Analysis techniques for dependability - Reliability block diagram and boolean methods

This International Standard describes procedures for modelling the dependability of a system and for using the model in order to calculate reliability and availability measures. The RBD modelling technique is intended to be applied primarily to systems without repair and where the order in which failures occur does not matter. For systems where the order of failures is to be taken into account or where repairs are to be carried out, other modelling techniques, such as Markov analysis, are more suitable.

Techniken für die Analyse der Zuverlässigkeit - Verfahren mit dem Zuverlässigkeitsblockdiagramm und Boole'sche Verfahren

Techniques d'analyse pour la sûreté de fonctionnement - Bloc-diagramme de fiabilité et méthodes booléennes

La présente Norme internationale décrit les procédures de modélisation de la sûreté de fonctionnement d'un système et l'utilisation du modèle pour calculer la fiabilité et la disponibilité. La technique de modélisation BDF est destinée à être appliquée principalement aux systèmes sans réparation et où l'ordre d'apparition des défaillances n'a pas d'importance. Pour les systèmes où l'ordre des défaillances est à prendre en compte, ou lorsque des réparations sont effectuées, d'autres techniques de modélisation, telle que l'analyse de Markov conviennent mieux.

Analizne tehnike za zagotovljivost – Zanesljivost, blokovni diagram in Boolove metode (IEC 61078:2006)

General Information

Status
Withdrawn
Publication Date
31-Dec-2006
Withdrawal Date
14-Nov-2019
Current Stage
9900 - Withdrawal (Adopted Project)
Start Date
15-Oct-2019
Due Date
07-Nov-2019
Completion Date
15-Nov-2019

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SLOVENSKI STANDARD
SIST EN 61078:2007
01-januar-2007
1DGRPHãþD
SIST EN 61078:2002
Analizne tehnike za zagotovljivost – Zanesljivost, blokovni diagram in Boolove
metode (IEC 61078:2006)

Analysis techniques for dependability - Reliability block diagram and boolean methods

Techniken für die Analyse der Zuverlässigkeit - Verfahren mit dem
Zuverlässigkeitsblockdiagramm und Boole'sche Verfahren

Techniques d'analyse pour la sûreté de fonctionnement - Bloc-diagramme de fiabilité et

méthodes booléennes
Ta slovenski standard je istoveten z: EN 61078:2006
ICS:
21.020 =QDþLOQRVWLLQQDþUWRYDQMH Characteristics and design of
VWURMHYDSDUDWRYRSUHPH machines, apparatus,
equipment
SIST EN 61078:2007 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN 61078:2007
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SIST EN 61078:2007
EUROPEAN STANDARD
EN 61078
NORME EUROPÉENNE
May 2006
EUROPÄISCHE NORM
ICS 03.120.01; 03.120.99 Supersedes EN 61078:1993
English version
Analysis techniques for dependability -
Reliability block diagram and boolean methods
(IEC 61078:2006)
Techniques d'analyse Techniken für die Analyse
pour la sûreté de fonctionnement - der Zuverlässigkeit -
Bloc-diagramme de fiabilité Verfahren mit dem
et méthodes booléennes Zuverlässigkeitsblockdiagramm
(CEI 61078:2006) und Boole'sche Verfahren
(IEC 61078:2006)

This European Standard was approved by CENELEC on 2006-03-01. CENELEC members are bound to comply

with the CEN/CENELEC Internal Regulations 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 Central Secretariat or to any CENELEC 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 Central Secretariat has the same status as the official versions.

CENELEC members are the national electrotechnical 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 United Kingdom.
CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für 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 61078:2006 E
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SIST EN 61078:2007
EN 61078:2006 - 2 -
Foreword

The text of document 56/1071/FDIS, future edition 2 of IEC 61078, prepared by IEC TC 56,

Dependability, was submitted to the IEC-CENELEC parallel vote and was approved by CENELEC as

EN 61078 on 2006-03-01.
This European Standard supersedes EN 61078:1993.

The major change with respect to EN 61078:1993 is that an additional clause on Boolean disjointing

methods (Annex B) has been added.
The following dates were fixed:
– latest date by which the EN has to be implemented
at national level by publication of an identical
national standard or by endorsement (dop) 2006-12-01
– latest date by which the national standards conflicting
with the EN have to be withdrawn (dow) 2009-03-01
Annex ZA has been added by CENELEC.
__________
Endorsement notice

The text of the International Standard IEC 61078:2006 was approved by CENELEC as a European

Standard without any modification.

In the official version, for Bibliography, the following note has to be added for the standard indicated:

IEC 60812 NOTE Harmonized as EN 60812:2006 (not modified).
__________
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SIST EN 61078:2007
- 3 - EN 61078:2006
Annex ZA
(normative)
Normative references to international publications
with their corresponding European publications

The following referenced documents are indispensable for the application of this document. For dated

references, only the edition cited applies. For undated references, the latest edition of the referenced

document (including any amendments) applies.

NOTE When an international publication has been modified by common modifications, indicated by (mod), the relevant EN/HD

applies.
Publication Year Title EN/HD Year
IEC 60050-191 1990 International Electrotechnical Vocabulary - -
(IEV)
Chapter 191: Dependability and quality of
service
1) 2)
IEC 61025 Fault tree analysis (FTA) HD 617 S1
- 1992
ISO 3534-1 1993 Statistics - Vocabulary and symbols - -
Part 1: Probability and general statistical
terms
Undated reference.
Valid edition at date of issue.
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SIST EN 61078:2007
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SIST EN 61078:2007
NORME CEI
INTERNATIONALE
IEC
61078
INTERNATIONAL
Deuxième édition
STANDARD
Second edition
2006-01
Techniques d'analyse pour la sûreté
de fonctionnement –
Bloc-diagramme de fiabilité et
méthodes booléennes
Analysis techniques for dependability –
Reliability block diagram and
boolean methods
 IEC 2006 Droits de reproduction réservés  Copyright - all rights reserved

Aucune partie de cette publication ne peut être reproduite ni No part of this publication may be reproduced or utilized in any

utilisée sous quelque forme que ce soit et par aucun procédé, form or by any means, electronic or mechanical, including

électronique ou mécanique, y compris la photocopie et les photocopying and microfilm, without permission in writing from

microfilms, sans l'accord écrit de l'éditeur. the publisher.

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Telephone: +41 22 919 02 11 Telefax: +41 22 919 03 00 E-mail: inmail@iec.ch Web: www.iec.ch

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Pour prix, voir catalogue en vigueur
For price, see current catalogue
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SIST EN 61078:2007
61078  IEC:2006 – 3 –
CONTENTS

FOREWORD...........................................................................................................................7

INTRODUCTION...................................................................................................................11

1 Scope.............................................................................................................................13

2 Normative references .....................................................................................................13

3 Terms and definitions .....................................................................................................13

4 Symbols and abbreviated terms......................................................................................15

5 Assumptions and limitations ...........................................................................................17

5.1 Independence of events ........................................................................................17

5.2 Sequential events..................................................................................................17

5.3 Distribution of times to failure ................................................................................17

6 Establishment of system success/failure definitions........................................................17

6.1 General considerations..........................................................................................17

6.2 Detailed considerations .........................................................................................19

7 Elementary models.........................................................................................................21

7.1 Developing the model............................................................................................21

7.2 Evaluating the model.............................................................................................25

8 More complex models.....................................................................................................31

8.1 General procedures...............................................................................................31

8.2 Models with common blocks ..................................................................................41

8.3 m out of n models (non-identical items) .................................................................45

8.4 Method of reduction...............................................................................................45

9 Extension of reliability block diagram methods to availability calculations .......................47

Annex A (informative) Summary of formulæ .........................................................................51

Annex B (informative) Boolean disjointing methods..............................................................59

Bibliography..........................................................................................................................71

Figure 1 – Series reliability block diagram.............................................................................21

Figure 2 – Duplicated (or parallel) series reliability block diagram.........................................21

Figure 3 – Series duplicated (or parallel) reliability block diagram .........................................23

Figure 4 – Mixed redundancy reliability block diagram ..........................................................23

Figure 5 – Another type of mixed redundancy reliability block diagram..................................23

Figure 6 – 2/3 redundancy ....................................................................................................23

Figure 7 – 2/4 redundancy ....................................................................................................23

Figure 8 – Diagram not easily represented by series/parallel arrangement of blocks.............25

Figure 9 – Parallel arrangement of blocks .............................................................................27

Figure 10 – Standby redundancy ..........................................................................................29

Figure 11 – Representation of Figure 8 when item A has failed.............................................33

Figure 12 – Representation of Figure 8 when item A is working ............................................33

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SIST EN 61078:2007
61078  IEC:2006 – 5 –

Figure 13 – One-out-of-three parallel arrangement ...............................................................35

Figure 14 – Reliability block diagram using an arrow to help define system success .............41

Figure 15 – Alternative representation of Figure 14 using common blocks ............................41

Figure 16 – 2-out-of-5 non-identical system ..........................................................................45

Figure 17 – Illustrating grouping of blocks before reduction ..................................................47

Figure 18 – Reduced reliability block diagrams .....................................................................47

Table 1 – Application of truth table to the example of Figure 13 ............................................37

Table 2 – Application of truth table to the example of Figure 8 ..............................................39

Table 3 – Application of truth table to the examples of Figures 14 and 15 .............................43

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SIST EN 61078:2007
61078  IEC:2006 – 7 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ANALYSIS TECHNIQUES FOR DEPENDABILITY –
RELIABILITY BLOCK DIAGRAM AND BOOLEAN METHODS
FOREWORD

1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardisation comprising

all national electrotechnical committees (IEC National Committees). The object of IEC is to promote

international co-operation on all questions concerning standardisation in the electrical and electronic fields. To

this end and in addition to other activities, IEC publishes International Standards, Technical Specifications,

Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC

Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested

in the subject dealt with may participate in this preparatory work. International, governmental and non-

governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely

with the International Organization for Standardization (ISO) in accordance with conditions determined by

agreement between the two organizations.

2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international

consensus of opinion on the relevant subjects since each technical committee has representation 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 responsible for the way in which they are used or for any

misinterpretation by any end user.

4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications

transparently to the maximum extent possible in their national and regional publications. Any divergence

between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in

the latter.

5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any

equipment declared to be in conformity with an IEC Publication.

6) All users should ensure that they have the latest edition of this publication.

7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and

members of its technical committees and IEC National Committees for any personal injury, property damage or

other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and

expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC

Publications.

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

patent rights. IEC shall not be held responsible for identifying any or all such patent rights.

International Standard IEC 61078 has been prepared by IEC technical committee 56:

Dependability.

This second edition cancels and replaces the first edition, published in 1991, and constitutes

a full technical revision. The major change with respect to the previous edition is that an

additional clause on Boolean disjointing methods (Annex B) has been added.
The text of this standard is based on the following documents:
FDIS Report on voting
56/1071/FDIS 56/1089/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.

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SIST EN 61078:2007
61078  IEC:2006 – 9 –

The committee has decided that the contents of this publication will remain unchanged until

the maintenance result date indicated on the IEC web site under "http://webstore.iec.ch" in

the data related to the specific publication. At this date, the publication will be

• reconfirmed;
• withdrawn;
• replaced by a revised edition, or
• amended.
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SIST EN 61078:2007
61078  IEC:2006 – 11 –
INTRODUCTION

Different analytical methods of dependability analysis are available, of which the reliability

block diagram (RBD) is one. The purpose of each method and their individual or combined

applicability in evaluating the reliability and availability of a given system or component should

be examined by the analyst prior to starting work on the RBD. Consideration should also be

given to the results obtainable from each method, data required to perform the analysis,

complexity of analysis and other factors identified in this standard.

A reliability block diagram (RBD) is a pictorial representation of a system's reliability perform-

ance. It shows the logical connection of (functioning) components needed for successful

operation of the system (hereafter referred to as “system success”).
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SIST EN 61078:2007
61078  IEC:2006 – 13 –
ANALYSIS TECHNIQUES FOR DEPENDABILITY –
RELIABILITY BLOCK DIAGRAM AND BOOLEAN METHODS
1 Scope

This International Standard describes procedures for modelling the dependability of a system

and for using the model in order to calculate reliability and availability measures.

The RBD modelling technique is intended to be applied primarily to systems without repair

and where the order in which failures occur does not matter. For systems where the order of

failures is to be taken into account or where repairs are to be carried out, other modelling

techniques, such as Markov analysis, are more suitable.

It should be noted that although the word “repair” is frequently used in this standard, the word

“restore” is equally applicable. Note also that the words “item” and “block” are used

extensively throughout this standard: in most instances interchangeably.
2 Normative references

The following referenced documents are indispensable for the application of this 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: Depend-

ability and quality of service
IEC 61025, Fault tree analysis (FTA)

ISO 3534-1:1993, Statistics – Vocabulary and symbols – Part 1: Probability and general

statistical terms
3 Terms and definitions

For the purposes of this document, the terms and definitions given in IEC 60050-191 and

ISO 3534-1 apply.
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SIST EN 61078:2007
61078  IEC:2006 – 15 –
4 Symbols and abbreviated terms
Symbol/Abbreviation Meaning
When used in Boolean expressions, these symbols indicate that items A, B, C,
A, B, C,K
... are in up states
When used in Boolean expressions, these symbols indicate that items A, B, C,
A, B, C,L
... are in down states
Probability of system failure
Probability density function of block A. The term “block” is used to denote a
f (t)
group of one or more components

Pr(SS|X failed) Conditional probability of system success, given that item X is failed

Reliability [probability that an item can perform a required function under given

R , R(t) , R (t)
conditions for a given time interval (0,t)]
Reliability of blocks A, B, ...
R , R , …
A B
System reliability
Reliability of switching and sensing mechanism
SF System failure (used in the Boolean expressions)
SS System success (used in the Boolean expressions)
t Mission time or time period of interest
Failure rate (constant) of blocks A, B and C
λ , λ , λ
A B C
Dormant failure rate of block B
Repair rates (constant) of blocks A, B and C
µ , µ , µ
A B C
Number of ways of selecting r items from n items
( )

0, 1 These symbols are used in truth tables to denote down and up states and apply

to whichever item is the column heading
Boolean symbols denoting AND logic, e.g. A ∩ B, A.B (intersection)
Boolean symbols denoting OR logic, e.g. A ∪ B, A+B (union)
Active (parallel) redundancy
I O
Standby redundancy
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SIST EN 61078:2007
61078  IEC:2006 – 17 –
Symbol/Abbreviation Meaning
m/n is symbol used to show m-out-of-n items needed for system success in an
m/n
I O
active redundant configuration
I indicates input
O indicates output
Such indications are used for convenience. They are not mandatory, but may
be useful where connections have a directional significance
I A
Grouping of equipment, components, units or other system elements
5 Assumptions and limitations
5.1 Independence of events

One of the most fundamental assumptions on which the procedures described in this standard

are based, is the assumption that components (or blocks representing them) can exist in only

two states: working (“up” state) or failed (“down” state).

Another important assumption is that failure (or repair) of any block must not affect the

probability of failure of (or repair to) ANY other block within the system being modelled. This

implies that there should be available, in effect, sufficient repair resources to service those

blocks needing repair and that when two or more persons are repairing a particular block at

the same time, neither gets in the other’s way. Thus failures of and repairs to individual blocks

are considered to be statistically independent events.
5.2 Sequential events

RBDs are not suitable for modelling order-dependent or time-dependent events. In such

instances, other methods such as Markov analysis or Petri nets should be used.
5.3 Distribution of times to failure

Provided the assumptions noted in 5.1 are valid, there is no restriction, other than

mathematical tractability, on the distribution that may be used to describe the times to failure

or repair.
6 Establishment of system success/failure definitions
6.1 General considerations

A prerequisite for constructing system reliability models is a sound understanding of the ways

in which the system can operate. Systems often require more than one success/failure

definition. These should be defined and listed. An RBD diagram can be made on different

levels: system level, sub-system (module) level or assembly level. When an RBD is made for

further analysis (for example for FMEA analysis), a level suitable for such analysis has to be

chosen.
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SIST EN 61078:2007
61078  IEC:2006 – 19 –
In addition, there should be clear statements concerning
– functions to be performed,
– performance parameters and permissible limits on such parameters,
– environmental and operating conditions.

Various qualitative analysis techniques may be employed in the construction of an RBD.

Therefore the system's success/failure definition has to be established. For each system

success/failure definition the next step is to divide the system into logical blocks appropriate

to the purpose of the reliability analysis. Particular blocks may represent system

substructures, which in turn may be represented by other RBDs (system reduction – see 8.4).

For the quantitative evaluation of an RBD, various methods are available. Depending on the

type of structure, simple Boolean techniques (see 8.1.3) and/or path and cut set analyses

may be employed. For a definition of cut set see IEC 61025 (FTA). Calculations may be made

using basic component reliability/availability methods and analytical methods or Monte Carlo

simulation. An advantage with Monte Carlo simulation is that the events in the RBD do not

have to be combined analytically since the simulation itself takes into account whether each

block is failed or functional (see 8.1).

Since the reliability block diagram describes the logical relations needed for system function,

the block diagram does not necessarily represent the way the hardware is physically

connected, although an RBD generally follows, as far as possible, the physical system

connections.
6.2 Detailed considerations
6.2.1 System operation

It may be possible to use a system in more than one functional mode. If separate systems

were used for each mode, such modes should be treated independently of other modes, and

separate reliability models should be used accordingly. When the same system is used to

perform all these functions, then separate diagrams should be used for each type of

operation. Clear statements of what constitutes system success/failure for each aspect of system

operation, is a prerequisite.
6.2.2 Environmental conditions

The system performance specifications should be accompanied by a description of the

environmental conditions under which the system is designed to operate. Also included

should be a description of all the conditions to which the system will be subjected during

transportation, storage and use.

A particular piece of equipment is often used in more than one environment; for example, on

board ship, in an aircraft or on the ground. When this is so, reliability evaluations may be

carried out using the same reliability block diagram each time but using the appropriate failure

rates for each environment.
6.2.3 Duty cycles

The relationship between calendar time, operating time and on/off cycles should be

established. If it can be assumed that the process of switching equipment on and off does not

in itself promote failures, and that the failure rate of equipment in storage is negligible, then

only the actual working time of the equipment need be considered.
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SIST EN 61078:2007
61078  IEC:2006 – 21 –

However, in some instances, the process of switching on and off is in itself the prime cause of

equipment failure, and equipment may have a higher failure rate in storage than when working

(e.g. moisture and corrosion). In complex cases where only parts of the system are switched on

and off, modelling techniques other than reliability block diagrams (e.g. Markov analysis) may

be more suitable.
7 Elementary models
7.1 Developing the model

The first step is to select a system success/failure definition. If more than one definition is

involved, a separate reliability block diagram may be required for each. The next step is to

divide the system into blocks to reflect the logical behaviour so that each block is statistically

independent of the others, and is as large as possible. At the same time each block should

contain (preferably) no redundancy.

In practice it may be necessary to make repeated attempts at constructing the reliability block

diagram (each time bearing in mind the steps referred to above) before a suitable block

diagram is finalized.

The next step is to refer to the system success/failure definition and construct a diagram that

connects the blocks to form a "success path". As indicated in the diagrams that follow, the

various success paths, between the input and output ports of the diagram, pass through those

combinations of blocks that need to function in order that the system functions. If all the

blocks are required to function for the system to function, then the corresponding reliability

block diagram will be one in which all the blocks are joined in series as illustrated in Figure 1.

A C Z O
IEC 2604/05
Figure 1 – Series reliability block diagram

In this diagram "I" is the input port, "O" the output port and A, B, C, ... Z are the blocks which

together constitute the system. Diagrams of this type are known as "series” reliability block

diagrams or “series models”.

A different type of reliability block diagram is needed when failure of one component or

"block" alone, does not affect system performance as far as the system success/failure

definition is concerned. For example, if in the above instance the entire link is duplicated

(made redundant), then the block diagram is as illustrated by Figure 2. Alternatively, if each

block within the link is duplicated, the block diagram is as illustrated by Figure 3. Diagrams of

this type are known as "parallel” reliability block diagrams or “parallel models”. Note that the

terms “duplicated”, “redundant” and “parallel” are very similar in meaning and are often used

interchangeably.
A1 C1 Z1
A2 B2 C2 Z2
IEC 2605/05
Figure 2 – Duplicated (or parallel) series reliability block diagram
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SIST EN 61078:2007
61078  IEC:2006 – 23 –
A1 C1
B1 Z1
A2 C2
B2 Z2
IEC 2606/05
Figure 3 – Series duplicated (or parallel) reliability block diagram

Reliability block diagrams used for modelling system reliability are often more complicated

mixtures of series and parallel diagrams. Such a diagram would arise if an example were to

be considered consisting of a duplicated communication link comprising three repeaters A, B

and C, and a common pow
...

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