{"id":343877,"date":"2024-10-20T00:08:36","date_gmt":"2024-10-20T00:08:36","guid":{"rendered":"https:\/\/pdfstandards.shop\/product\/uncategorized\/bs-en-617032016\/"},"modified":"2024-10-25T23:28:29","modified_gmt":"2024-10-25T23:28:29","slug":"bs-en-617032016","status":"publish","type":"product","link":"https:\/\/pdfstandards.shop\/product\/publishers\/bsi\/bs-en-617032016\/","title":{"rendered":"BS EN 61703:2016"},"content":{"rendered":"

IEC 61703:2016 provides mathematical expressions for selected reliability, availability, maintainability and maintenance support measures defined in IEC 60050\u00ad192:2015. In addition, it introduces some terms not covered in IEC 60050-192:2015. They are related to aspects of the system of item classes (see hereafter). According to IEC 60050-192:2015, dependability [192-01-22] is the ability of an item to perform as and when required and an item [192-01-01] can be an individual part, component, device, functional unit, equipment, subsystem, or system. To account for mathematical constraints, this standard splits the items between the individual items considered as a whole (e.g. individual components) and the systems made of several individual items. It provides general considerations for the mathematical expressions for systems as well as individual items but the individual items which are easier to model are analysed in more detail with regards to their repair aspects. This standard is mainly applicable to hardware dependability, but many terms and their definitions may be applied to items containing software. This second edition cancels and replaces the first edition published in 2001. This edition constitutes a technical revision. This edition includes the following significant technical changes with respect to the previous edition: – standard made as self containing as possible; – item split between individual items and systems; – generalization of the dependability concepts for systems made of several components [introduction of the conditional failure intensity (Vesely failure rate); – introduction of the state-transition and the Markovian models; – generalization of the availability to production availability]; – introduction of curves to illustrate the various concepts. Keywords: mathematical expressions for dependability<\/p>\n

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PDF Pages<\/th>\nPDF Title<\/th>\n<\/tr>\n
6<\/td>\nEnglish
CONTENTS <\/td>\n<\/tr>\n
10<\/td>\nFOREWORD <\/td>\n<\/tr>\n
12<\/td>\nINTRODUCTION <\/td>\n<\/tr>\n
13<\/td>\n1 Scope <\/td>\n<\/tr>\n
14<\/td>\n2 Normative references
3 Terms and definitions <\/td>\n<\/tr>\n
17<\/td>\n4 Glossary of symbols and abbreviations
4.1 General
4.2 Acronyms used in this standard <\/td>\n<\/tr>\n
19<\/td>\n4.3 Symbols used in this standard <\/td>\n<\/tr>\n
22<\/td>\n5 General models and assumptions
5.1 Constituents of up and down times
Figures
Figure 1 \u2013 Constituents of up time <\/td>\n<\/tr>\n
23<\/td>\n5.2 Introduction to models and assumptions
Figure 2 \u2013 Constituents of down time
Figure 3 \u2013 Acronyms related to failure times <\/td>\n<\/tr>\n
24<\/td>\n5.3 State-transition approach <\/td>\n<\/tr>\n
25<\/td>\nFigure 4 \u2013 Simple state-transition diagram <\/td>\n<\/tr>\n
26<\/td>\n5.4 Model and assumptions for non-repairable individual items
Figure 5 \u2013 Sample realization (chronogram) related to the system in Figure 4
Figure 6 \u2013 State-transition diagram of a non-repairable individual item <\/td>\n<\/tr>\n
27<\/td>\n5.5 Assumptions and model for repairable individual items
5.5.1 Assumption for repairable individual items
Figure 7 \u2013 Sample realization of a non-repairable individual item <\/td>\n<\/tr>\n
28<\/td>\n5.5.2 Instantaneous repair
Figure 8 \u2013 State-transition diagram of an instantaneously repairable individual item <\/td>\n<\/tr>\n
29<\/td>\n5.5.3 Non-instantaneous repair
Figure 9 \u2013 Sample realization of a repairable individual item with zero time to restoration
Figure 10 \u2013 State-transition diagram of a repairable individual item <\/td>\n<\/tr>\n
30<\/td>\n5.6 Continuously operating items (COI) versus intermittently operating individual items (IOI)
Figure 11 \u2013 Sample realization of a repairable individual item with non-zero time to restoration
Figure 12 \u2013 Comparison of an enabled time for a COI and an IOI <\/td>\n<\/tr>\n
31<\/td>\n6 Mathematical models and expressions
6.1 Systems
6.1.1 General
Figure 13 \u2013 Equivalent operating time for IOI items
Figure\u00a014 \u2013 State-transition graph for a simple redundant system <\/td>\n<\/tr>\n
32<\/td>\nFigure 15 \u2013 Markov graph for a simple redundant system
Figure 16 \u2013 Evolution of the state probabilities related to the Markov model in Figure 15 <\/td>\n<\/tr>\n
33<\/td>\n6.1.2 Availability related expressions
Figure 17 \u2013 Evolution of A(t) and U(t) related to the Markov model in Figure 15 <\/td>\n<\/tr>\n
35<\/td>\nFigure 18 \u2013 Evolution of the Asti(0, t) related to the Markov model in Figure 15 <\/td>\n<\/tr>\n
37<\/td>\nFigure 19 \u2013 Instantaneous availability and mean availability of a periodically tested item <\/td>\n<\/tr>\n
38<\/td>\nFigure 20 \u2013 Example of a simple production system <\/td>\n<\/tr>\n
39<\/td>\nFigure 21 \u2013 Evolution of A(t) and K(t) <\/td>\n<\/tr>\n
40<\/td>\n6.1.3 Reliability related expressions
Figure 22 \u2013 Illustration of a system reliable behaviour over [0, t] <\/td>\n<\/tr>\n
41<\/td>\nFigure 23 \u2013 Illustration of a system reliable behaviour over time interval [t1, t2]
Figure 24 \u2013 State-transition and Markov graphs for reliability calculations <\/td>\n<\/tr>\n
42<\/td>\nFigure 25 \u2013 Evolution of the state probabilities related to the Markov model in Figure 24 <\/td>\n<\/tr>\n
43<\/td>\nFigure 26 \u2013 Evolution of R(t) and F(t) related to the Markov model in Figure 24 <\/td>\n<\/tr>\n
44<\/td>\n6.1.4 Mean operating time between failures [192-05-13] and mean time between failures
Figure 27 \u2013 Evolution of Asti(0, t) related to the Markov model in Figure 24
Figure 28 \u2013 Time between failures versus operating time between failures <\/td>\n<\/tr>\n
45<\/td>\n6.1.5 Instantaneous failure rate [192-05-06] and conditional failure intensity (Vesely failure rate) <\/td>\n<\/tr>\n
47<\/td>\nFigure 29 \u2013 Comparison between \u03bb(t) and \u03bbV(t) related to the model in Figure 24 <\/td>\n<\/tr>\n
48<\/td>\n6.1.6 Failure density and unconditional failure intensity [192-05-08] <\/td>\n<\/tr>\n
50<\/td>\nFigure 30 \u2013 Comparison between z(t) and f(t) <\/td>\n<\/tr>\n
51<\/td>\n6.1.7 Comparison of \u03bb(t), \u03bbV(t), z(t) and f(t) for high and small MTTRs
6.1.8 Restoration related expressions
Figure 31 \u2013 Comparison of \u03bb(t), \u03bbV(t), z(t) and f(t) for high and small values of MTTRs <\/td>\n<\/tr>\n
53<\/td>\n6.2 Non-repairable individual items
6.2.1 General <\/td>\n<\/tr>\n
54<\/td>\n6.2.2 Instantaneous availability [192-08-01]
6.2.3 Reliability [192-05-05] <\/td>\n<\/tr>\n
55<\/td>\n6.2.4 Instantaneous failure rate [192-05-06] <\/td>\n<\/tr>\n
56<\/td>\n6.2.5 Mean failure rate [192-05-07] <\/td>\n<\/tr>\n
57<\/td>\n6.2.6 Mean operating time to failure [192-05-11] <\/td>\n<\/tr>\n
58<\/td>\n6.3 Repairable individual items with zero time to restoration
6.3.1 General
6.3.2 Reliability [192-05-05] <\/td>\n<\/tr>\n
59<\/td>\nFigure 32 \u2013 Illustration of reliable behaviour over [t1, t2] for a zero time to restoration individual item <\/td>\n<\/tr>\n
60<\/td>\n6.3.3 Instantaneous failure intensity [192-05-08]
Figure 33 \u2013 Sample of possible number of failures at the renewal time t <\/td>\n<\/tr>\n
62<\/td>\n6.3.4 Asymptotic failure intensity [192-05-10] <\/td>\n<\/tr>\n
63<\/td>\n6.3.5 Mean failure intensity [192-05-09] <\/td>\n<\/tr>\n
64<\/td>\n6.3.6 Mean time between failures (see 3.3)
6.3.7 Mean operating time to failure [192-05-11] <\/td>\n<\/tr>\n
65<\/td>\n6.3.8 Mean operating time between failures [192-05-13]
6.3.9 Instantaneous availability [192-08-01], mean availability [192-08-05] and asymptotic availability [192-08-07]
6.3.10 Mean up time [192-08-09] <\/td>\n<\/tr>\n
66<\/td>\n6.4 Repairable individual items with non-zero time to restoration
6.4.1 General
6.4.2 Reliability [192-05-05]
Figure 34 \u2013 Illustration of reliable behaviour over [t1 ,t2] for a non-zero time to restoration individual item <\/td>\n<\/tr>\n
68<\/td>\n6.4.3 Instantaneous failure intensity [192-05-08]
Figure 35 \u2013 Evolution of R(t, t + 1\/4)
Figure 36 \u2013 Sample of possible number of failures at the renewal time t <\/td>\n<\/tr>\n
70<\/td>\nFigure 37 \u2013 Evolution of the failure intensity z(t) <\/td>\n<\/tr>\n
71<\/td>\n6.4.4 Asymptotic failure intensity [192-05-10] <\/td>\n<\/tr>\n
72<\/td>\n6.4.5 Mean failure intensity [192-05-09] <\/td>\n<\/tr>\n
73<\/td>\n6.4.6 Mean operating time to failure [192-05-11]
Figure 38 \u2013 Evolution of the mean failure intensity z(t, t + 1\/4) <\/td>\n<\/tr>\n
74<\/td>\n6.4.7 Mean time between failures (see 3.3) <\/td>\n<\/tr>\n
75<\/td>\n6.4.8 Mean operating time between failures [192-05-13]
6.4.9 Instantaneous availability [192-08-01]
Figure 39 \u2013 Illustration of available behaviour at time t for a non-zero time to restoration individual item <\/td>\n<\/tr>\n
77<\/td>\n6.4.10 Instantaneous unavailability [192-08-04]
Figure 40 \u2013 Evolution of the instantaneous availability A(t)
Figure 41 \u2013 Illustration of unavailable behaviour at time t for a non-zero time to restoration individual item <\/td>\n<\/tr>\n
78<\/td>\n6.4.11 Mean availability [192-08-05]
Figure 42 \u2013 Evolution of the instantaneous unavailability U(t) <\/td>\n<\/tr>\n
80<\/td>\n6.4.12 Mean unavailability [192-08-06]
Figure 43 \u2013 Evolution of the mean availability <\/td>\n<\/tr>\n
81<\/td>\nFigure 44 \u2013 Evolution of the mean unavailability <\/td>\n<\/tr>\n
82<\/td>\n6.4.13 Asymptotic availability [192-08-07]
6.4.14 Asymptotic unavailability [192-08-08] <\/td>\n<\/tr>\n
83<\/td>\n6.4.15 Mean up time [192-08-09] <\/td>\n<\/tr>\n
84<\/td>\nFigure 45 \u2013 Sample realization of the individual item state
Figure 46 \u2013 Plot of the up-time hazard rate function <\/td>\n<\/tr>\n
85<\/td>\n6.4.16 Mean down time [192-08-10] <\/td>\n<\/tr>\n
86<\/td>\n6.4.17 Maintainability [192-07-01] <\/td>\n<\/tr>\n
88<\/td>\n6.4.18 Instantaneous repair rate [192-07-20]
Figure 47 \u2013 Evolution of the maintainability M(t, t+16h) <\/td>\n<\/tr>\n
90<\/td>\n6.4.19 Mean repair time [192-07-21]
Figure 48 \u2013 Evolution of the lognormal repair rate \u03bc(t) <\/td>\n<\/tr>\n
91<\/td>\n6.4.20 Mean active corrective maintenance time [192-07-22] <\/td>\n<\/tr>\n
92<\/td>\n6.4.21 Mean time to restoration [192-07-23] <\/td>\n<\/tr>\n
93<\/td>\n6.4.22 Mean administrative delay [192-07-26] <\/td>\n<\/tr>\n
94<\/td>\n6.4.23 Mean logistic delay [192-07-27] <\/td>\n<\/tr>\n
95<\/td>\nAnnex A (informative) Performance aspects and descriptors
Figure A.1 \u2013 Performance aspects and descriptors <\/td>\n<\/tr>\n
96<\/td>\nAnnex B (informative) Summary of measures related to time to failure
Tables
Table B.1 \u2013 Relations among measures related to time to failure of continuously operating items <\/td>\n<\/tr>\n
97<\/td>\nTable B.2 \u2013 Summary of characteristics for some continuous probability distributions of time to failure of continuously operating items <\/td>\n<\/tr>\n
98<\/td>\nTable B.3 \u2013 Summary of characteristics for some probability distributions of repair time <\/td>\n<\/tr>\n
99<\/td>\nAnnex C (informative) Comparison of some dependability measures for continuously operating items
Table C.1 \u2013 Comparison of some dependability measures of continuously operating items with constant failure rate \u03bb and restoration rate \u03bcR <\/td>\n<\/tr>\n
101<\/td>\nBibliography <\/td>\n<\/tr>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Mathematical expressions for reliability, availability, maintainability and maintenance support terms<\/b><\/p>\n\n\n\n\n
Published By<\/td>\nPublication Date<\/td>\nNumber of Pages<\/td>\n<\/tr>\n
BSI<\/b><\/a><\/td>\n2016<\/td>\n104<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":343887,"template":"","meta":{"rank_math_lock_modified_date":false,"ep_exclude_from_search":false},"product_cat":[97,2641],"product_tag":[],"class_list":{"0":"post-343877","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-03-120-30","7":"product_cat-bsi","9":"first","10":"instock","11":"sold-individually","12":"shipping-taxable","13":"purchasable","14":"product-type-simple"},"_links":{"self":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product\/343877","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media\/343887"}],"wp:attachment":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media?parent=343877"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_cat?post=343877"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_tag?post=343877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}