CEN/TR 13205-3:2014

Workplace exposure - Assessment of sampler performance for measurement of airborne particle concentrations - Part 3: Analysis of sampling efficiency data

This Technical Report specifies evaluation methods for analysing the data obtained from a type A test of aerosol samplers under prescribed laboratory conditions as specified in prEN 13205-2:2012.
The methods can be applied to all samplers used for the health-related sampling of particles in workplace air.

Exposition am Arbeitsplatz - Beurteilung der Leistungsfähigkeit von Sammlern für die Messung der Konzentration luftgetragener Partikel - Teil 3: Analyse der Daten zum Probenahmewirkungsgrad

Exposition sur les lieux de travail - Évaluation des performances des instruments de mesurage des concentrations d'aérosols - Partie 3: Analyse des données d'efficacité de prélèvement

Le présent rapport technique spécifie des méthodes d'évaluation pour l'analyse des données obtenues à partir d'un essai type A pour des dispositifs de prélèvement d'aérosols dans des conditions de laboratoire prescrites, telles que spécifiées dans la prEN 13205-2:2012.
Ces méthodes peuvent être appliquées à tous les dispositifs de prélèvement utilisés pour le prélèvement, à des fins sanitaires, des particules présentes sur les lieux de travail.

Izpostavljenost na delovnem mestu - Ocenjevanje lastnosti merilnikov za merjenje koncentracij lebdečih delcev - 3. del: Analiza podatkov o učinkovitosti vzorčenja

CEN/TR 13205-3 določa metode ocenjevanja za analizo podatkov, pridobljenih pri preskusu tipa A za merilnike aerosolov pod laboratorijskimi pogoji, določenimi v standardu EN 13205-2. Metode veljajo za vse merilnike, ki se uporabljajo za vzorčenje delcev v zraku, ki vplivajo na zdravje na delovnem mestu.

General Information

• Status: Published
• Publication Date: 24-Jun-2014
• ICS: 13.040.30 - Workplace atmospheres
• Technical Committee: CEN/TC 137 - Assessment of workplace exposure
• Drafting Committee: CEN/TC 137/WG 3 - Particulate matter
• Current Stage: 6060 - Definitive text made available (DAV) - Publishing
• Start Date: 25-Jun-2014
• Due Date: 06-Apr-2013
• Completion Date: 25-Jun-2014
• Ref Project: SIST-TP CEN/TR 13205-3:2014 - Workplace exposure - Assessment of sampler performance for measurement of airborne particle concentrations - Part 3: Analysis of sampling efficiency data

Relations

• Replaces: EN 13205:2001 - Workplace atmospheres - Assessment of performance of instruments for measurement of airborne particle concentrations
• Effective Date: 08-Jun-2022
• Splited From: prEN 13205 - Workplace exposure - Assessment of sampler performance for measurement of airborne particle concentrations
• Effective Date: 07-Mar-2023
• Parent: prEN 13205 - Workplace exposure - Assessment of sampler performance for measurement of airborne particle concentrations
• Effective Date: 29-Jun-2011

Standards Content (Sample)

SLOVENSKI STANDARD
01-september-2014
1DGRPHãþD
SIST EN 13205:2002
,]SRVWDYOMHQRVWQDGHORYQHPPHVWX2FHQMHYDQMHODVWQRVWLPHULOQLNRY]DPHUMHQMH
NRQFHQWUDFLMOHEGHþLKGHOFHYGHO$QDOL]DSRGDWNRYRXþLQNRYLWRVWLY]RUþHQMD
Workplace exposure - Assessment of sampler performance for measurement of airborne
particle concentrations - Part 3: Analysis of sampling efficiency data
Exposition am Arbeitsplatz - Bewertung der Leistungsfähigkeit von Sammlern für die
Messung der Konzentration luftgetragener Partikel - Teil 3: Analyse der Daten zum
Probenahmewirkungsgrad
Exposition sur les lieux de travail - Évaluation des performances des instruments de
mesurage des concentrations d'aérosols - Partie 3: Analyse des données d'efficacité de
prélèvement
Ta slovenski standard je istoveten z: CEN/TR 13205-3:2014
ICS:
13.040.30 Kakovost zraka na delovnem Workplace atmospheres
mestu
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

TECHNICAL REPORT
CEN/TR 13205-3
RAPPORT TECHNIQUE
TECHNISCHER BERICHT
June 2014
ICS 13.040.30 Supersedes EN 13205:2001
English Version
Workplace exposure - Assessment of sampler performance for
measurement of airborne particle concentrations - Part 3:
Analysis of sampling efficiency data
Exposition sur les lieux de travail - Évaluation des Exposition am Arbeitsplatz - Beurteilung der
performances des instruments de mesurage des Leistungsfähigkeit von Sammlern für die Messung der
concentrations d'aérosols - Partie 3: Analyse des données Konzentration luftgetragener Partikel - Teil 3: Analyse der
d'efficacité de prélèvement Daten zum Probenahmewirkungsgrad

This Technical Report was approved by CEN on 14 January 2013. It has been drawn up by the Technical Committee CEN/TC 137.

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, 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
© 2014 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TR 13205-3:2014 E
worldwide for CEN national Members.

Contents Page
Foreword . 3
Introduction . 4
1 Scope . 5
2 Normative references . 5
3 Terms and definitions . 5
4 Symbols and abbreviations . 5
4.1 Symbols . 5
4.1.1 Latin . 5
4.1.2 Greek . 10
4.2 Enumerating subscripts . 11
4.3 Abbreviations . 12
5 Analysis of sampling efficiency data from a performance test according EN 13205-2. 12
5.1 General . 12
5.2 Presumption of exactly balanced data . 13
5.3 Examples of balanced experimental designs . 13
5.4 Analysis of efficiency data based on monodisperse test aerosols using the polygonal
approximation method . 14
5.4.1 Statistical model for the efficiency values . 14
5.4.2 Estimation of mean sampled concentration . 15
5.4.3 Estimation of uncertainty (of measurement) components . 17
5.5 Analysis of efficiency data based on monodisperse or polydisperse test aerosols using
the curve-fitting method . 27
5.5.1 Statistical model of the sampling efficiency data . 27
5.5.2 Estimation of mean sampled concentration . 28
5.5.3 Estimation of uncertainty (of measurement) components . 30
Bibliography . 46

Foreword
This document (CEN/TR 13205-3:2014) has been prepared by Technical Committee CEN/TC 137
“Assessment of workplace exposure to chemical and biological agents”, the secretariat of which is held by
DIN.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
This document together with EN 13205-1, EN 13205-2, EN 13205-4, EN 13205-5 and EN 13205-6
supersedes EN 13205:2001.
EN 13205, Workplace exposure — Assessment of sampler performance for measurement of airborne particle
concentrations, consists of the following parts:
— Part 1: General requirements;
— Part 2: Laboratory performance test based on determination of sampling efficiency;
— Part 3: Analysis of sampling efficiency data [Technical Report] (the present document);
— Part 4: Laboratory performance test based on comparison of concentrations;
— Part 5: Aerosol sampler performance test and sampler comparison carried out at workplaces;
— Part 6: Transport and handling tests.
Introduction
EN 481 defines sampling conventions for the particle size fractions to be collected from workplace
atmospheres in order to assess their impact on human health. Conventions are defined for the inhalable,
thoracic and respirable aerosol fractions. These conventions represent target specifications for aerosol
samplers, giving the ideal sampling efficiency as a function of particle aerodynamic diameter.
In general, the sampling efficiency of real aerosol samplers will deviate from the target specification, and the
aerosol mass collected will therefore differ from that which an ideal sampler would collect. In addition, the
behaviour of real samplers is influenced by many factors such as external wind speed. In many cases there is
an interaction between the influence factors and fraction of the airborne particle size distribution of the
environment in which the sampler is used.
This Technical Report presents how data obtained in a type A test (see EN 13205-2) can be analysed in order
to calculate the uncertainty components specified in EN 13205-2.
The evaluation method described in this Technical Report shows how to estimate the candidate sampler’s
sampling efficiency as a function of particle aerodynamic diameter based on the measurement of sampling
efficiency values for individual sampler specimen, whether all aspirated particles are part of the sample (as for
most inhalable samplers) or if a particle size-dependent penetration occurs between the inlet and the
collection substrate (as for thoracic and respirable samplers).
The document shows how various sub-components of sampling errors due non-random and random sources
of error can be calculated from measurement data, for example, for individual sampler variability, estimation of
sampled concentration and experimental errors.
1 Scope
This Technical Report specifies evaluation methods for analysing the data obtained from a type A test of
aerosol samplers under prescribed laboratory conditions as specified in EN 13205-2.
The methods can be applied to all samplers used for the health-related sampling of particles in workplace air.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
EN 1540, Workplace exposure — Terminology
EN 13205-1:2014, Workplace exposure — Assessment of sampler performance for measurement of airborne
particle concentrations — Part 1: General requirements
EN 13205-2:2014, Workplace exposure — Assessment of sampler performance for measurement of airborne
particle concentrations — Part 2: Laboratory performance test based on determination of sampling efficiency
3 Terms and definitions
For the purpose of this document, the term and definitions given in EN 1540, EN 13205-1 and EN 13205-2
apply.
NOTE With regard to EN 1540, in particular, the following terms are used in this document: total airborne particles,
respirable fraction, sampling efficiency, static sampler, thoracic fraction, measuring procedure, non-random uncertainty,
random uncertainty, expanded uncertainty, standard uncertainty, combined standard uncertainty, uncertainty (of
measurement), coverage factor, precision and analysis.
4 Symbols and abbreviations
4.1 Symbols
4.1.1 Latin
relative lognormal aerosol size distribution, with mass median aerodynamic
A D ,σ , D
( )
A A
diameter and geometric standard deviation , [1/µm]
D σ
A A
∞
NOTE The word “relative” means that the total amount of particles is unity [-], i.e. A D ,σ , D d D= 1.
( )
A A
∫
integration of aerosol size distribution A between two particle sizes, [-] –
A
p
(polygonal approximation method)
integration of aerosol size distribution A between two particle sizes, calculated
A
t, p
using set t of the simulated test particle sizes, [-] – (polygonal approximation
method)
left right top front coefficients in Formula (19) to estimate the test aerosol concentration at a
b ,b ,b ,b ,b
ipr ipr ipr
ipr ipr
specific sampler position e.g. in a wind tunnel based on nearby concentrations (to
the left, right, above and in front of) the sampler measured by thin-walled sharp-
edged probes, [-]
regression coefficient q for calibration of particle counter/sizer or similar,
b
q
[dimension depends on particle counter], (curve-fitting method)
sampled relative aerosol concentration, calculated to be obtained when using the
C
is
candidate sampler individual s, for aerosol size distribution A at influence variable
value , [-] – (curve-fitting method)
ς
i
sampled relative aerosol concentration, calculated to be obtained when using the
C
is,t
candidate sampler individual s, for aerosol size distribution A at influence variable
value , using simulated set t of test particle sizes, [-] – (curve-fitting method)
ς
i
mean sampled relative aerosol concentration, calculated to be obtained when
C
i,t
using the candidate sampler, for aerosol size distribution A at influence variable
value , using simulated set t of test particle sizes, [-] – (polygonal
ς
i
approximation method)
correction factor for the measured efficiency values if the total airborne aerosol
c
Ref
is[ r ]
concentration varies between repeats, [-] – (curve-fitting method)
aerodynamic diameter, [µm]
D
mass median aerodynamic diameter of a lognormal aerosol size distribution A,
D
A
[µm]
mass median aerodynamic diameter a of a lognormal aerosol size distribution A,
D
A
a
[µm]
D
aerodynamic particle size of calibration particle c (c=1 to ), [µm] – (curve-
c N
C
fitting method)
diameter of the end of the integration range of the sampled aerosol, [µm] –and H

D
max
diameter of the beginning of the integration range of the sampled aerosol, [µm]

D
min
D
aerodynamic diameter of test particle p (p=1 to ), [µm]
N
p
P
simulated test particle size, [µm]
D
t, p
D
aerodynamic particle size of small particles u (u=1 to ) for which the sampling
N
u
U
efficiency is known to be , [µm]– (curve-fitting method)
e
expectation value of the efficiency for test particle size p at influence variable
E
ip
value , [-] – (polygonal approximation method)
ς
i
est inlet
fitted sampling efficiency curve (of the inlet stage) of the candidate sampler
E
is
individual s at influence variable value , [-] – (curve-fitting method)
ς
i
est pen
fitted penetration curve (of the separation stage) of the candidate sampler
E
is
individual s at influence variable value , [-] – (curve-fitting method)
ς
i
est tot
fitted sampling efficiency curve (of the combined inlet and penetration stages) of
E
is
, [-] – (curve-
the candidate sampler individual s at influence variable value
ς
i
fitting method)
est
fitted sampling efficiency curve of the candidate sampler individual s at influence
E
is,t
variable value using simulated set t of particle sizes, [-] – (curve-fitting
ς N
i P
method)
experimentally determined efficiency value, with notation for polygonal
e
ips[r]
e and
ipr[s] approximation and curve-fitting methods, respectively. The subscripts are for
influence variable value , particle size p (p=1 to ), sampler individual s (s=1
ς N
i P
to ) and repeat r (r=1 to ), [-] – (notation for polygonal approximation and
N N
S R
curve-fitting methods, respectively)
known efficiency value for small particle sizes, [-] – (curve-fitting method)
e
F
ˆ
LoF test variable for “lack of fit” for the regression model for the sampling
is E
is
efficiency of candidate sampler individual s and influence variable value , [-] –
ς
i
(curve-fitting method)
test variable for the check whether the individual sampler variability exceeds that
F
CandSamplVar
i
of the uncertainty of the calculated concentrations, for influence variable value
, [-]
ς
i
ν ν
F ν ,ν
( )
N D
0.95 N D 95-percentile of F distribution with and degrees of freedom, [-]

functions (of Ξ ) used to build the regression model of the efficiency curve (index
f(Ξ)
k
k=1 to ), [-] – (curve-fitting method)
N
K
inlet
Ξ
functions (of ) used to build the regression model of the efficiency curve of the
f (Ξ)
k
inlet stage (index k=1 to ), [-] – (curve-fitting method)
N
K
pen
Ξ
functions (of ) used to build the regression model of the penetration curve of
f (Ξ)
k
the separation stage (index k=1 to ), [-] – (curve-fitting method)
N
K
uncertainty inflation factor for the “lack of fit” uncertainty of the regression model
G
LoF
is
for candidate sampler individual s and influence variable value , [-]
ς
i
uncertainty inflation factor for the “pure error” uncertainty of the regression model
G
pe
is
for candidate sampler individual s and influence variable value , [-]
ς
i
left right top front
nearby thin-walled sharp-edged probe concentrations measured in order to be
h , h , h , h
ip ip ip ip
able to estimate the test aerosol concentration at a specific sampler position, e.g.
in a wind tunnel (to the left, right, above and in front of) the candidate sampler
3 3
(see Formula (19)), [mg/m ] or [1/m ] depending on the application
est total airborne aerosol concentration estimated from the sharp-edged probe
h
ipr
values; the subscripts are for influence variable value i (i=1 to N ), particle size
IV
p (p=1 to N ) and repeat r (r=1 to N )
P R
number of sizes for calibration particles – (curve-fitting method)
N
C
number of regression coefficients for calibration of particle counter/sizer or similar
N
CR
– (curve-fitting method)
number of values for the other influence variables at which tests were performed
N
IV
number of regression coefficients in the model for the candidate sampler –
N
K
(curve-fitting method)
inlet
number of regression coefficients in the model (inlet stage) for the candidate
N
K
sampler – (curve-fitting method)
pen
number of regression coefficients in the model of the penetration through the
N
K
separation stage for the candidate sampler – (curve-fitting method)
number of test particle sizes
N
P
number of repeats per tested individual sampler
N
R
number of reference samplers (thin-walled sharp-edged probes) used per
N
Ref
experiment – (polygonal approximation method)
number of repeats at particle size p for candidate sampler individual s at influence
N
Rep
variable value – (in the polygonal approximation method equals the
ς N
i Rep
number of repeats, whereas in the curve-fitting method it equals the number of
repeats per candidate sampler individual)
*
recalculated number of repeats if the variation among candidate samplers
N
Rep
statistically does not exceed that of the uncertainty of the calculated
concentration – (curve-fitting method)
number of candidate sampler individuals – (in the polygonal approximation
N
S
method equals the number of sampler individuals tested per repeat, whereas
N
S
in the curve-fitting method it equals the total number of sampler individuals
tested.)
number of aerosol size distributions A according to EN 13205-2:2014, Table 2
N
SD
N
number of simulated sets of test particle sizes
Sim N
P
number of repeats per sampler individual tested – (polygonal approximation
N
SR
method, see Formula (24))
*
recalculated number of candidate samplers if the variation among candidate
N
S
samplers statistically does not exceed that of the uncertainty of the calculated
concentration – (curve-fitting method)
number of different sampler individuals tested – (polygonal approximation
N
TSI
method, see Formula (24))
N
number of small particle sizes at which the efficiency is known to be – (curve-
e
U
fitting method)
nominal flow rate of sampler, [l/min]
Q
pooled relative standard deviation of the estimate of the thin-walled sharp-edged
RSD ς
()
Est[Ref] i
probe concentration at influence variable , [-] – (polygonal approximation
ς
i
method)
pooled relative standard deviation of the concentrations sampled by the
RSD ς
()
CandSampl i
candidate sampler at influence variable , [-], (polygonal approximation method)
ς
i
pooled relative standard deviation of the thin-walled sharp-edged probe
RSD ς
()
Ref i
concentrations at influence variable , [-], (polygonal approximation method)
ς
i
residual standard deviation of the calibration of particle counter/sizer or similar,
s
CalibrRes
[dimension depends on particle counter] – (curve-fitting method)
combined non-random and random uncertainty (of measurement) of the
s
CandSampl-Calibr
ia
calculated sampled concentration, due to the calibration uncertainty of the
experiment, for aerosol size distribution A at influence variable value , [-]
ς
i
uncertainty of calculated sampled concentration due to uncertainty of efficiency
s
CandSampl-Eff
for aerosol size distribution A at influence variable value , [-] (polygonal
ς
i
approximation method)
uncertainty of calculated sampled concentration (at the inlet stage) due to
s
CandSampl-Eff(inlet)
uncertainty of efficiency for aerosol size distribution A at influence variable value
, [-] – (polygonal approximation method)
ς
i
uncertainty of calculated sampled concentration (at the separation stage) due to
s
CandSampl-Eff(pen)
uncertainty of efficiency for aerosol size distribution A at influence variable value
, [-] – (polygonal approximation method)
ς
i
random uncertainty (of measurement) of the calculated sampled concentration,
s
CandSampl-ModelCalc
th
ia
aerosol size distribution A at
due to the uncertainty of the fitted model, for the a
influence variable value , [-]
ς
i
uncertainty of calculated sampled concentration due to polygonal approximation
s
CandSampl-PGapprox
for aerosol size distribution A at influence variable value , [-] – (polygonal
ς
i
approximation method)
uncertainty of calculated sampled concentration due to uncertainty of measured
s
CandSampl-Ref
total airborne concentrations for aerosol size distribution A at influence variable
value , [-] – (polygonal approximation method)
ς
i
uncertainty of calculated sampled concentration (at the inlet stage) due to
s
CandSampl-Ref(inlet)
uncertainty of measured total airborne concentrations for aerosol size distribution
A at influence variable value , [-] – (polygonal approximation method)
ς
i
uncertainty of calculated sampled concentration (at the separation stage) due to
s
CandSampl-Ref(pen)
uncertainty of measured total airborne concentrations for aerosol size distribution
A at influence variable value , [-] – (polygonal approximation method)
ς
i
random uncertainty (of measurement) of the calculated sampled concentration,
s
CandSampl-Variability
ia th
due to individual sampler variability, for the a aerosol size distribution A and
influence variable value , [-]
ς
i
RMS value of all relative uncertainties of the actual sizes of the monodisperse
s
D
test aerosols, [-]
relative uncertainty of the actual size of calibration particle c, [-] – (curve-fitting
s
Dc
method) [If the particle size is specified to be within the relative size interval ,
±β
c
then can be calculated as .]
s s =β 3
Dc Dcc
relative uncertainty of the actual size of monodisperse test aerosol p, [-] – [If the

s
D
p
particle size is specified to be within the relative size interval , then can
±β s
p D p
be calculated as .]
s =β 3
D p
p
standard deviation pertaining to the possible lack of fit of the regression model for
s
LoF
is
the Ω -transformed sampling efficiency of candidate sampler individual s at
influence variable value , [-] – (curve-fitting method)
ς
i
random uncertainty (of measurement) of the calculated sampled concentration,
s
ModelCalc-LoF
is
due to the “lack of fit” of the model for candidate sampler individual s, for aerosol
size distribution A at influence variable value , [-]
ς
i
random uncertainty (of measurement) of the calculated sampled concentration,
s
ModelCalc-pe
is
due to the “pure error” of the experiment for candidate sampler individual s, for
aerosol size distribution A at influence variable value , [-]
ς
i
s
“pure error” standard deviation of the Ω -transformed experimental data of
pe
is
candidate sampler individual s at influence variable value , [-] – (curve-fitting
ς
i
method)
random uncertainty (of measurement) of the calculated sampled concentration,
s
RefCorr
is
due to the correction of measured sampler efficiency values because of variations
in e.g. time, for candidate sampler individual s, at influence variable value , [-]
ς
i
s
residual standard deviation of the regression model for the Ω -transformed
res
is
sampling efficiency of candidate sampler individual s at influence variable value
, [-] – (curve-fitting method)
ς
i
residual standard deviation of the model for the estimation of the total airborne
s
res(Est[Ref])
ip
3 3
aerosol concentration for particle size p at influence variable , [mg/m ] or [1/m ]
ς
i
depending on the application – (polygonal approximation method)
SS
Ω
“pure error” sum of squares of the -transformed experimental data of candidate
pe
is
sampler individual s at influence variable value , [-] – (curve-fitting method)
ς
i
SS
Ω
residual sum of squares of the regression model for the -transformed sampling
res
is
efficiency of candidate sampler individual s at influence variable value , [-] –
ς
i
(curve-fitting method)
standard uncertainty (of measurement) of the calculated sampled concentration
u
CandSampl-ModelCalc
i
(random errors), due to the uncertainty of the fitted model, calculated as the RMS
of the corresponding relative uncertainties over all aerosol size distributions
N
SD
A at influence variable value , [-]
ς
i
standard uncertainty (of measurement) of the sampled concentration (random
u
CandSampl-Variability
i
errors) due to differences among candidate sampler individuals at influence
variable value , [-]
ς
i
weighted average of integration of aerosol size distribution A between two particle
W
p
sizes, [-] – (polygonal approximation)
weighted average of integration of aerosol size distribution A between two particle
W
t, p
sizes, calculated using set t of the simulated test particle sizes, [-] – (polygonal
approximation method)
y
instrument response of calibrated particle counter/sizer or similar, [dimension
depends on particle counter] – (curve-fitting method)
random number with a normal distribution, with expectation value equal to zero
z
t, p
and standard deviation equal to unity, [-]

4.1.2 Greek
specified size range within which actual particle size is found with high probability for
∆D
p
monodisperse test aerosols with nominal particle size , [µm]
D
p
relative adjustment of calibration particle size c to obtain a smooth spline, [-] – (curve-
δ D
c
fitting method)
random experimental error at particle size p, repeat r and candidate sampler s at
and
ε
ε
ipr[]s
ips[]r
influence variable value , [-] – (notations for polygonal approximation and curve-fitting
ς
i
methods, respectively)
ς
value of other influence variable values, as for example wind speed and mass loading of
sampler, with values for i=1 to , [various dimensions]
N
IV
th
i value of another influence variable
ς
i
NOTE  The dimension of each ς depends on the influence variable. The dimension selected, however, is not critical, as
i
the values are never part in any calculation.
est
regression coefficient number k for candidate sampler individual s at influence variable
θ
isk
value , [dimension depends on selected regression model for the sampling efficiency]
ς
i
– (curve-fitting method)
est inlet
regression coefficient number k for model of inlet stage efficiency for candidate sampler
θ
isk
individual s at influence variable value , [dimension depends on selected regression
ς
i
model for the sampling efficiency] – (curve-fitting method)
est pen
regression coefficient number k for model of penetration through the separation stage
θ
isk
for candidate sampler individual s at influence variable value , [dimension depends on
ς
i
selected regression model for the sampling efficiency] – (curve-fitting method)
number of degrees of freedom for the “pure error” standard deviation of the
ν
pe
is
experimental data of candidate sampler individual s at influence variable value –
ς
i
(curve-fitting method)
number of degrees of freedom for the residual standard deviation of the regression
ν
res
is
model for the -transformed sampling efficiency of candidate sampler individual s at
Ω
influence variable value , (curve-fitting method)
ς
i
transformation of particle size, [dimension depends on transformation] – (curve-fitting
Ξ
method)
inlet
transformation of particle size for inlet stage, [dimension depends on transformation] –
Ξ
(curve-fitting method)
pen
transformation of particle size for separation stage, [dimension depends on
Ξ
transformation] – (curve-fitting method)
geometric standard deviation of a lognormal aerosol size distribution A from EN 13205-
σ
A
2:2014, Table 2, [-]
Geometric standard deviation a of a lognormal aerosol size distribution A, [µm]
σ
A
a
−1
inverse of normal distribution function, [-] – (curve-fitting method)
Φ
transformation of efficiency data, [-] – (curve-fitting method)
Ω
−1
inverse -transformation of regression model of the -transformed efficiency curve,
Ω Ω
Ω
[-] – (curve-fitting method)
−1
inverse -transformation of regression model of the -transformed efficiency curve
Ω Ω
Ω
inlet
for the inlet stage, [-] – (curve-fitting method)
−1
inverse -transformation of regression model of the -transformed efficiency curve
Ω Ω Ω
pen
for the separation stage, [-] – (curve-fitting method)
4.2 Enumerating subscripts
a for test aerosols
c for calibration particle
i for influence variable values,
ς
j for the second estimated regression coefficient in the determination of the covariance
est est

CoVar θθ,
isk isj

k
ˆ
for regression coefficient and for the first estimated regression coefficient in the determination of
θ
isk
est est
the covariance

CoVar θθ,
isk isj

p for test particle size
r for repeats
s for candidate sampler individual
t
for simulated set of test particle sizes
N
P
u
for small particle sizes at which the efficiency is known to be
e
w for repeat within candidate sampler individual z – (polygonal approximation method)
z
for candidate sampler individual – (polygonal approximation method)
4.3 Abbreviations
est est
est
  Covariance of the estimated regression coefficients, , for the regression
CoVar θ , θ
θ
isk isj isk
 
est
model for the sampling efficiency of candidate sampler individual s at
E
is
influence variable value i, [dimension depends on selected regression model] –
(curve-fitting method)
RMS Root Mean Square
5 Analysis of sampling efficiency data from a performance test according
EN 13205-2
5.1 General
This subclause provides illustrations of suitable experimental designs for Type A sampler performance
evaluations (see EN 13205-1:2014, Clause 7), and gives two examples of how the experimental data can be
statistically analysed. The choice of data analysis method depends primarily on whether the laboratory
experiment is carried out using monodisperse or polydisperse aerosols. Two alternative calculation methods,
termed the polygonal approximation method and the curve-fitting method, are described. Alternative methods
can be employed provided they are able to calculate the same entities. For monodisperse aerosol tests either
method can be used, whereas for polydisperse tests it is better to use the curve-fitting method. The small
quantity of data typically yielded by monodisperse aerosol experiments can render the curve-fitting method
difficult to apply. The curve-fitting method is used when (different) sampling efficiency curves can be
determined for the individual candidate samplers.
The simplified treatments of aerosol sampler performance data described allow samplers to be evaluated
under specified laboratory conditions, although the results can not necessarily reflect performance under
)
conditions of use.
) For worked examples of these and other methods for analysing aerosol sampler performance data, see Bibliography,
references [1] to [5).
5.2 Presumption of exactly balanced data
The formulae presented here presume that the number of test particle sizes, , the number of samplers,
N
P
, the number of repeats, , the number of influence variable values, , and (in the case of the curve-
N N N
S Rep IV
fitting method) the number of regression coefficients, , are identical over the whole experiment, i.e. the
N
K
data are exactly balanced. If this is not so, these numbers will vary across the experimental data, and we will
have
 N = N
P P
isr

N = N

S S
ipr


N = N
(1)
 Rep Rep
ips

N = N
 IV IV
psr

N = N
K K

ipsr

Consequently many of the formulae presented below will need to be modified accordingly.
5.3 Examples of balanced experimental designs
Table 1 illustrates an experiment in which six sampler individuals are tested at (=9) diameters
N
P
(monodisperse test aerosols) in a series of (=2) repeats with (=3) sampler individuals tested in each
N N
Rep S
repeat. The diameters will be tested sequentially, and the sampler individuals can be tested either in
N
P
groups as shown, or sequentially.
Table 1 — Example of a balanced design using monodisperse test aerosols
Test Repeat 1 Repeat 2
particle
Sampler Sampler Sampler Sampler Sampler Sampler
size
individual 1 individual 2 individual 3 individual 4 individual 5 individual 6
1 x X x x x x
2 x X x x x x
3 x X x x x x
4 x X x x x x
5 x X x x x x
6 x X x x x x
7 x X x x x x
8 x X x x x x
9 x X x x x x
Table 2 illustrates an experiment in which (=6) sampler individuals are tested with polydisperse test
N
S
aerosols with (=5) repeats for each sampler (and all test particle sizes).
N
Rep
Table 2 — Example of a balanced design using polydisperse test aerosols
Repeat Sampler Sampler Sampler Sampler Sampler Sampler
individual 1 individual 2 individual 3 individual 4 individual 5 individual 6
1 x X x x x x
2 x X x x x x
3 x X x x x x
4 x X x x x x
5 x X x x x x
Both designs in Tables 1 and 2 can be part of a larger experiment in which the shown design is repeated for
different influential variable conditions, such as wind speeds and sampler loadings. A difference between the
two designs is that the subscripts sampler individual and repeat has different meanings in the two methods. In
an experiment with monodisperse test aerosols, the sampler individuals are nested within the repeats, so that
(generally) it can be a different set of sampler individuals participating in a different repeat. The number of
, is therefore equal to the number of sampler individuals tested per repeat, not
sampler individuals tested,
N
S
the total number of tested candidate sampler individuals. (At the extreme all sampler individuals can be
N
S
tested together (i.e. ≥ 1). Where there is a possibility of significant variations between sampler
N
Rep
individuals, the number of sampler individuals tested per repeat, , should be as large as possible.) In an
N
S
experiment with polydisperse test aerosols, on the other hand, the repeats are nested within each sampler
individual. equals the total number of sampler individuals tested, and equals the number of repeats
N N
S R
per tested individual sampler.
5.4 Analysis of efficiency data based on monodisperse test aerosols using the polygonal
approximation method
5.4.1 Statistical model for the efficiency values
The efficiency values at particle diameter p, influence variable value number i, repeat r, candidate
e
ipr[]s
sampler s (within repeat r) are analysed according to the model
e = E +ε (2)
ipr[s] ip ipr[s]
where
E is the expectation value of the efficiency of the sampler type at particle diameter D= D for
ip p
influence variable value number i, [-];
is the random experimental error, including experimental flow deviation and inter-specimen
ε
ipr[s]
variability where present, [-].
The polygonal approximation to the estimated mean relative concentration [see EN 13205-2:2014,
Formula (2)], , can be written as a weighed sum over the sampling efficiencies at diameters D [µm],
EC p
[ ]
i
p=1 to N , (though a similar approach could be used with other integration schemes)
p
∞
 
E C = A D ,σ , D E D dD≈
( ) ()
 i ∫ A A i
(3)
N N
P P
≈ E D W D ,σ , D ≈ E W
( ) ( )
∑ ∑
i p p A A ip p
p=0 p=0
with
D D
p p

 A = A (D ,σ )= A(D)dD= A(D ,σ , D)dD
p p A A ∫ ∫ A A

D D
( p−1) ( p−1)

A + A

p ( p+1)
W = W (D ,σ )= ,   0 
p p A A p


A
1 (4)

W =


A + A
N N +1
( )
p P

W = ,   respirable or thoracic samplers
N
 P

A
N

P
W = ,     inhalable samplers
N

P
 2
where
is the relative lognormal aerosol size distribution, with mass median aerodynamic
A D ,σ , D
( )
A A
diameter D and geometric standard deviation σ ;
A A
is the integration of aerosol size distribution A between two particle sizes;
A
p
is the polygonal approximation to the estimated mean relative concentration;
 
E C
i
 
is the sampling efficiency of the candidate sampler for test particle size p at influence
E D = E
( )
i p ip
variable valueς ; and
i
is the weighted average of integration of aerosol size distribution A between two
W
p
particle sizes.
est
This method presumes that sampling efficiency at can be estimated by linear extra
ED D = 0µm
( )
i 0 0
est
polation or if it is known to be unity, can be assigned the value of 1,00. For samplers of the
ED
( )
i 0
respirable and thoracic aerosol fractions, one also needs to estimate the value of an extrapolated particle
est est est
diameter , at which . This is done by linear extrapolation of the two
D = D ED ≈ 0
( )
NN++11 i N +1
( ) ( ) ( )
P P P
highest diameter data points. However, for samplers of the inhalable aerosol fraction, the integration is
terminated at , and thus the upper extrapolation is not necessary, and hence is calculated differently.
D W
N N
p P
NOTE The approach for samplers for the respirable and thoracic fractions presumes that the final term of the
summation in Formula (3), 0,5ED A , is small compared to C .
( )
iN
( N +1) i
P P
5.4.2 Estimation of mean sampled concentration
The raw data (efficiency values) are where subscript i denotes an influence variable value (i = 1 to ),
e N
ipr[]s IV
subscript p denotes particle aerodynamic diameter (p = 1 to ), subscript r denotes a repeat (r =1 to )
N N
P Rep
and subscript s denotes candidate sampler individual (s=1 to ) within the repeat r. In the case of static
N
S
samplers, the repeats can concern either sampler individuals or repeats, i.e. they are not necessarily true
replicates. (For personal samplers, however, at least six different sampler individuals should be tested, see
EN 13205-2:2014, 6.3.8.) The mean sampling efficiency at each measured diameter for each influence
D
p
variable value i, , is estimated as
ED
( )
i p
N
N
Rep
S
1 1
E D = e (5)
( ) ∑∑
i p ipr[s]
N N
r=1 s=1
Rep S
where
is the mean is the sampling efficiency of the candidate sampler for test particle size p
E D
( )
i p
at influence variable valueς ,
i
is the experimentally determined efficiency value,
e
ipr[s]
is the number of repeats; and
N
Rep
is the number of samplers.
N
S
This is a point estimate of the sampling efficiency curve of the sampler at particle aerodynamic
ED()
diameter . The polygonal approximation to estimate the mean relative concentration sampled from
DD= C
p
an arbitrary aerosol A(D) should be calculated using the trapezoidal rule following Formula (3):
N
P
C≈ E D W (6)
∑ ( )
i i p p
p=0
where
is the mean sampled relative concentration from an arbitrary aerosol A(D);
C
i
is the mean sampling efficiency of the candidate sampler for test particle size p at influence
E D
( )
i p
variable valueς ; and
i
is the weighted average of integration of aerosol size distribution A between two particle
W
p
sizes.
The ‘weights’ are calculated according to Formula (4) and the discussion at the latter part of 5.4.1.
W
p
For experiments in which the inlet efficiency and the internal penetration are measured in two separate
experiments, Formula (6) is modified accordingly
N
P
inlet pen
C≈ E D E D W (7)
∑ ( ) ( )
i i p i p p
p=1
where
is the mean sampled relative concentration from an arbitrary aerosol A(D);
C
i
inlet is the sampling efficiency of the inlet stage;
E D
( )
i p
pen is the penetration through the separation stage;
E D
( )
i p
is the weighted average of integration of aerosol size distribution A between two particle
W
p
sizes.
5.4.3 Estimation of uncertainty (of measurement) components
5.4.3.1 General
Three uncertainty (of measurement) components are estimated: the uncertainty of the calibration of the
sampler test system, the uncertainty in the estimate of the sampled concentration, and the individual sampler
variability.
5.4.3.2 Calibration of sampler test system
This uncertainty (of measurement) component stems from the uncertainty of the actual size of the
monodisperse test aerosols, not the width of their particle size distributions. Each of the particle sizes
associated with the monodisperse test aerosols has a relative uncertainty, . If the uncertainty of the
N s
P D
p
particle size of a monodisperse test aerosol of size [µm] is specified within a range, [µm], rather
D ±∆D
p p
than as a relative standard deviation, is calculated as
s
D
p
∆D
p
s = (8)
D
p
D
p
where
D is the aerodynamic diameter of test particle p (p=1 to N );
p P
is the size of the uncertainty range of the particle size of a monodisperse test aerosol; and
∆D
p
is the relative uncertainty of the actual size of the monodisperse test aerosol p.
s
D
p
The RMS test particle size uncertainty is calculated, from
N
P
2 2
s = s (9)
∑
D D
p
N
p=1
P
where
is the RMS value of all relative uncertainties of the actual sizes of the monodisperse
s
D
test aerosols;
is the number of samplers; and
N
P
is the relative uncertainty of the actual size of monodisperse test aerosol p.
s
D
p
The uncertainty (of measurement) of the calibration of the sampler test system is calculated by first simulating
sets of particle sizes, (subscript t=1 to ), based on the RMS uncertainty of the size
N =1000 N D N
Sim P tp, Sim
of the test aerosols, . A random number generator is used to generate a set of values of , which
s NN z
D Sim P tp,
have a normal distribution with an estimation value of zero and a standard deviation of unity. is simulated
D
tp,
by using the formula
D = (1+ z s ) D (10)
t,p t,p D p
where
D is the a
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