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BS EN 61703:2016

BS EN 61703:2016

$215.11

Mathematical expressions for reliability, availability, maintainability and maintenance support terms

Published By Publication Date Number of Pages
BSI 2016 104
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IEC 61703:2016 provides mathematical expressions for selected reliability, availability, maintainability and maintenance support measures defined in IEC 60050­192:2015. 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

PDF Catalog

PDF Pages PDF Title
6 English
CONTENTS
10 FOREWORD
12 INTRODUCTION
13 1 Scope
14 2 Normative references
3 Terms and definitions
17 4 Glossary of symbols and abbreviations
4.1 General
4.2 Acronyms used in this standard
19 4.3 Symbols used in this standard
22 5 General models and assumptions
5.1 Constituents of up and down times
Figures
Figure 1 – Constituents of up time
23 5.2 Introduction to models and assumptions
Figure 2 – Constituents of down time
Figure 3 – Acronyms related to failure times
24 5.3 State-transition approach
25 Figure 4 – Simple state-transition diagram
26 5.4 Model and assumptions for non-repairable individual items
Figure 5 – Sample realization (chronogram) related to the system in Figure 4
Figure 6 – State-transition diagram of a non-repairable individual item
27 5.5 Assumptions and model for repairable individual items
5.5.1 Assumption for repairable individual items
Figure 7 – Sample realization of a non-repairable individual item
28 5.5.2 Instantaneous repair
Figure 8 – State-transition diagram of an instantaneously repairable individual item
29 5.5.3 Non-instantaneous repair
Figure 9 – Sample realization of a repairable individual item with zero time to restoration
Figure 10 – State-transition diagram of a repairable individual item
30 5.6 Continuously operating items (COI) versus intermittently operating individual items (IOI)
Figure 11 – Sample realization of a repairable individual item with non-zero time to restoration
Figure 12 – Comparison of an enabled time for a COI and an IOI
31 6 Mathematical models and expressions
6.1 Systems
6.1.1 General
Figure 13 – Equivalent operating time for IOI items
Figure 14 – State-transition graph for a simple redundant system
32 Figure 15 – Markov graph for a simple redundant system
Figure 16 – Evolution of the state probabilities related to the Markov model in Figure 15
33 6.1.2 Availability related expressions
Figure 17 – Evolution of A(t) and U(t) related to the Markov model in Figure 15
35 Figure 18 – Evolution of the Asti(0, t) related to the Markov model in Figure 15
37 Figure 19 – Instantaneous availability and mean availability of a periodically tested item
38 Figure 20 – Example of a simple production system
39 Figure 21 – Evolution of A(t) and K(t)
40 6.1.3 Reliability related expressions
Figure 22 – Illustration of a system reliable behaviour over [0, t]
41 Figure 23 – Illustration of a system reliable behaviour over time interval [t1, t2]
Figure 24 – State-transition and Markov graphs for reliability calculations
42 Figure 25 – Evolution of the state probabilities related to the Markov model in Figure 24
43 Figure 26 – Evolution of R(t) and F(t) related to the Markov model in Figure 24
44 6.1.4 Mean operating time between failures [192-05-13] and mean time between failures
Figure 27 – Evolution of Asti(0, t) related to the Markov model in Figure 24
Figure 28 – Time between failures versus operating time between failures
45 6.1.5 Instantaneous failure rate [192-05-06] and conditional failure intensity (Vesely failure rate)
47 Figure 29 – Comparison between λ(t) and λV(t) related to the model in Figure 24
48 6.1.6 Failure density and unconditional failure intensity [192-05-08]
50 Figure 30 – Comparison between z(t) and f(t)
51 6.1.7 Comparison of λ(t), λV(t), z(t) and f(t) for high and small MTTRs
6.1.8 Restoration related expressions
Figure 31 – Comparison of λ(t), λV(t), z(t) and f(t) for high and small values of MTTRs
53 6.2 Non-repairable individual items
6.2.1 General
54 6.2.2 Instantaneous availability [192-08-01]
6.2.3 Reliability [192-05-05]
55 6.2.4 Instantaneous failure rate [192-05-06]
56 6.2.5 Mean failure rate [192-05-07]
57 6.2.6 Mean operating time to failure [192-05-11]
58 6.3 Repairable individual items with zero time to restoration
6.3.1 General
6.3.2 Reliability [192-05-05]
59 Figure 32 – Illustration of reliable behaviour over [t1, t2] for a zero time to restoration individual item
60 6.3.3 Instantaneous failure intensity [192-05-08]
Figure 33 – Sample of possible number of failures at the renewal time t
62 6.3.4 Asymptotic failure intensity [192-05-10]
63 6.3.5 Mean failure intensity [192-05-09]
64 6.3.6 Mean time between failures (see 3.3)
6.3.7 Mean operating time to failure [192-05-11]
65 6.3.8 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]
66 6.4 Repairable individual items with non-zero time to restoration
6.4.1 General
6.4.2 Reliability [192-05-05]
Figure 34 – Illustration of reliable behaviour over [t1 ,t2] for a non-zero time to restoration individual item
68 6.4.3 Instantaneous failure intensity [192-05-08]
Figure 35 – Evolution of R(t, t + 1/4)
Figure 36 – Sample of possible number of failures at the renewal time t
70 Figure 37 – Evolution of the failure intensity z(t)
71 6.4.4 Asymptotic failure intensity [192-05-10]
72 6.4.5 Mean failure intensity [192-05-09]
73 6.4.6 Mean operating time to failure [192-05-11]
Figure 38 – Evolution of the mean failure intensity z(t, t + 1/4)
74 6.4.7 Mean time between failures (see 3.3)
75 6.4.8 Mean operating time between failures [192-05-13]
6.4.9 Instantaneous availability [192-08-01]
Figure 39 – Illustration of available behaviour at time t for a non-zero time to restoration individual item
77 6.4.10 Instantaneous unavailability [192-08-04]
Figure 40 – Evolution of the instantaneous availability A(t)
Figure 41 – Illustration of unavailable behaviour at time t for a non-zero time to restoration individual item
78 6.4.11 Mean availability [192-08-05]
Figure 42 – Evolution of the instantaneous unavailability U(t)
80 6.4.12 Mean unavailability [192-08-06]
Figure 43 – Evolution of the mean availability
81 Figure 44 – Evolution of the mean unavailability
82 6.4.13 Asymptotic availability [192-08-07]
6.4.14 Asymptotic unavailability [192-08-08]
83 6.4.15 Mean up time [192-08-09]
84 Figure 45 – Sample realization of the individual item state
Figure 46 – Plot of the up-time hazard rate function
85 6.4.16 Mean down time [192-08-10]
86 6.4.17 Maintainability [192-07-01]
88 6.4.18 Instantaneous repair rate [192-07-20]
Figure 47 – Evolution of the maintainability M(t, t+16h)
90 6.4.19 Mean repair time [192-07-21]
Figure 48 – Evolution of the lognormal repair rate μ(t)
91 6.4.20 Mean active corrective maintenance time [192-07-22]
92 6.4.21 Mean time to restoration [192-07-23]
93 6.4.22 Mean administrative delay [192-07-26]
94 6.4.23 Mean logistic delay [192-07-27]
95 Annex A (informative) Performance aspects and descriptors
Figure A.1 – Performance aspects and descriptors
96 Annex B (informative) Summary of measures related to time to failure
Tables
Table B.1 – Relations among measures related to time to failure of continuously operating items
97 Table B.2 – Summary of characteristics for some continuous probability distributions of time to failure of continuously operating items
98 Table B.3 – Summary of characteristics for some probability distributions of repair time
99 Annex C (informative) Comparison of some dependability measures for continuously operating items
Table C.1 – Comparison of some dependability measures of continuously operating items with constant failure rate λ and restoration rate μR
101 Bibliography

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BS EN 61703:2016
$215.11