Amendment 1 - Industrial communication networks - Profiles - Part 3: Functional safety fieldbuses - General rules and profile definitions

Amendement 1 - Réseaux de communication industriels - Profils - Partie 3: Bus de terrain de sécurité fonctionnelle - Règles générales et définitions de profils

General Information

Publication Date
Technical Committee
Current Stage
DELPUB - Deleted Publication
Completion Date
Ref Project

Buy Standard

IEC 61784-3:2016/AMD1:2017 - Amendment 1 - Industrial communication networks - Profiles - Part 3: Functional safety fieldbuses - General rules and profile definitions
English and French language
30 pages
sale 15% off
sale 15% off

Standards Content (sample)

IEC 61784-3
Edition 3.0 2017-08
Industrial communication networks – Profiles –
Part 3: Functional safety fieldbuses – General rules and profile definitions
Réseaux de communication industriels – Profils –
Partie 3: Bus de terrain de sécurité fonctionnelle – Règles générales et
définitions de profils
IEC 61784-3:2016-05/AMD1:2017-08(en-fr)
---------------------- Page: 1 ----------------------
Copyright © 2017 IEC, Geneva, Switzerland

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form

or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from

either IEC or IEC's member National Committee in the country of the requester. If you have any questions about IEC

copyright or have an enquiry about obtaining additional rights to this publication, please contact the address below or

your local IEC member National Committee for further information.

Droits de reproduction réservés. Sauf indication contraire, aucune partie de cette publication ne peut être reproduite

ni utilisée sous quelque forme que ce soit et par aucun procédé, électronique ou mécanique, y compris la photocopie

et les microfilms, sans l'accord écrit de l'IEC ou du Comité national de l'IEC du pays du demandeur. Si vous avez des

questions sur le copyright de l'IEC ou si vous désirez obtenir des droits supplémentaires sur cette publication, utilisez

les coordonnées ci-après ou contactez le Comité national de l'IEC de votre pays de résidence.

IEC Central Office Tel.: +41 22 919 02 11
3, rue de Varembé Fax: +41 22 919 03 00
CH-1211 Geneva 20
About the IEC

The International Electrotechnical Commission (IEC) is the leading global organization that prepares and publishes

International Standards for all electrical, electronic and related technologies.
About IEC publications

The technical content of IEC publications is kept under constant review by the IEC. Please make sure that you have the

latest edition, a corrigenda or an amendment might have been published.
IEC Catalogue - Electropedia -

The stand-alone application for consulting the entire The world's leading online dictionary of electronic and

bibliographical information on IEC International Standards, electrical terms containing 20 000 terms and definitions in

Technical Specifications, Technical Reports and other English and French, with equivalent terms in 16 additional

documents. Available for PC, Mac OS, Android Tablets and languages. Also known as the International Electrotechnical

iPad. Vocabulary (IEV) online.

IEC publications search - IEC Glossary -

The advanced search enables to find IEC publications by a 65 000 electrotechnical terminology entries in English and

variety of criteria (reference number, text, technical French extracted from the Terms and Definitions clause of

committee,…). It also gives information on projects, replaced IEC publications issued since 2002. Some entries have been

and withdrawn publications. collected from earlier publications of IEC TC 37, 77, 86 and

IEC Just Published -

Stay up to date on all new IEC publications. Just Published IEC Customer Service Centre -

details all new publications released. Available online and If you wish to give us your feedback on this publication or

also once a month by email. need further assistance, please contact the Customer Service

A propos de l'IEC

La Commission Electrotechnique Internationale (IEC) est la première organisation mondiale qui élabore et publie des

Normes internationales pour tout ce qui a trait à l'électricité, à l'électronique et aux technologies apparentées.

A propos des publications IEC

Le contenu technique des publications IEC est constamment revu. Veuillez vous assurer que vous possédez l’édition la

plus récente, un corrigendum ou amendement peut avoir été publié.
Catalogue IEC - Electropedia -

Application autonome pour consulter tous les renseignements Le premier dictionnaire en ligne de termes électroniques et

bibliographiques sur les Normes internationales, électriques. Il contient 20 000 termes et définitions en anglais

Spécifications techniques, Rapports techniques et autres et en français, ainsi que les termes équivalents dans 16

documents de l'IEC. Disponible pour PC, Mac OS, tablettes langues additionnelles. Egalement appelé Vocabulaire

Android et iPad. Electrotechnique International (IEV) en ligne.

Recherche de publications IEC - Glossaire IEC -

La recherche avancée permet de trouver des publications IEC 65 000 entrées terminologiques électrotechniques, en anglais

en utilisant différents critères (numéro de référence, texte, et en français, extraites des articles Termes et Définitions des

comité d’études,…). Elle donne aussi des informations sur les publications IEC parues depuis 2002. Plus certaines entrées

projets et les publications remplacées ou retirées. antérieures extraites des publications des CE 37, 77, 86 et

IEC Just Published -

Restez informé sur les nouvelles publications IEC. Just Service Clients -

Published détaille les nouvelles publications parues. Si vous désirez nous donner des commentaires sur cette

Disponible en ligne et aussi une fois par mois par email. publication ou si vous avez des questions contactez-nous:
---------------------- Page: 2 ----------------------
IEC 61784-3
Edition 3.0 2017-08
Industrial communication networks – Profiles –
Part 3: Functional safety fieldbuses – General rules and profile definitions
Réseaux de communication industriels – Profils –
Partie 3: Bus de terrain de sécurité fonctionnelle – Règles générales et
définitions de profils
ICS 25.040.40; 35.100.05 ISBN 978-2-8322-4585-9

Warning! Make sure that you obtained this publication from an authorized distributor.

Attention! Veuillez vous assurer que vous avez obtenu cette publication via un distributeur agréé.

® Registered trademark of the International Electrotechnical Commission
Marque déposée de la Commission Electrotechnique Internationale
---------------------- Page: 3 ----------------------
– 2 – IEC 61784-3:2016/AMD1:2017
© IEC 2017

This amendment has been prepared by subcommittee 65C: Industrial networks, of IEC

technical committee 65: Industrial-process measurement, control and automation.
The text of this amendment is based on the following documents:
FDIS Report on voting
65C/879/FDIS 65C/886/RVD

Full information on the voting for the approval of this amendment can be found in the report

on voting indicated in the above table.

The committee has decided that the contents of this amendment and the base publication will

remain unchanged until the stability date indicated on the IEC website under

"" in the data related to the specific publication. At this date, the

publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.

IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates

that it contains colours which are considered to be useful for the correct

understanding of its contents. Users should therefore print this document using a

colour printer.
---------------------- Page: 4 ----------------------
IEC 61784-3:2016/AMD1:2017 – 3 –
© IEC 2017

This Amendment 1 discusses the concepts of implicit data safety mechanisms for use in

functional safety communications protocols (FSCPs) as specified in IEC 61784-3:2016.

3 Terms, definitions, symbols, abbreviated terms and conventions
3.1 Terms and definitions
Add the following new terms and definitions 3.1.56 and 3.1.57:
explicit data
data that is transmitted
implicit data
additional data that is not transmitted but is known to the sender and receiver
[SOURCE: IEC 62280:2014, 3.1.25]
3.2 Symbols and abbreviated terms
Add two new Subclauses 3.2.1 and 3.2.2, as specified below.
3.2.1 Abbreviated terms

Move the existing list of symbols and abbreviated terms to this new Subclause 3.2.1.

Delete “Pe” and “RP” from the existing list of abbreviated terms. Add, in alphabetical order, in

the list of abbreviated terms the following new abbreviated terms:
A-code Authenticity code
T-code Timeliness code
3.2.2 Symbols
Add, in this new Subclause 3.2.2 the following list of symbols:
A Weight distribution of the code: number of valid
codewords having k bits set to “one”
e Bit length of explicit data
err Bitwise disjunction of impl and impl
impl S R
expl Explicit data
expl Explicit data in the receiver
expl Explicit data in the sender
FCS Frame check sequence calculated in the receiver
FCS Frame check sequence received
FCS Frame check sequence sent
i Bit length of implicit data
ID Incorrect delivery
impl Implicit data in the receiver
impl Implicit data in the sender
---------------------- Page: 5 ----------------------
– 4 – IEC 61784-3:2016/AMD1:2017
© IEC 2017
n Bit length of SPDU
P Bit error probability
P Probability of incorrect delivery
r Bit length of FCS (degree of generator polynomial)
RP Residual error probability
Add, after Annex F, the following new informative Annex G:
---------------------- Page: 6 ----------------------
IEC 61784-3:2016/AMD1:2017 – 5 –
© IEC 2017
Annex G
Implicit data safety mechanisms for IEC 61784­3 functional
safety communication profiles (FSCPs)
G.1 Overview

Annex G discusses the concepts of implicit data safety mechanisms for use in functional

safety communications protocols (FSCPs) as specified in this standard. Implicit data is that

which is not explicitly transmitted in a PDU. Instead, the implicit data values are known by

both the sender (source) and the receiver (sink). Implicit data values are validated by the

value of one or more transmitted frame check sequence(s) (FCS) which are calculated using

an overall data string comprised of the implicit data string appended with the explicit data

string. Because the implicit data is not transmitted, the load on the transmission media is


Today, the FSCPs that use implicit data mechanisms do so in order to communicate complete

or partial timeliness codes (T-codes) and/or authenticity codes (A-codes), see Annex E.

These FSCPs also use cyclic redundancy check (CRC) algorithms for the frame check

sequence (FCS) exclusively. Therefore, Annex G is limited to the analysis of implicitly

transmitted T-codes and A-codes using CRC-algorithms.

According to Clause E.8, with regard to implicit data, "Due to the various possible approaches

generic formulae cannot be provided. It is up to the individual FSCP to prove sufficient

residual error probabilities." In the hope of advancing IEC 61784-3 for the next edition and

beyond, the subject of this new Annex G is to improve the understanding of formulating

models for the residual error probabilities of FSCPs using CRC-algorithms to implicitly

transmit T-codes and A-codes when a single FCS code is used by the protocol.

Presented in Annex G are two formulae examples, applicable for two special cases, and from

which a better understanding is promoted for the development of additional (specific and

general) formulae.

Also presented is a summation method generally applicable when conditional weight

distributions for implicit data error patterns are known and can be quantified in a way either

leading to a closed-form solution, or suitable for iterative summation with a reasonably

bounded execution time.
G.2 Basic principles

Calculations in Annex G also use the binary symmetric channel (BSC) model as specified in

Annex B.

NOTE 1 Although it does not take into account burst errors, the BSC model with a sufficiently conservative bit

error probability is so far the most practical known for use in probability calculations needed for the determination

of the FSCP residual error rate.

Figure G.1 shows the basic principle of an FSCP using single FCS protection mechanisms

involving implicit data. In the sender, a CRC-checksum over the implicit data impl

concatenated with the explicit data expl is generated, resulting in a frame check sequence

FCS . When multiple FCS codes are used in an FCSP format, the calculation shall be done

for each FCS code. While expl and FCS are explicitly transmitted over the black channel,


impl is not transmitted, but impacts the value of the FCS . Therefore, it can only contain


data whose value is already known to the receiver. Implicit data is used to detect e.g. SPDUs

which were misdirected in either space (“authentication error”) or time (“timeliness error”).

This is accomplished by deriving the implicit data from the A-code (e.g. connection identifier)

and/or the T-code (e.g. sequence number) of an SPDU.
---------------------- Page: 7 ----------------------
– 6 – IEC 61784-3:2016/AMD1:2017
© IEC 2017
NOTE 2 Initialization details are addressed in F.12.1.
Sender Receiver
calculation calculation
impl expl
impl expl
expl FCS
expl FCS
expl FCS
Black channel
Key Symbols are specified in 3.2.2
Figure G.1 – FSCP with implicit transmission of authenticity
and/or timeliness codes

When the SPDU comprising expl and FCS is delivered to the FSCP-layer in the receiver, it

may contain transmission errors, i.e. the value delivered may differ from the value sent. For

discrimination, the symbols expl and FCS are used in the receiver.

The expected value of the implicit data is called impl . In the error free case, this expectation

is identical to impl . In case of, for example, a misdirected SPDU, impl and impl may differ.


The receiver generates one or more frame check sequence(s) FCS by building a CRC-

checksum over the concatenation of impl and expl . When each FCS is identical to its


corresponding FCS , it is assumed that no error occurred. Otherwise an error has been

The lengths of the bitstrings for a single FCS are defined as follows:
r length of FCS (degree of generator-polynomial);
i length of implicit data (it is assumed that i ≥ r);
e length of explicit data;
n length of SPDU, with n = e + r.
G.3 Problem statement: constant values for implicit data

In FSCPs using implicit data, the CRC-check in the receiver is used for both the detection of

data integrity errors as well as the detection of mis-directed or mis-timed SPDUs. Therefore, it

may happen that the CRC-mechanism becomes “overburdened” by multiple simultaneous

errors, resulting in an increase of the overall residual error probability. This is exemplified in

the following scenario in Figure G.2.
---------------------- Page: 8 ----------------------
IEC 61784-3:2016/AMD1:2017 – 7 –
© IEC 2017
A-code: 0x0001
Authenticity error
S Router
Data corruption
For receiver R1
A-code: 0x1156
Misdirected and corrupted content
Figure G.2 – Example of an incorrect transmission with multiple error causes

The scenario assumes a sender S sending SPDUs to receiver R1 and receiver R2, using a

black channel containing a router. The implicit data used comprises a single field containing

an authenticity-code (A-code) of length 16 bits, identifying the receiver (see Figure E.4). For

each SPDU sent from S to R1, the A-code of R1 is used as implicit data, and similarly the

A-code of R2 for SPDUs sent from S to R2. It is further assumed that the following errors can

occur during the transmission of an SPDU.

a) Authenticity error: Due to a fault within the router, the SPDU is delivered to the incorrect

receiver (receiver R2 instead of receiver R1 or vice versa). Thus, the implicit authenticity

code impl used to calculate the FCS in the sender is unequal to the expected
authenticity code impl in the receiver.

b) Data corruption: Due to for example interference or noise on the transmission media, the

content of the SPDU is corrupted (expl and/or FCS).

It is further assumed that the black channel itself does not detect any of these errors.

Therefore, the errors, and possibly a combination of errors shall be detected by the check

within the safety layer of the receiver. The error pattern err caused by the authenticity


error is defined by the bit-wise exclusive disjunction (XOR) of the A-codes in use. In this case

with only two receivers, this error pattern is constant. The error pattern err is defined as


the bit-wise exclusive disjunction (XOR) of expl and expl . It is modelled by a BSC (see

Annex B).

Figure G.3 shows the residual error probabilities for different parameters when using the

16 14 11 10 9 7 5 3
proper generator polynomial x +x +x +x +x +x +x +x +x+1 (0x14EAB) of degree 16.
---------------------- Page: 9 ----------------------
– 8 – IEC 61784-3:2016/AMD1:2017
© IEC 2017
1 × 10
err = 0x1157,
P = 0,01
1 × 10
1 × 10
1 × 10
1 × 10
1 × 10
err = 0x0003,
1 × 10 err = 0x0000,
P = 1
P = 0
err = 0x1157,
–10 P = 0,001
1 × 10 ID
1 × 10
-7 -6 -5 -4 -3
1 × 10 1 × 10 1 × 10 1 × 10 1 × 10 0,01 0,1 1
Figure G.3 – Impact of errors in implicit data on the residual error probability

Figure G.3 is based on data which was generated by a brute force algorithm checking all

possible error patterns. In addition to the generator polynomial, the following input data was

used in the algorithm:
probability of incorrect delivery (here: addressing error);

err constant error pattern caused by an addressing error (bitwise disjunction of the


It is important to note that the residual error probability does not only depend on p and P ,

but also on the constant err and hence on the values of the A-codes chosen during

= 0 (solid black) proves the properness of the generator polynomial. In this
The curve for P

case of no errors in implicit data, the residual error probability is always below the limit 2

and the curve is monotonically increasing.

The dashed purple curve and the dotted-dashed green curve show the characteristics when

using A-codes resulting in an err of 0x1157 (for example the A-codes 0x0001 and 0x1156).


The residual error probability is no longer monotonically increasing but has a maximum

-16 -3
. For P = 10 , the corresponding curve (dotted-dashed green) does not
greater than 2
-16 -2

pass the limit of 2 . However, if P is set to 10 (dashed purple), the maximum is greater

-16 -r

(worse) than the limit 2 . As a consequence the limit 2 cannot be used as an approximation

even if the generator polynomial has proven properness for the case P = 0.

The green and purple curve is only observed for certain rare values of err . For most other


values of err , the curves are below the limit even for a probability of occurrence P = 1.

impl ID
= 0x0003 (e.g. A-codes equal to 0x0001 and 0x0002)
As an example, the curve for err
shows this characteristics (solid blue).
---------------------- Page: 10 ----------------------
IEC 61784-3:2016/AMD1:2017 – 9 –
© IEC 2017

Conclusion: When using implicit transmission mechanisms, the residual error probability is not

necessarily bounded by 2 . This bound is only valid if the FSCP provides additional

mechanisms such as the ones shown in the following clauses.

NOTE Improper bounding of an FCS would not necessarily lead to insufficient residual error when other FSCP

specific protocol measures are combined in the error detection scheme.
G.4 RP for FSCPs with random, uniformly distributed err
G.4.1 General

Clause G.4 investigates the case of a random err taking each possible value with equal


probability (“uniform distribution”). As seen in Clause G.3 where err is constant, this


assumption is not always justified and shall be provably guaranteed by the design of the

respective FSCP.

As already defined earlier, err is the bitwise exclusive disjunction (XOR) between the


implicit data impl used in the sender of the erroneous packet, and the expected value for the

implicit data impl in the receiver. Clearly, if impl and impl are uniformly distributed,


independent random variables, also err is uniformly distributed, i.e. takes each possible


value with equal possibility. However, because errors can be assumed to happen at ‘random’

points of time, it is also possible to achieve a uniformly distributed err if impl and impl

impl S R

are non-random variables. In order to validate whether err follows a uniform distribution,


statistical checks such as the Chi-Square-Test or the Kolmogoroff-Smirnoff-Test can be used,

(see for example [35]).

NOTE 1 err being a uniformly distributed random variable, it does not require that all possible values are


observed with equal frequency during a finite interval of time. It is therefore not always possible to evaluate a

random number generator by simply counting the number of occurrences within a limited time interval.

Depending on the design of the FSCP, there are two reasonable variants of the assumption

“err is uniformly distributed”:
i -i
a) err takes each value out of [0;2 -1] with probability 2 ;
i i
b) err takes each value out of [1;2 -1] with probability 1/(2 -1).

NOTE 2 There is a slight difference in the two variants: in the second variant, a value of err = 0 means that


the SPDU was delivered correctly, as an incorrectly delivered SPDU will always result in a value err ≠ 0. In the

first variant, a value of err = 0 does not necessarily imply a correct delivery.

In the second case, measures shall be implemented to ensure that each SPDU is assigned a

unique value for implicit data. Hence, the error pattern in case of a misdirected SPDU can

never become zero. In the first case, no such measures are implemented and hence the error

pattern ‘zero’ may occur. Clearly, such an error cannot be detected in the receiver unless

there are additional detectable data integrity errors or other FSCP specific checks.

In the following, the two variants are shown separately.

Other and perhaps more detailed models are beyond the scope of this document. For

example, it is possible to eliminate data error patterns with demonstrated certainty of

detection by the CRC polynomial.

EXAMPLE Examples of these data error patterns include: Hamming distances less than the minimum Hamming

distance for the CRC polynomial over the data block length; burst errors of length r; odd number of bit errors; and


Subclause G.4.2 shows an example where the implicit data field is at least as long as the FCS

and the implicit data values are randomly generated in such a way that A-codes are not

guaranteed unique for each endpoint, T-codes are not guaranteed unique for each SPDU

time, and the combinations of A-code and T-code are not guaranteed unique.
---------------------- Page: 11 ----------------------
– 10 – IEC 61784-3:2016/AMD1:2017
© IEC 2017

Subclause G.4.3 shows an example where the implicit data field is exactly as long as the FCS

and A-codes and T-codes are guaranteed unique for each endpoint and SPDU time. In actual

application, additional terms may be necessary to account for exceptions such as T-code

wrap around.

Clause G.5 shows a summation method for general applicability when conditional weight

distributions for implicit data error patterns are known and can be quantified.
G.4.2 Uniform distribution within the interval [0;2 ­1], i ≥ r

This case applies in particular to FSCPs that use random number generators to derive implicit

data values.
At a coarse-grained level, two main types of errors can be discriminated:
• Incorrect content of an SPDU, i. e. data integrity errors;

• Incorrect delivery of an SPDU, i.e. the SPDU is delivered to the wrong receiver or at the

wrong instance of time.
In combination, the following disjoint cases can be discriminated:
• Case 1. CC: No error (correct delivery, and correct explicit data);
• Case 2. IC: Incorrect delivery, and correct explicit data;
• Case 3. CI: Correct delivery, and incorrect explicit data;
• Case 4. II: Incorrect delivery, and incorrect data.

The residual error probabilities RP , RP , and RP for each of the cases 2, 3, and 4 are

2 3 4
calculated from the following parameters:

P is the “probability of incorrect delivery”, i.e. the probability that due to for example an

authenticity or timeliness error an SPDU is erroneously delivered to the FSCP;

NOTE 1 The event “incorrect delivery” can result in an err ≠ 0. However, due to the uniform

distribution within [0;2 -1] the case err = 0 can also occur.

P is the probability of incorrect explicit data, i.e. the probability that data corruption


P is the probability that an error is not detected in the receiver under the condition that

case 2 occurs;

P is the probability that an error is not detected in the receiver under the condition that

case 3 occurs;

P is the probability that an error is not detected in the receiver under the condition that

case 4 occurs;
RP is the residual error probability for data corruption as defined in Annex F.

R is the residual error probability for CRC polynomials as defined in Equation B.3.


NOTE 2 RP ≤ R because other safety measures than CRC can further reduce the value of RP .

r is the length of the FCS, identical to the degree of the CRC polynomial;
i is the length of the implicit data, with i ≥ r;
n is the number of bits of the SPDU.

Because the events IC, CI, and II are disjoint, the overall residual error probability can be

obtained by building the sum of the respective RP values.
In general, RP is calculated by:
RP = P(“error case x takes place”) × P(“error case x is not detectable”).
---------------------- Page: 12 ----------------------
IEC 61784-3:2016/AMD1:2017 – 11 –
© IEC 2017

This leads to the formulae for cases 2, 3 and 4 detailed in the following paragraphs.

Case 2 (IC)
RP = P × (1 – P ) × P
= P × (1 – P ) × 2
Explanations on P :
• If i > r, this probability is 2 , because

– by assumption, the bitwise disjunction of impl and impl is uniformly distributed in the

interval [0;2 -1];

– therefore, the bitwise disjunction of FCS = FCS and FCS is uniformly distributed in

the interval [0;2 -1];
and FCS equals zero is
– therefore, the probability that the bitwise disjunction of FCS
2 ;
– therefore, the probability that FCS is equal to FCS is 2 .
• If i = r, this probability is 2 , because

– FCS is equal to FCS , if and only if err = 0, because the length of err does not

R C impl impl

exceed the degree of the CRC polynomial. CRC-codes detect all burst errors of length

less than or equal to r;

– the probability that err = 0 is 2 because of the uniform distribution in the interval

[0;2 -1].
Case 3 (CI)
RP = (1-P ) × P × P
= (1-P ) × RP
≤ (1-P ) × 2 for proper polynomials.
Case 4 (II)
RP = P × P × P
= P × P × 2

• Due to the assumptions, err takes all values from [0;2 -1] with equal probability.

• Hence, each bit of err takes the value 0 or 1 with equal probability 0,5.
• Because CRC-codes are linear codes, and because |err | ≥ r, each bit of err
impl impl

determines the result of one bit in the bitwise exclusive disjunction of FCS and FCS .


• Hence, the bits in the bitwise exclusive disjunction of FCS and FCS can be treated as


independent random variables, each taking the values 0 and 1 with equal probability 0,5.

• The bitwise exclusive disjunction of FCS and FCS is a uniformly distributed random

R c
variable, taking all values from [0;2 -1] with equal probability.

• The probability that the bitwise exclusive disjunction of FCS and FCS equals zero is 2 .

• The probability that FCS is identical to FCS is 2 .

In summary, the residual error probability of an FSCP using implicit mechanisms for the

detection of timeliness and authenticity error (guaranteeing that the error in the implicit data is

-1] can be calculated using the following formula:
uniformly distributed in the interval [0;2
---------------------- Page: 13 ----------------------
– 12 – IEC 61784-3:2016/AMD1:2017
© IEC 2017
RP = RP2 + RP3 + RP4
-r -r
= (P × (1 – P ) × 2 ) + ((1-P ) × P × P ) + (P × P × 2 )
= (P × 2 ) + ((1-P ) × P × P )
= (P × 2 ) + ((1-P ) × RP )
• Cases 2 to 4 are disjoint events.
In case of a proper polynomial, the following applies:
RP = RP2 + RP3 + RP4
-r -r
= (P × (1 – P ) × 2 ) + ((1-P ) × P × P ) + (P × P × 2 )
-r -r -r
≤ (P × (1 – P ) × 2 ) + ((1-P ) × 2 ) + (P × P × 2 )

Questions, Comments and Discussion

Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.