIA-61703NOTICEEIA Engineering Standards and Publ
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5、wner, nor does it assume any obligation whatever to parties adopting the Standard or Publication. This EIA Standard is identical (IDT) with the International Standard IEC Publication 61703:2016 Edition 2: Mathematical Expressions for Reliability, Availability, Maintainability and Maintenance Support
6、 Terms.This document is the EIA Standard EIA-61703-2017: Mathematical Expressions for Reliability, Availability, Maintainability and Maintenance Support Terms.The text, figures and tables of IEC 61703:2016 are used in this Standard with the consent of the IEC and the American National Standards Inst
7、itute (ANSI). The IEC copyrighted material has been reproduced with permission from ANSI. The IEC Foreword and Introduction are not part of the requirements of this standard but are included for information purposes only. This Standard does not purport to address all safety problems associated with
8、its use or all applicable regulatory requirements. It is the responsibility of the user of this Standard to establish appropriate safety and health practices and to determine the applicability of regulatory limitations before its use. (From Standards Proposal No. 5391.02, formulated under the cogniz
9、ance of the ECIA Dependability Standards Committee).Published by Electronic Components Industry Association 2017 Engineering Department 2214 Rock Hill Road, Suite 265 Herndon, VA 20170 PLEASE ! DONT VIOLATE THE LAW!This document is copyrighted by the ECIA and may not be reproduced without permission
10、. Organizations may obtain permission to reproduce a limited number of copies through entering into a license agreement. For information, contact: IHS Markit 15 Inverness Way East Englewood, CO 80112-5704 or call USA and Canada (1-877-413-5186), International (303-397-7956) i CONTENTS FOREWORD . vIN
11、TRODUCTION . vii1 Scope 12 Normative references 23 Terms and definitions 24 Glossary of symbols and abbreviations 54.1 General . 54.2 Acronyms used in this standard 54.3 Symbols used in this standard 75 General models and assumptions 105.1 Constituents of up and down times 105.2 Introduction to mode
12、ls and assumptions . 115.3 State-transition approach 125.4 Model and assumptions for non-repairable individual items . 145.5 Assumptions and model for repairable individual items . 155.5.1 Assumption for repairable individual items . 155.5.2 Instantaneous repair 165.5.3 Non-instantaneous repair . 17
13、5.6 Continuously operating items (COI) versus intermittently operating individual items (IOI). 186 Mathematical models and expressions. 196.1 Systems 196.1.1 General . 196.1.2 Availability related expressions 216.1.3 Reliability related expressions . 286.1.4 Mean operating time between failures 192-
14、05-13 and mean time between failures 326.1.5 Instantaneous failure rate 192-05-06 and conditional failure intensity (Vesely failure rate) . 336.1.6 Failure density and unconditional failure intensity 192-05-08 . 366.1.7 Comparison of (t), V(t), z(t) and f(t) for high and small MTTRs . 396.1.8 Restor
15、ation related expressions . 396.2 Non-repairable individual items . 416.2.1 General . 416.2.2 Instantaneous availability 192-08-01 426.2.3 Reliability 192-05-05 426.2.4 Instantaneous failure rate 192-05-06 . 436.2.5 Mean failure rate 192-05-07 . 446.2.6 Mean operating time to failure 192-05-11 . 456
16、.3 Repairable individual items with zero time to restoration . 466.3.1 General . 466.3.2 Reliability 192-05-05 466.3.3 Instantaneous failure intensity 192-05-08 486.3.4 Asymptotic failure intensity 192-05-10 . 506.3.5 Mean failure intensity 192-05-09 51ii 6.3.6 Mean time between failures (see 3.3) 5
17、26.3.7 Mean operating time to failure 192-05-11 . 526.3.8 Mean operating time between failures 192-05-13 . 536.3.9 Instantaneous availability 192-08-01, mean availability 192-08-05 and asymptotic availability 192-08-07 536.3.10 Mean up time 192-08-09 536.4 Repairable individual items with non-zero t
18、ime to restoration 546.4.1 General . 546.4.2 Reliability 192-05-05 546.4.3 Instantaneous failure intensity 192-05-08 566.4.4 Asymptotic failure intensity 192-05-10 . 586.4.5 Mean failure intensity 192-05-09 606.4.6 Mean operating time to failure 192-05-11 . 616.4.7 Mean time between failures (see 3.
19、3) 626.4.8 Mean operating time between failures 192-05-13 . 636.4.9 Instantaneous availability 192-08-01 636.4.10 Instantaneous unavailability 192-08-04 656.4.11 Mean availability 192-08-05 . 666.4.12 Mean unavailability 192-08-06 . 686.4.13 Asymptotic availability 192-08-07. 706.4.14 Asymptotic una
20、vailability 192-08-08 . 706.4.15 Mean up time 192-08-09 716.4.16 Mean down time 192-08-10 . 736.4.17 Maintainability 192-07-01 . 746.4.18 Instantaneous repair rate 192-07-20 766.4.19 Mean repair time 192-07-21 . 786.4.20 Mean active corrective maintenance time 192-07-22 796.4.21 Mean time to restora
21、tion 192-07-23 . 806.4.22 Mean administrative delay 192-07-26 816.4.23 Mean logistic delay 192-07-27 . 82Annex A (informative) Performance aspects and descriptors 83Annex B (informative) Summary of measures related to time to failure . 84Annex C (informative) Comparison of some dependability measure
22、s for continuously operating items . 87Bibliography 89Figure 1 Constituents of up time 10Figure 2 Constituents of down time 11Figure 3 Acronyms related to failure times . 11Figure 4 Simple state-transition diagram 13Figure 5 Sample realization (chronogram) related to the system in Figure 4 . 14Figur
23、e 6 State-transition diagram of a non-repairable individual item . 14Figure 7 Sample realization of a non-repairable individual item 15Figure 8 State-transition diagram of an instantaneously repairable individual item . 16Figure 9 Sample realization of a repairable individual item with zero time to
24、restoration 17Figure 10 State-transition diagram of a repairable individual item 17iii Figure 11 Sample realization of a repairable individual item with non-zero time to restoration 18Figure 12 Comparison of an enabled time for a COI and an IOI . 18Figure 13 Equivalent operating time for IOI items .
25、 19Figure 14 State-transition graph for a simple redundant system . 19Figure 15 Markov graph for a simple redundant system . 20Figure 16 Evolution of the state probabilities related to the Markov model in Figure 15 20Figure 17 Evolution of A(t) and U(t) related to the Markov model in Figure 15 21Fig
26、ure 18 Evolution of the Asti(0, t) related to the Markov model in Figure 15 . 23Figure 19 Instantaneous availability and mean availability of a periodically tested item 25Figure 20 Example of a simple production system 26Figure 21 Evolution of A(t) and K(t) 27Figure 22 Illustration of a system relia
27、ble behaviour over 0, t . 28Figure 23 Illustration of a system reliable behaviour over time interval t1, t2 29Figure 24 State-transition and Markov graphs for reliability calculations . 29Figure 25 Evolution of the state probabilities related to the Markov model in Figure 24 30Figure 26 Evolution of
28、 R(t) and F(t) related to the Markov model in Figure 24 31Figure 27 Evolution of Asti(0, t) related to the Markov model in Figure 24 32Figure 28 Time between failures versus operating time between failures . 32Figure 29 Comparison between (t) and V(t) related to the model in Figure 24. 35Figure 30 C
29、omparison between z(t) and f(t) 38Figure 31 Comparison of (t), V(t), z(t) and f(t) for high and small values of MTTRs . 39Figure 32 Illustration of reliable behaviour over t1, t2 for a zero time to restoration individual item . 47Figure 33 Sample of possible number of failures at the renewal time t
30、. 48Figure 34 Illustration of reliable behaviour over t1 ,t2 for a non-zero time to restoration individual item . 54Figure 35 Evolution of R(t, t + 1/4) 56Figure 36 Sample of possible number of failures at the renewal time t . 56Figure 37 Evolution of the failure intensity z(t) 58Figure 38 Evolution
31、 of the mean failure intensity z(t, t + 1/4) 61Figure 39 Illustration of available behaviour at time t for a non-zero time to restoration individual item . 63Figure 40 Evolution of the instantaneous availability A(t) 65Figure 41 Illustration of unavailable behaviour at time t for a non-zero time to
32、restoration individual item . 65Figure 42 Evolution of the instantaneous unavailability U(t) . 66Figure 43 Evolution of the mean availability ( )41/, +ttA . 68Figure 44 Evolution of the mean unavailability ( )41/, +ttU . 69Figure 45 Sample realization of the individual item state 72Figure 46 Plot of
33、 the up-time hazard rate function )(U t . 72Figure 47 Evolution of the maintainability M(t, t+16h) . 76iv Figure 48 Evolution of the lognormal repair rate (t) 78Figure A.1 Performance aspects and descriptors . 83Table B.1 Relations among measures related to time to failure of continuously operating
34、items . 84Table B.2 Summary of characteristics for some continuous probability distributions of time to failure of continuously operating items . 85Table B.3 Summary of characteristics for some probability distributions of repair time . 86Table C.1 Comparison of some dependability measures of contin
35、uously operating items with constant failure rate and restoration rate R . 87v INTERNATIONAL ELECTROTECHNICAL COMMISSION_ MATHEMATICAL EXPRESSIONS FOR RELIABILITY, AVAILABILITY, MAINTAINABILITY AND MAINTENANCE SUPPORT TERMS FOREWORD 1) The International Electrotechnical Commission (IEC) is a worldwi
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45、cations. 8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is indispensable for the correct application of this publication. 9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
46、patent rights. IEC shall not be held responsible for identifying any or all such patent rights. International Standard IEC 61703 has been prepared by IEC technical committee 56: Dependability. This second edition cancels and replaces the first edition published in 2001. This edition constitutes a te
47、chnical revision. This edition includes the following significant technical changes with respect to the previous edition: a) standard made as self containing as possible; b) item split between individual items and systems; c) generalization of the dependability concepts for systems made of several c
48、omponents; introduction of the conditional failure intensity (Vesely failure rate); introduction of the state-transition and the Markovian models; vi generalization of the availability to production availability; d) introduction of curves to illustrate the various concepts. The text of this standard
49、 is based on the following documents: FDIS Report on voting 56/1682/FDIS 56/1693/RVD Full information on the voting for the approval of this standard can be found in the report on voting indicated in the above table. This publication has been drafted in accordance with the ISO/IEC Directives, Part 2. This International Standard is to be used in conjunction with IEC 60050-192:
