SIST EN ISO 13843:2017

Water quality - Requirements for establishing performance characteristics of quantitative microbiological methods (ISO 13843:2017)

This document deals with characterization of microbiological methods. In terms of this document,
characterization means the study of parameters that can be measured to describe how the method is
likely to perform in a given set of conditions, which can be described as performance characteristics.
The document describes procedures for the determination of performance characteristics which can be
used for subsequent validation or verification of methods.
The emphasis is on selective quantitative methods and this document applies to all types of water. For
methods that are not based upon direct microscopic count, colony count or most probable number, the
applicability of the procedures described in this document should be considered carefully.

Wasserbeschaffenheit - Anforderungen zur Bestimmung von Leistungsmerkmalen von quantitativen mikrobiologischen Verfahren (ISO 13843:2017)

Diese Internationale Norm behandelt die Charakterisierung der biologischen Methoden. Im Rahmen dieses Dokuments bezeichnet die Charakterisierung die Parameteruntersuchung für eine Verfahrensbeschreibung zur Durchführung unter vorgegebenen Bedingungen, die als Leistungsmerkmale beschrieben werden können. Die Norm beschreibt Verfahrensabläufe für die Bestimmung der Leistungsmerkmale, die für eine anschließende Validierung oder Verifizierung der Verfahren verwendet werden können.
Die Betonung liegt auf den selektiven quantitativen Methoden und die Norm gilt für alle Wasserarten.
Verfahren, die als mikrobiologisch betrachtet werden, bei denen der quantitative Schätzwert auf der Auszählung von Partikeln beruht, entweder direkt mit Hilfe eines Mikroskops oder indirekt durch Wachstum (Vermehrung) in Kolonien oder Trübung. Die Grundlagen und Verfahrensabläufe in diesem Anwendungsbereich sind allgemein bekannt als direkte (mikroskopisch) Zählung, die wahrscheinlichste Zahl (MPN) und die Koloniezählung. Die meisten Verfahrensabläufe für die Bestimmung der Leistungsmerkmale, die in diesem Dokument beschrieben werden, gelten für alle drei Typen dieses Verfahrens. Wenn diese Verfahrensabläufe jedoch nicht anwendbar sind, werden alternative Vorschläge innerhalb dieses Dokuments oder in den Anhängen D und E gemacht (in Bezug auf Wiederhol- und Vergleichspräzision und Zählunsicherheit).
Plaques von Bakteriophagen ähneln in überwiegender Hinsicht den bakteriellen Koloniezahlen.
Einige der „neueren“ mikrobiologischen Verfahren, bei denen man sich der Fluoreszenz-in-situ-Hybridisierung (FISH) oder Polymerase-Kettenreaktion (PCR) bedient, können durch dieses Dokument ebenso abgedeckt werden, erfordern jedoch eine besondere Berücksichtigung, abhängig von ihrer Anwendungsweise. Wichtige Themen in diesen Situationen umfassen den Mechanismus der Bestimmung der Anzahl der vorhandenen Mikroben (z. B. Normkurve für qPCR oder mikroskopisches Auszählen für FISH) und die Lebensfähigkeit der erkannten Organismen. Wenn solche Techniken für eine Bestätigung als ein Teil des Verfahrens verwendet werden, sind alle Abschnitte dieses Dokuments relevant. Für Verfahren, die eine Erkennung der Zellkomponenten oder ihrer Stoffwechselprodukte umfassen, sollte die Anwendbarkeit dieses Dokuments aufgrund einer Einzelfallbetrachtung beurteilt werden.
Sollte es für die Charakterisierung der mikrobiologischen Verfahren nicht wesentlich sein, ist es vorteilhaft, Daten mit Organismen unter Stress zu erzeugen. Verschiedene Verfahren können angewandt werden, um die Organismen in Stress zu versetzen, die zwei nützlichsten für Wasser jedoch sind Stress durch Desinfektionsmittel (normalerweise Schädigung durch Chlor) und Nährstoffauszehrung, die durch Organismen verursacht wird, die vor der Prüfung eine Zeit lang in einer Umgebung mit niedrigem Nährstoffgehalt (d. h. Trinkwasser und andere oligotrophe Wasserarten) gelebt haben. Die Wirkung auf einige der Leistungsmerkmale bei „Strapazierung“ der Organismen hängt fast völlig von der Art und dem Grad der Strapazierung ab, daher ist die Aufnahme solcher Details in diese Norm unangemessen. Es gibt jedoch Beschreibungen in der Literatur, die Laboratorien befolgen können, im Falle, dass sie die Leistungsmerkmale eines Verfahrens mit strapazierten Zellen bestimmen möchten [17].

Qualité de l'eau - Exigences pour l'établissement des caractéristiques de performance des méthodes microbiologiques quantitatives (ISO 13843:2017)

L'ISO 13843:2017 traite de la caractérisation des méthodes microbiologiques. Au sens de l'ISO 13843:2017, la caractérisation signifie l'étude de paramètres mesurables dans le but de décrire la manière dont les méthodes sont susceptibles d'être appliquées dans un ensemble donné de conditions, qui peuvent être décrits comme des caractéristiques de performance. L'ISO 13843:2017 décrit les modes opératoires pour la détermination des caractéristiques de performance qui peuvent être utilisées pour la validation ou la vérification ultérieure de méthodes.
L'accent est mis sur les méthodes quantitatives sélectives et l'ISO 13843:2017 s'applique à tous les types d'eau. Pour les méthodes qui ne reposent pas sur un comptage microscopique direct, un comptage des colonies ou le nombre le plus probable, il convient de vérifier de manière approfondie l'applicabilité des modes opératoires décrits dans l'ISO 13843:2017.

Kakovost vode - Zahteve za določitev delovnih karakteristik kvantitativnih mikrobioloških metod (ISO 13843:2017)

Ta dokument obravnava karakterizacijo mikrobioloških metod. V smislu tega dokumenta
karakterizacija pomeni preučevanje parametrov, ki jih je mogoče meriti in opisujejo način delovanja metode v danih pogojih, kar je mogoče opisati kot delovne karakteristike.
Ta dokument opisuje postopke za določitev delovnih karakteristik, ki se lahko uporabijo pri nadaljnjem vrednotenju ali preverjanju metod.
Poudarek je na selektivnih kvantitativnih metodah, ta dokument pa se uporablja za vse vrste vod. Pri metodah, ki ne temeljijo na neposrednem štetju pod mikroskopom, štetju kolonij ali najbolj verjetni številki, je treba uporabnost postopka, opisanega v tem dokumentu, skrbno preučiti.

General Information

• Status: Published
• Public Enquiry End Date: 04-Jun-2016
• Publication Date: 19-Nov-2017
• ICS: 07.100.20 - Microbiology of water
• Technical Committee: KAV - Water quality
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 20-Oct-2017
• Due Date: 25-Dec-2017
• Completion Date: 20-Nov-2017
• Directive: 98/83/EC - Quality of water intended for human consumption
• Ref Project: EN ISO 13843:2017 - Water quality - Requirements for establishing performance characteristics of quantitative microbiological methods (ISO 13843:2017)

Relations

• Replaces: SIST-TS ENV ISO 13843:2004 - Water quality - Guidance on validation of microbiological methods (ISO/TR 13843:2000)
• Effective Date: 01-Dec-2017

Standards Content (Sample)

SLOVENSKI STANDARD
SIST EN ISO 13843:2017
01-december-2017
1DGRPHãþD
SIST-TS ENV ISO 13843:2004
.DNRYRVWYRGH=DKWHYH]DGRORþLWHYGHORYQLKNDUDNWHULVWLNNYDQWLWDWLYQLK
PLNURELRORãNLKPHWRG,62
Water quality - Requirements for establishing performance characteristics of quantitative
microbiological methods (ISO 13843:2017)
Wasserbeschaffenheit - Anforderungen zur Bestimmung von Leistungsmerkmalen von
quantitativen mikrobiologischen Verfahren (ISO 13843:2017)
Qualité de l'eau - Exigences pour l'établissement des caractéristiques de performance
des méthodes microbiologiques quantitatives (ISO 13843:2017)
Ta slovenski standard je istoveten z: EN ISO 13843:2017
ICS:
07.100.20 Mikrobiologija vode Microbiology of water
SIST EN ISO 13843:2017 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 13843:2017

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SIST EN ISO 13843:2017


EN ISO 13843
EUROPEAN STANDARD

NORME EUROPÉENNE

July 2017
EUROPÄISCHE NORM
ICS 07.100.20 Supersedes ENV ISO 13843:2001
English Version

Water quality - Requirements for establishing
performance characteristics of quantitative
microbiological methods (ISO 13843:2017)
Qualité de l'eau - Exigences pour l'établissement des Wasserbeschaffenheit - Anforderungen zur
caractéristiqes de performance des méthodes Bestimmung von Leistungsmerkmalen von
microbiologiques quantitatives (ISO 13843:2017) quantitativen mikrobiologischen Verfahren (ISO
13843:2017)
This European Standard was approved by CEN on 5 June 2017.

CEN 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 CEN-CENELEC Management Centre or to any CEN
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 CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and United Kingdom.





EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2017 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 13843:2017 E
worldwide for CEN national Members.

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SIST EN ISO 13843:2017
EN ISO 13843:2017 (E)
Contents Page
European foreword . 3

2

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SIST EN ISO 13843:2017
EN ISO 13843:2017 (E)
European foreword
This document (EN ISO 13843:2017) has been prepared by Technical Committee ISO/TC 147 "Water
quality" in collaboration with Technical Committee CEN/TC 230 “Water analysis” the secretariat of
which is held by DIN.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by January 2018 and conflicting national standards shall
be withdrawn at the latest by January 2018.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes ENV ISO 13843:2001.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
Endorsement notice
The text of ISO 13843:2017 has been approved by CEN as EN ISO 13843:2017 without any modification.
3

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SIST EN ISO 13843:2017

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SIST EN ISO 13843:2017
INTERNATIONAL ISO
STANDARD 13843
First edition
2017-06
Water quality — Requirements
for establishing performance
characteristics of quantitative
microbiological methods
Qualité de l’eau — Exigences pour l’établissement des caractéristiqes
de performance des méthodes microbiologiques quantitatives
Reference number
ISO 13843:2017(E)
©
ISO 2017

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SIST EN ISO 13843:2017
ISO 13843:2017(E)

COPYRIGHT PROTECTED DOCUMENT
© ISO 2017, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. [phone]
Fax [phone]
[e-mail]
www.iso.org
ii © ISO 2017 – All rights reserved

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SIST EN ISO 13843:2017
ISO 13843:2017(E)

Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Basic concepts . 6
4.1 General . 6
4.2 Characterization . 7
4.3 Verification . 8
4.4 Method comparison . 8
4.5 Samples . 9
5 Specifications: some guideline values . 9
6 Designs for determining performance characteristics of a method .10
6.1 General considerations .10
6.2 Determination of sensitivity, specificity, efficiency, selectivity, false positive rate
and false negative rate .10
6.2.1 Type of samples to be used .10
6.2.2 Number of samples .11
6.2.3 Procedure .11
6.2.4 Categorical performance characteristics .11
6.2.5 Worked example . . .12
6.3 Determination of the upper limit and consideration of the lower limit of detection .14
6.3.1 Working range .14
6.3.2 Upper limit related to linearity.14
6.3.3 Type and number of samples to be used .14
6.3.4 Worked example . . .15
6.3.5 The lower limit of detection .16
6.4 Assessment of precision: Determination of repeatability and reproducibility .16
6.4.1 General.16
6.4.2 Repeatability .17
6.4.3 Intralaboratory reproducibility .18
6.5 Robustness .20
6.5.1 General.20
6.5.2 Experimental designs for effects due to time and temperature .20
6.6 Relative recovery .21
6.6.1 General.21
6.6.2 Determination of relative recovery .21
6.7 Uncertainty of counting .22
6.7.1 General.22
6.7.2 Experimental design for assessing the uncertainty of counting colonies .22
6.7.3 Example of individual (or personal) uncertainty of counting colonies .22
6.7.4 Example of intralaboratory uncertainty of counting colonies .23
6.7.5 Example of intralaboratory uncertainty of reading MPN .23
7 Designs for single laboratory verification of a method .24
7.1 General considerations .24
7.2 Calculation of sensitivity, specificity, efficiency, selectivity, false positive rate and
false negative rate .24
7.2.1 Type of sample to be used .24
7.2.2 Number of samples .25
7.2.3 Procedure for confirmation .25
7.2.4 Categorical performance characteristics .25
7.3 Determination of repeatability .26
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SIST EN ISO 13843:2017
ISO 13843:2017(E)

7.4 Uncertainty of counting .26
7.5 Procedure for single laboratory verification .26
Annex A (informative) Mathematical models of variation.30
Annex B (normative) Assessment of the lower limits .40
Annex C (normative) Assessment of the upper limit .43
Annex D (normative) Determination of the operational variability in repeatability and
intralaboratory reproducibility conditions .44
Annex E (normative) Uncertainty of counting .48
Annex F (normative) Determination of the operational variability (interlaboratory
reproducibility) in a collaborative performance study .50
Annex G (informative) Glossary of principal symbols .58
Bibliography .60
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SIST EN ISO 13843:2017
ISO 13843:2017(E)

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO’s adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following
URL: w w w . i s o .org/ iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 147, Water quality, Subcommittee SC 4,
Microbiological methods.
This first edition of ISO 13843 cancels and replaces ISO/TR 13843:2000, which has been technically
revised.
© ISO 2017 – All rights reserved v

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SIST EN ISO 13843:2017
ISO 13843:2017(E)

Introduction
Methods are considered microbiological when the quantitative estimate is based on counting of
microbial particles either directly with the aid of a microscope or indirectly on the basis of growth
(multiplication) into colonies, turbidity, a colour change or fluorescence. The principles and procedures
within the scope of this document are commonly known as microscopic count, most probable number
(MPN) and colony count. Most of the procedures for the determination of performance characteristics
described in this document are applicable to all three types of method. However, where the procedures
are not applicable, alternative suggestions are made within the body of the document or in Annexes D
and E (for repeatability, reproducibility and uncertainty of counting).
Plaque counts of bacteriophages are in most respects similar to bacterial colony counts.
Some of the ”newer” microbiological methods such as those utilizing fluorescent in situ hybridization
(FISH) or polymerase chain reaction (PCR) can also be covered by this document. However, they may
require special consideration, depending upon how they are used. The issues of importance in these
situations include the mechanism of determining the numbers of microbes present (e.g. standard curve
for qPCR or microscopic count for FISH) and the viability of the organisms detected. If such techniques
are used for confirmation as part of a method then all sections of this document are relevant.
While not essential, during the characterization of microbiological methods it may be beneficial
to generate data using stressed organisms. Various methods can be used to stress organisms, but
the two that are most useful for water are disinfectant stress (usually chlorine injury) and nutrient
depletion caused by organisms being in a low nutrient environment (i.e. drinking water and other
oligotrophic waters) for a period prior to testing. The effect on some of the performance characteristics
of “stressing” organisms is almost totally dependent on the type and degree of stress applied and it is
inappropriate to include such detail in this document. However, there are descriptions in the literature
that laboratories can follow in case they should wish to determine performance characteristics of a
method with stressed cells.
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SIST EN ISO 13843:2017
INTERNATIONAL STANDARD ISO 13843:2017(E)
Water quality — Requirements for establishing
performance characteristics of quantitative
microbiological methods
1 Scope
This document deals with characterization of microbiological methods. In terms of this document,
characterization means the study of parameters that can be measured to describe how the method is
likely to perform in a given set of conditions, which can be described as performance characteristics.
The document describes procedures for the determination of performance characteristics which can be
used for subsequent validation or verification of methods.
The emphasis is on selective quantitative methods and this document applies to all types of water. For
methods that are not based upon direct microscopic count, colony count or most probable number, the
applicability of the procedures described in this document should be considered carefully.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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.
ISO 17994:2014, Water quality — Requirements for the comparison of the relative recovery of
microorganisms by two quantitative methods
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http:// www .electropedia .org/
— ISO Online browsing platform: available at http:// www .iso .org ./ obp
3.1
accuracy
measurement accuracy
closeness of agreement between a measured quantity value and an assigned quantity value of a
measurand
Note 1 to entry: The concept ‘measurement accuracy’ is not a quantity and is not given a numerical quantity
value. A measurement is said to be more accurate when it offers a smaller measurement error.
Note 2 to entry: ‘Measurement accuracy’ is sometimes understood as closeness of agreement between measured
quantity values that are being attributed to the measurand.
[16]
[SOURCE: ISO/IEC Guide 99:2007, 2.13 , modified — “…a true quantity value” replaced by “… an
assigned quantity value; Notes 1 and 2 to entry added]
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SIST EN ISO 13843:2017
ISO 13843:2017(E)

3.2
analyte
component represented in the name of a measurable quantity
Note 1 to entry: In water microbiology, the analyte is ideally defined as a list of taxonomically defined species.
In most cases, in practice the analyte can only be defined by group designations less accurate than taxonomic
definitions.
[14]
[SOURCE: ISO 17511:2003, 3.2 ]
3.3
analytical portion
test portion
volume of particle suspension (sample) inoculated into a detector unit (agar plate, membrane filter, test
tube, microscopic grid square)
3.4
bias
measurement bias
estimate of a systematic measurement error, or the systematic difference between the quantitative
assigned value and the average of measurement replicate results
3.5
categorical characteristics
method performance characteristic numerically expressed as a relative frequency based on P/A or
+/‑ classification
3.6
colony-forming unit
CFU
colony‑forming particle
CFP
organism (or cluster of organisms) with the ability to form a colony under certain specified conditions
Note 1 to entry: The term was originally introduced to convey the idea that a colony may originate not only from
a single cell but from a solid chain or aggregate of cells, a cluster of spores, a piece of mycelium, etc. It mistakenly
equates the number of colonies observed to the number of living entities seeded on the medium. Growth unit,
viable particle, propagule and germ are terms with the same meaning but convey the original idea better and
apply not only to colony count methods but also to the most probable number (MPN).
3.7
collaborative method performance
method or laboratory performance test where several laboratories join in an experiment planned and
co‑ordinated by a leader laboratory
Note 1 to entry: Collaborative tests are mainly of two types. Intercalibration exercises are made to allow
laboratories to compare their analytical results with those of other participating laboratories.
Note 2 to entry: Method performance tests produce precision estimates (repeatability, reproducibility) out of data
accumulated when several participating laboratories study identical samples with a strictly standardized method.
3.8
confirmed colony count
verified colony count
presumptive colony count corrected for false positives
Note 1 to entry: Mathematically:
k
pc= c
n
where
2 © ISO 2017 – All rights reserved

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SIST EN ISO 13843:2017
ISO 13843:2017(E)

c is the presumptive count;
p is the true positive rate;
n is the number of presumptive positives isolated for confirmation;
k is the number confirmed.
3.9
corroborated count
count obtained when using a secondary confirmation procedure
3.10
detection level
minimum concentration of organisms that produce evidence of growth with a probability of P = 0,95
when inoculated into a specified culture medium and incubated under defined conditions
Note 1 to entry: The theoretical level that conforms to this definition is an average of three viable cells in an
inoculum volume.
3.11
detection set
combination of plates or tubes on which quantitative estimation of sample microbial concentration
is based
Note 1 to entry: The detection set is the set of plates or tubes utilized for numerical estimation of a single value.
EXAMPLE Parallel plates of a suspension, plates from consecutive dilutions, 3 × 5 tube MPN system,
microtitre plate.
3.12
detector
particle detector
plate of solid matrix or a tube of liquid containing a nutrient medium for counting or detecting
biologically active particles
3.13
efficiency
E
fraction of colonies that are correctly assigned as positives and negatives
Note 1 to entry: Mathematically:
ad+
E =
n
where
a is the number of typical colonies confirmed as being the target organism (true positives);
d is the number of atypical colonies confirmed as not being the target organism (true negatives);
n is the total number of colonies tested for confirmation.
3.14
false negative
result indicated by the test method to be negative which has subsequently been shown to contain the
target organism
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ISO 13843:2017(E)

3.15
false positive
result indicated by the test method to be positive which was subsequently shown not to contain the
target organism
3.16
germ
entity capable of biological activity (e.g. respiration or reproduction in a nutrient medium)
3.17
limit of determination
lowest analyte concentration per analytical portion where the expected relative standard uncertainty,
equals a specified value
3.18
method-defined count
count obtained by using only the procedures in the described method
3.19
negative binomial distribution
particular “overdispersed” statistical distribution of counts
2 22
Note 1 to entry: Its variance can be expressed as sx=+ux ()x =mean .
0
Note 2 to entry: In this document, the square of the relative operational standard deviation (u ) is substituted for
0
the inverse of the exponent (1/k) of the standard equation for the negative binomial distribution.
3.20
outlier
member of a set of values which is inconsistent with other members of that set
Note 1 to entry: An extre
...