— The five major sources of uncertainty due to aspects of the sampling performance of an aerosol sampler calibration of sampler test system, estimation of sampled concentration, bias rel
Symbols
Latin
A D ( A , σ A , D ) relative lognormal aerosol size distribution, with mass median aerodynamic diameter
D A and geometric standard deviation σ A, [1/àm]
NOTE The word “relative” means that the total amount of particles is unity [-], i.e A D ( A ,σ A , D )dD
The C std target represents the sampled relative aerosol concentration, expressed as a fraction of the total airborne aerosol concentration This measurement reflects what would have been captured by an ideal sampler, which has a sampling efficiency equivalent to the sampling convention, F D ( ), for a specific aerosol size distribution, A.
The sampled relative aerosol concentration, denoted as C, represents the fraction of total airborne aerosol concentration obtained using the candidate sampler for aerosol size distribution A at the influence variable value ς i Additionally, the candidate sampler correction factor, c, is used for bias correction and can either be specified by the sampler manufacturer or the measuring procedure, or it may be assigned a value of c = 1.00.
D A mass median aerodynamic diameter of a lognormal aerosol size distribution A, [àm]
D A a mass median aerodynamic diameter a of a lognormal aerosol size distribution A,
D max diameter of the end of the integration range of the sampled aerosol, [àm]
D min diameter of the beginning of the integration range of the sampled aerosol, [àm]
D p aerodynamic diameter of test particle p (p = 1 to N P ), [àm]
E i ( ) D p mean sampling efficiency of the candidate sampler for test particle size p at influence variable valueς i , [-] – (polygonal approximation method)
The sampling efficiency curve, denoted as \( E_i(Q, D_p) \), represents the performance of the candidate sampler at a specific flow rate \( Q \) and particle size \( p \) for the influence variable value \( \zeta_i \) The estimated sampling efficiency curve, \( E_{est}(D) \), is derived using the polygonal approximation method, while \( E_{est}(Q, D) \) is obtained through the curve-fitting method The experimentally determined efficiency values, \( e_{ipr[s]} \) and \( e_{ips[r]} \), correspond to the polygonal approximation and curve-fitting methods, respectively The subscripts indicate the influence variable value \( \zeta_i \), particle size \( F \) (ranging from \( p = 1 \) to \( N_P \)), sampler individual \( s \) (from \( s = 1 \) to \( N_S \)), and repeat \( r \) (from \( r = 1 \) to \( N_R \)).
The target sampling convention, denoted as F D ( ), involves measuring aerosol concentration using candidate samplers, represented as [-] ipr s [ ] g and g ips r [ ] The subscripts indicate the influence variable value ς i, particle size p (where p ranges from 1 to N P), individual sampler s (with s ranging from 1 to N S), and repeat r (where r varies from 1 to N R) The concentrations are measured in units of [mg/m³] or [1/m³], corresponding to polygonal approximation and curve-fitting methods, respectively Additionally, h ipr and h ips[r] represent the total airborne aerosol concentration estimated from sharp-edged probe values, with subscripts for influence variable value i (i = 1 to N IV), particle size p (p = 1 to N P), individual sampler s (s = 1 to N S), and repeat r (r = 1 to N R).
The notation [mg/m³] and [1/m³] refers to polygonal approximation and curve-fitting methods, respectively The term \( m_i(D_A, \sigma_A, Q) \) represents the mean sampled aerosol mass, expressed as a fraction of the total airborne aerosol mass This value is calculated using the candidate sampler with a flow rate \( Q \) to sample the aerosol size distribution \( A \) at the influence variable value \( \zeta_i \).
N IV number of values for the other influence variables at which tests were performed,
N P number of test particle sizes
The variable \( N_{Rep} \) represents the number of repeats at particle size \( p \) for candidate sampler individual \( s \) at the influence variable value \( \varsigma_i \) In the polygonal approximation method, \( N_{Rep} \) corresponds to the total number of repeats, while in the curve-fitting method, it refers to the number of repeats per candidate sampler individual.
N S number of candidate sampler individuals – (In the polygonal approximation method
N S equals the number of sampler individuals tested per repeat, whereas in the curve-fitting method it equals the total number of sampler individuals tested.)
Q actual flow rate of candidate sampler, [l/min]
The nominal flow rate of the sampler, denoted as \$Q_0\$ [l/min], is a crucial parameter that determines whether the nominal or actual flow rate is utilized in calculating the sampled respirable and thoracic aerosol fractions The flow rate dependence of the sampled mass for aerosol size distribution A is represented by \$q_i(D_A, \sigma_A)\$ at the influence variable value \$\zeta_i\$ Additionally, \$s_{CandSampl-Flow}\$ indicates the non-random uncertainty in the measured sampled concentration, which arises from deviations from the nominal flow and initial flow conditions for the aerosol size distribution A at the influence variable value \$\zeta_i\$.
( ) random uncertainty for combined rectangular distribution based on allowed initial flow deviation from nominal flow rate and pump flow deviation, [-]
The expanded uncertainty of measurement for the calculated sampled concentration due to the candidate sampler is denoted as \$u_{CandSampl}\$ The combined uncertainty, represented as \$u_{CandSampl}\$, accounts for various factors affecting the measurement The individual combined uncertainty, \$u_{CandSampl_i}\$, reflects the influence of variable value \$\zeta_i\$ Additionally, the standard uncertainty due to bias, \$u_{CandSampl-Bias_i}\$, addresses non-random errors related to the sampling convention at the same variable value The calibration uncertainty, \$u_{CandSampl-Calibr_i}\$, encompasses both non-random and random errors, calculated as the root mean square of the relative uncertainties across all \$N\$ SD aerosol size distributions at variable value \$\zeta_i\$ Finally, the standard uncertainty due to flow rate deviation is represented as \$u_{CandSampl-Flow_i}\$, while the model calculation uncertainty is denoted as \$u_{CandSampl-ModelCalc_i}\$.
The random errors arise from the uncertainty of the fitted model, quantified as the root mean square (RMS) of the relative uncertainties across all N SD aerosol size distributions at the influence variable value \( \zeta_i \) The combined uncertainty of the sampled concentration due to the candidate sampler includes both non-random errors, denoted as \( u_{\text{CandSampl-nR}} \) and \( u_{\text{CandSampl-nR} \, i} \), and random errors, represented as \( u_{\text{CandSampl-R}} \) and \( u_{\text{CandSampl-R} \, i} \), at the same influence variable value \( \zeta_i \) Additionally, the standard uncertainty of the sampled concentration due to variability among candidate sampler individuals is indicated as \( u_{\text{CandSampl-Variability} \, i} \) at the influence variable value \( \zeta_i \).
W p weighted average of integration of aerosol size distribution A between two particle sizes, [-] – (polygonal approximation)
Greek
The bias or relative error in aerosol concentration measured by the candidate sampler for aerosol size distribution A is influenced by the variable value ς i Additionally, the maximum relative error permitted in setting the flow rate is denoted as δ FlowSet, while δ Pump represents the maximum relative change in flow rate allowed due to pump flow rate stability.
Random experimental error is denoted as \$\epsilon\$ at particle size \$p\$, with repetitions \$r\$ and candidate sampler \$s\$ influenced by variable values \$\zeta_i\$ The notations for polygonal approximation and curve-fitting methods are represented as \$[ ]\$ and \$[-]\$, respectively The variable \$\zeta\$ encompasses other influencing factors, such as wind speed and mass loading of the sampler, with values ranging from \$i = 1\$ to \$N_{IV}\$ Each \$\zeta_i\$ represents the \$i^{th}\$ value of any additional influence variable.
The dimension of each variable \( \xi_i \) is determined by the influencing variable, but the specific dimension chosen is not crucial since the values are not used in any calculations The geometric standard deviation \( \sigma_A \) of a lognormal aerosol size distribution \( A \) is referenced in Table A.2.
Enumerating subscripts
For a chosen set of distinguishable values of an influence variable \( i \), the values of the influence variable are denoted as \( ς_{i0} \) This selection aims to identify the non-distinguishable values that result in the highest combined standard uncertainty for the candidate sampler Additionally, \( p \) represents the test particle size, \( r \) indicates the number of repeats, and \( s \) refers to the individual candidate sampler.
Abbreviations
The test method outlined in EN 13205 evaluates the sampling efficiency of candidate samplers based on particle aerodynamic diameter It assesses whether all aspirated particles are included in the sample, as seen in most inhalable samplers, or if there is a size-dependent penetration between the inlet and the collection substrate, typical of thoracic and respirable samplers The bias relative to the sampling convention is derived from the measured sampling efficiencies, while additional sampling errors from both random and non-random sources, such as individual sampler variability, deviations from the nominal flow rate, concentration estimation, and experimental errors, are also analyzed.
The laboratory experiments aim to assess sampling efficiency based on particle aerodynamic diameter and other relevant variables, as outlined in EN 13205-1:2014, 6.2 By employing mathematical modeling, the study estimates concentrations from ideal log-normally distributed aerosols, utilizing both measured sampler efficiency and target sampling conventions to evaluate sampler performance.
General
Sampling efficiency is determined by dividing the aerosol concentrations obtained from the candidate sampler by the total airborne particle concentration measurements An experimental design will be developed that emphasizes randomization and the estimation of main effects, with a detailed explanation provided in the test report A suitable design example can be found in CEN/TR 13205-3:2014.
Test conditions
Experiments to evaluate inhalable fraction samplers must be conducted in a wind tunnel or aerosol chamber Personal inhalable samplers designed for outdoor use or environments with strong ventilation (wind speeds over 0.5 m/s) should be tested on a life-size mannequin or simulated torso This setup must accurately replicate the aerodynamic effects of a human-shaped head and torso Research indicates that in a wind tunnel measuring 1.2 × 1.8 m, a simulated torso with dimensions matching those of a human is essential for accurate testing.
The study found that using samplers mounted on all four vertical planes yielded results comparable to those obtained with a life-size mannequin measuring 33 cm, 21 cm, and 21 cm It is essential to provide a detailed description of the size and characteristics of the mannequin or simulated torso utilized in the experiment.
2) For examples of performance evaluations of personal inhalable samplers, see Bibliography, references [2] to [5]
When evaluating candidate samplers, it is crucial to note that results obtained from testing a personal sampler in moving air cannot be applied to its performance as a static sampler, and the reverse is also true For detailed experiments, refer to the bibliography, specifically references [6] and [7].
The sampling efficiencies of samplers for thoracic or respirable fractions depend on the combination of the samplers' inlet efficiency and internal penetration These efficiencies can be tested collectively, with the particle size range limited to that specified for the relevant fraction in Table 1 Alternatively, they can be measured through two separate experiments: one assessing the sampler's inlet efficiency and the other evaluating its internal penetration For inlet efficiency tests, the same criteria as inhalable samplers apply, with the particle size range again restricted to the specified fraction in Table 1 Penetration tests can be conducted in a low-wind aerosol chamber using isolated samplers.
Test variables
General
Laboratory tests for sampling efficiency are essential to measure the impact of key influence variables identified in the critical review Table 1 outlines these important variables, categorizing them as compulsory (C), compulsory for specific sampler types or uses (C*), or optional (O) Additionally, any excluded variables will be clearly stated in the test report's scope section.
Table 1 — Influence variables to be tested
Variable Status Range Number of values Subclause
Inhalable: 1 àm to 100 àm Thoracic: 0,5 àm to 35 àm Respirable: 0,5 àm to 15 àm
≥ 9: spaced to cover important features of the efficiency curve
Wind Speed C Indoor workplaces only: 1: ≤ 0,1 m/s 6.3.3
Wind Direction C Omnidirectional average Continuous revolution or ≥ 4 values stepwise 6.3.4 Aerosol composition O Phase: solid and/or liquid;
Particles of known shape Choose suitable materials 6.3.5
Highly agglomerated dust Choose and document 6.3.5 Collected mass and/or internally separated mass
O Collected mass corresponding to: up to maximum concentration x nominal flow rate x sampling time
Internally separated mass corresponding to: maximum uncollected concentration x nominal flow rate x sampling time
Aerosol charge O Charged or neutralised aerosol;
Conducting or insulating sampler Choose and document 6.3.7 Sampler specimen variability
C* Test group to be as large as possible ≥ 6 6.3.8
Excursion from the nominal flow rate
C* Nominal flow rate plus lower and higher flow rates at one wind speed ≥ 6 specimen tested at 3 flow rates 6.3.9
O Choice of materials (e g filters, foams) and details of any surface treatments to be stated
C* compulsory for some samplers for the respirable and thoracic aerosol fractions only
Table 1 summarizes the value ranges for the selected variables to be tested, along with the number of values within these ranges Generally, the chosen values do not need to include the extremes, although specific requirements may apply in certain cases When the experimental design necessitates a decision, such as the aerosol composition or the type of collection substrate, the impact of these choices on the relevance of the test results for routine sampling must be evaluated in the critical review and documented in the test report.
EN 13205 outlines the calculation of uncertainty components and their integration into expanded uncertainty for compulsory test influence variables For optional test influence variables, users must define the tests, their evaluation methods, and the incorporation of related uncertainty components into the expanded uncertainty.
Particle size
Inhalable aerosol samplers must test particles with a minimum size of 90 µm For samplers targeting respirable and thoracic aerosol fractions, at least one particle size should range from 0.5 µm to 0.9 µm, and the largest particle size must be selected to ensure that the lowest measured sampling efficiency is below 0.04.
NOTE For the respirable and thoracic sampling conventions a sampling efficiency of 0,04 corresponds to approximately 8 àm and 22 àm, respectively.
Wind speed
In indoor work environments, air movement typically averages between 0.1 m/s and 0.3 m/s or lower For samplers designed for forced ventilation, the outdoor workplace wind speed range of over 0.25 m/s is applicable The recommended maximum wind speed may be adjusted based on a critical review to establish a more appropriate upper limit, depending on the sampler's intended use.
Wind direction
According to the inhalable convention, wind direction effects must be averaged by rotating the mannequin or samplers during each test run, either continuously or in at least four steps However, static samplers may be exempt from this requirement if they are designed to maintain a preferred orientation to the wind, are omnidirectional, or are used in fixed positions relative to forced ventilation.
Aerosol composition
For testing samplers, particles must be spherical (solid or liquid) or nearly isometric The agglomeration level of the test aerosol can be assessed through visual microscopic inspection of particles collected on slides in the wind tunnel or test chamber Typically, the chemical composition of the test aerosol is considered non-influential; however, if a critical review indicates a potential composition-related effect on particle retention on sampler surfaces, this should be acknowledged in the test report.
Sampled or internally separated mass
The test aims to assess the dependency of the sampler efficiency curve on the collected or internally separated mass, rather than to evaluate analytical errors The dust sampled, calculated as the rosol concentration multiplied by the sampled volume, should not exceed typical values found in workplace sampling unless proven insignificant If testing is conducted, it is essential to select a maximum concentration and sampling duration that align with the intended measurement objectives.
NOTE An example of such a test is given in EN 13205–5:2014, 6.5.5 and its evaluation in EN 13205–5:2014, 7.4.7.
Aerosol charge
When testing a non-conducting sampler, it should be evaluated using a neutralized aerosol, unless it can be proven that the performance with charged aerosols during mechanical generation and dispersal is not significantly different However, the results may not accurately represent performance in typical sampling scenarios where charged aerosols are present It is essential to minimize electrostatic influences whenever possible.
4) See Bibliography, reference [8], for the data presented by BALDWIN and MAYNARD
5) See, for example, Bibliography, reference [9] on a study regarding the electrical charge on dry airborne particles produced by mechanical aerosol generators and Bibliography, reference [10] on a study regarding the effect of electrical particle charge on cyclone penetration choosing samplers made from conducting materials, cleaning them thoroughly, and earthing them during the tests where the information for use requires it.
Specimen variability
NOTE The given requirements are compulsory for personal thoracic and respirable samplers only
Testing should be conducted on commercial samplers rather than prototypes, with a preference for used specimens over new ones, and the age of these specimens must be specified In cases where variability among specimens is expected to be minimal, a minimum of six test results should be collected, although tests may be repeated on two specimens (refer to EN 13205-1:2014, Tables 2 and 3).
Surface treatments
C* compulsory for some samplers for the respirable and thoracic aerosol fractions only
Table 1 outlines the value ranges for the selected variables to be tested, including the number of values within these ranges Generally, the chosen values do not need to encompass the extremes, although specific requirements may apply When making choices in experimental design, such as the aerosol composition or the type of collection substrate, it is essential to evaluate how these choices impact the relevance of the test results for routine sampling, and this should be documented in the test report.
EN 13205 outlines the calculation of uncertainty components and their integration into the expanded uncertainty for compulsory test influence variables For optional test influence variables, users must define the tests, their evaluation methods, and the incorporation of the related uncertainty components into the expanded uncertainty.
Inhalable aerosol samplers must test particles no smaller than 90 µm For samplers targeting respirable and thoracic aerosol fractions, at least one particle size should range from 0.5 µm to 0.9 µm, with the largest particle size selected to ensure that the lowest measured sampling efficiency is below 0.04.
NOTE For the respirable and thoracic sampling conventions a sampling efficiency of 0,04 corresponds to approximately 8 àm and 22 àm, respectively
In indoor work environments, air movement typically averages between 0.1 m/s and 0.3 m/s or lower For samplers designed for forced ventilation, the outdoor workplace wind speed range of over 0.25 m/s should be considered The recommended maximum wind speed may be adjusted based on a critical review to establish a more appropriate upper limit, depending on the sampler's intended use.
According to the inhalable convention, wind direction effects must be averaged by rotating the mannequin or samplers during each test run, either continuously or in at least four steps However, static samplers may be exempt from this requirement if they are designed to maintain a preferred orientation to the wind, are omnidirectional, or are used in fixed positions relative to forced ventilation.
For testing samplers, particles must be spherical or nearly isometric, whether solid or liquid The degree of agglomeration in the test aerosol can be assessed through visual microscopic inspection of particles collected on slides in the wind tunnel or test chamber Typically, the chemical composition of the test aerosol is considered non-influential; however, if a critical review indicates a potential composition-related effect on particle retention on sampler surfaces, this should be acknowledged in the test report.
6.3.6 Sampled or internally separated mass
The test aims to assess the dependency of the sampler efficiency curve on the collected or internally separated mass, rather than to evaluate analytical errors The dust sampled, calculated as the rosol concentration multiplied by the sampled volume, should not exceed typical workplace sampling values unless proven insignificant If testing is conducted, it is essential to select a maximum concentration and sampling duration that align with the intended measurement tasks.
NOTE An example of such a test is given in EN 13205–5:2014, 6.5.5 and its evaluation in EN 13205–5:2014, 7.4.7
When testing a non-conducting sampler, it should be evaluated using a neutralized aerosol, unless it can be proven that the performance with charged aerosols during mechanical generation and dispersal is not significantly different However, the results may not accurately represent performance in typical sampling scenarios where charged aerosols are present It is essential to minimize electrostatic influences whenever possible.
4) See Bibliography, reference [8], for the data presented by BALDWIN and MAYNARD
5) See, for example, Bibliography, reference [9] on a study regarding the electrical charge on dry airborne particles produced by mechanical aerosol generators and Bibliography, reference [10] on a study regarding the effect of electrical particle charge on cyclone penetration choosing samplers made from conducting materials, cleaning them thoroughly, and earthing them during the tests where the information for use requires it
NOTE The given requirements are compulsory for personal thoracic and respirable samplers only
Testing should be conducted on commercial samplers rather than prototypes, with a preference for used specimens over new ones, and the age of these specimens must be specified In cases where variability among specimens is expected to be minimal, a minimum of six test results should be collected, although tests may be repeated on two specimens (refer to EN 13205-1:2014, Tables 2 and 3).
6.3.9 Excursion from the nominal flow rate
NOTE The given requirements are compulsory for thoracic and respirable samplers only
Flow dependence should be evaluated at the wind speed that best represents actual usage conditions If reliable data exists in published literature, additional testing is unnecessary All candidate sampler specimens must maintain non-nominal flow rates within ± 5% to ± 10% of the nominal flow rate.
Surface treatments include greasing and cleaning collection substrates, neutralizing filters and foams, and cleaning samplers It is essential to clearly state and explain any differences between the surface treatments tested and those recommended in the sampler's usage information.
7.1 The experimental system shall have the characteristics as described in 7.2 to 7.12
7.2 The experiments shall be carried out in an environment with temperature from 15 °C to 25 °C, pressure
The sampler is designed for use in environments with a pressure range of 960 hPa to 1050 hPa and relative humidity between 20% and 70% If the sampler is intended for more extreme conditions, those specific conditions must be closely replicated The test report will include a comprehensive description of the test environment, along with documentation of the actual conditions present during testing.
7.3 Tests may be carried out with either polydisperse or monodisperse aerosols, or a combination of both 6 ) When monodisperse test aerosols are used, a single experiment gives rise to a single measurement of sampling efficiency at a single aerodynamic diameter Therefore it is necessary to use (at least) nine different aerosols in order to obtain sampling efficiency values corresponding to at least nine particle sizes, covering the desired range (as required in Table 1) Correction factors for particle shape and particle density, where used, shall be determined for each aerosol 7 ) or obtained from appropriate reliable literature With a polydisperse aerosol a single experiment gives rise to several sampling efficiency values corresponding to adjacent aerodynamic diameters within the desired range Correction factors for particle density and shape, where used, shall be determined as functions of particle size The test aerosols shall consist of non- condensing, non-evaporating and non-coagulating particles
7.4 The choice of aerosol depends on the availability of a suitable method for the measurement of particle aerodynamic diameter; this may be done by any method having a unique, monotonic calibration curve over
6) For examples of published performance evaluations using polydisperse aerosols (generally for respirable or thoracic samplers) see Bibliography, references [11] to [18]
General
A sampler's performance is assessed through its bias and expanded uncertainty, as outlined in CEN/TR 13205-3 This standard describes two calculation methods: polygonal approximation and curve-fitting The polygonal approximation is typically applied when multiple sampler candidates are tested at the same time with monodisperse test aerosols, while curve-fitting is preferred for sequential testing of candidates using polydisperse test aerosols Published papers with worked examples of these calculations are referenced for further guidance.
The experimental data includes aerosol concentration values obtained from both the candidate sampler and sharp-edged probes, analyzed based on particle aerodynamic diameter Additional data sets can be gathered for various influencing factors, such as external wind speed and sampler mass loading Consequently, the calculations outlined will be repeated for each set of measured efficiency values corresponding to the tested influence variables Accurate measurements are challenging and necessitate advanced equipment For reliable estimates regarding grid-generated turbulence, refer to Bibliography, reference [28].
Determination of the sampling efficiency
To determine the sampling efficiency value, \( e \), for each particle size and influence variable, we analyze all tested candidate sampler individuals and their repeats The efficiency is calculated using the formula \( e_{ipr[s]} = g_{ipr[s]} \cdot h_{ipr} \) for polygonal approximation, and \( e_{ips[r]} = g_{ips[r]} \cdot h_{ips[r]} \) for curve-fitting.
The calculated efficiency value for the polygonal approximation method is denoted as \$e_{ipr}[s]\$, while the efficiency value for the curve-fitting method is represented as \$e_{ips}[r]\$ The concentration measured by the candidate sampler is indicated as \$g\$ (in mg/m³ or 1/m³), and the concentration measured by the sharp-edged probe(s) is represented as \$h\$ (also in mg/m³ or 1/m³).
The subscripts i, p, r and s enumerate influence variable values, particle size, repeat experiment and tested candidate sampler individual, respectively
The concentrations measured by the sharp-edged probe, h, may require adjustments prior to calculating the sampling efficiency values, e, as outlined in Formula (1), or before they are modeled through curve-fitting techniques, such as those described in CEN/TR 13205-3.
To determine sampling efficiency curves from the individual values e ipr[s] and e ips[r], utilize one of the methods outlined in CEN/TR 13205-3 If employing polygonal approximation, calculate a mean sampling efficiency value for each test particle size and for each influence variable, E i ( ) D p.
When employing curve-fitting, it is essential to create a distinct sampling efficiency curve for each value of an influence variable for every candidate sampler The fitted curve must be physically reasonable, approaching an efficiency value of unity at an aerodynamic diameter of zero and an efficiency value of zero at large aerodynamic diameters, unless the sampler exhibits different behavior Additionally, the curve should demonstrate minimal lack of fit to ensure accuracy.
A regression curve may exhibit an unreasonable shape when it is extrapolated beyond the particle size range for which it was originally fitted In such cases, any non-physical segments of the curve should be replaced with a linear extrapolation to ensure accuracy.
Calculation of sampler bias
Calculation of the sampled aerosol concentration
This article presents two methods for calculating sampled aerosol concentration, allowing researchers to choose the most suitable approach based on their experimental data For detailed guidance on employing these methods for accurate calculations, refer to CEN/TR 13205-3.
For samplers designed to capture the inhalable fraction, the maximum particle size for calculations, as specified in sections 8.3.1.2, 8.3.1.3, and 8.3.2, is set at 90 µm This upper limit applies regardless of whether the sampler collects larger particles, as the inhalable fraction is not defined for particles exceeding 100 µm.
Calculate the mean sampled relative concentration, C i , which can be approximately calculated for each aerosol size distribution A using the summation according to Formula (2):
C i is the mean sampled relative concentration and is a function of the sampled aerosol size distribution, A;
D A is the mass median aerodynamic diameter of the sampled aerosol, A;
E i ( ) D is the mean sampling efficiency of the candidate sampler for influence variable value ς i ;
N P is the number of test particle sizes;
W p is a function of the aerosol size distribution A; and σ A is the geometric standard deviation of the sampled aerosol, A
NOTE For information on how the W p values can be calculate over the whole of the summation range, see FprCEN/TR 13205–3:2012, 5.4.1
Calculate the mean sampled relative concentration, C i , which can be calculated for each aerosol size distribution A using the integral according to Formula (3):
A D ( A ,σ A ,D ) is the relative lognormal aerosol size distribution, with mass median aerodynamic diameter D A and geometric standard deviation σ A, [1/μm];
C i is the mean sampled relative concentration and is a function of the sampled aerosol size distribution, A;
D A is the mass median aerodynamic diameter of the sampled aerosol, A;
D min is the lower limit of the integral;
D max is the upper limit of the integral;
11) For a discussion of the potential difference between an inhalable sampler that has a sharp (impactor-like) cut off at
100 àm and a more realistic sampler, see Bibliography, reference [29] est E is ( ) D is the mean sampling efficiency of the candidate sampler for influence variable value ς i ;
N S is the number of candidate sampler individuals; and σ A is the geometric standard deviation of the sampled aerosol, A
The integral can be numerically evaluated using an appropriate method that achieves a numerical error of less than one part in 10,000 The integration limits, \(D_{\text{min}}\) and \(D_{\text{max}}\), are determined by the value of the integrand.
A est E is ( ) D is less than 0,5 × 10 −3 , or for inhalable samplers when D max is equal to the maximum aerodynamic diameter value tested in the experiments For more information, see CEN/TR 13205-3:2014, 5.5.1.
Calculation of the ideal sampled aerosol concentration
The concentration of the sampled aerosol size distribution, denoted as C std, is determined through numerical integration using the ideal sampler This calculation involves substituting the relevant sampling convention, F D ( ), for the measured sampling efficiency, as outlined in the provided formulas.
A D ( A ,σ A ,D ) is the relative lognormal aerosol size distribution, with mass median aerodynamic diameter D A and geometric standard deviation σ A, [1/μm];
C std is the concentration that would be sampled by a sampler that perfectly follows the sampling convention and is a function of the sampled aerosol size distribution, A;
D A is the mass median aerodynamic diameter of the sampled aerosol, A;
D max is the upper limit of the integral;
D min is the lower limit of the integral;
F D ( ) is the sampling convention relevant to the candidate sampler;
N P is the number of test particle sizes;
W p is a function of the aerosol size distribution A; and σ A is the geometric standard deviation of the sampled aerosol, A
According to CEN/TR 13205-3:2014, section 4.4.1, the polygonal approximation provides guidance on determining the integral values at the boundaries of the summation range In contrast, when employing the curve-fitting method, the integration limits must align with those specified in Formula (3).
12) For example by using Romberg integration, see Bibliography, reference [30].
Calculation of the sampler bias
For any aerosol size distribution A, the bias in the sampled concentration is defined according to Formula (5) as
C std represents the concentration measured by a sampler adhering to the sampling convention, which depends on the aerosol size distribution, A The correction factor, c, is specified in the manufacturer's instructions or the applicable measuring procedure.
C i is the mean sampled relative concentration and is a function of the sampled aerosol size distribution, A;
D A is the mass median aerodynamic diameter of the sampled aerosol, A;
The bias or relative error in aerosol concentration measured by the candidate sampler for aerosol size distribution A at the influence variable value ς i is denoted as ∆ i, while σ A represents the geometric standard deviation of the sampled aerosol A.
Only correction factors specified in the manufacturer's instructions or relevant measuring procedures are permitted for adjusting the bias of a sampler No alternative correction factors should be applied to the sampled concentrations In the absence of a stated correction factor, a value of 1.00 is assigned The selected value for the correction factor must be clearly indicated in the sampler test report.
Calculate the bias values for the aerosol size distributions listed in Table 2, and present these values in a test report Additionally, create bias maps that illustrate the σ A and D A values on the axes, connecting points of equal bias to form contours A separate diagram should be generated for each tested wind speed or influencing variable The aerosol size distributions relevant to the sampler's performance assessment, as detailed in Table 2, must be clearly marked on the bias maps.
Calculation of the expanded uncertainty of the sampler
General
The sources of uncertainty components of an aerosol sampler associated with the sampler, its calibration and flow deviations from nominal flow rate are
— calibration of sampler test system (see 8.4.2);
— estimation of sampled concentration (see 8.4.3);
— bias relative to the sampling convention (see 8.4.4);
— excursion from the nominal flow rate (see 8.4.6)
Uncertainty in aerosol measurements is influenced by factors such as aerosol size distribution A, wind speed, and sampler loading To streamline the data analysis, the process involves several steps: first, calculate the root mean square (RMS) of each uncertainty component for all aerosol size distributions listed in Table 2, based on the values of the influence variables; second, combine the variances of the five uncertainty components into a single standard uncertainty squared for each influence variable; third, if possible, assign a combined standard uncertainty squared to each distinct value of the influence variables; fourth, if distinguishing between values is not feasible, identify the largest combined standard uncertainty squared among the influence variable values and use it as the sampler's combined standard uncertainty squared; finally, the overall combined standard uncertainty of the sampler is obtained by taking the square root of this value.
The expected values presented are indicative of reasonably optimized experiments and samplers, highlighting the anticipated magnitudes rather than definitive measurements Calibration uncertainties in the experimental test system may contribute a measurement uncertainty component of 0.01 to 0.02 Additionally, the calculated concentration may also exhibit a similar uncertainty range Variability among individual samplers could introduce a measurement uncertainty component of 0.03 to 0.07, while bias related to the sampling convention may result in an uncertainty component of 0.05 to 0.10, depending on the optimization of the sampler Poorly optimized samplers could experience uncertainties as high as 0.20 to 0.25 For samplers targeting respirable and thoracic aerosol fractions, deviations from the nominal flow rate may lead to measurement uncertainties of 0.02 to 0.05 when using nominal flow rates, and 0.05 to 0.09 when actual flow rates are applied Inhalable aerosol fraction samplers are expected to have a flow deviation uncertainty of approximately 0.03.
In addition to the sampling per se, a measuring procedure for an aerosol fraction consists additionally of the three stages:
1) Flow measurement, 2) Transport of samples back to the analytical laboratory and 3) (chemical) Analysis A complete evaluation of a measuring procedure requires knowledge of the losses/ biases (and possible corrections) and the uncertainties of these stages EN 13205-1:2014, Annex A specifies how the expanded uncertainty is calculated for a measuring procedure.
Calibration of sampler test system
In a well-structured experiment, the uncertainty related to the calibration of the sampler test system should be minimal This uncertainty can be determined by propagating errors from the diameter of the calibration particles, and may also involve using calibration functions for particle sizers to assess the uncertainty in the sampled mass fraction.
Calibration uncertainty arises from the accuracy of the known absolute sizes of test particles, which directly affects the uncertainty in calculated concentration This uncertainty includes both non-random and random components, stemming from factors such as monodisperse test aerosols, calibration particles used in conjunction with polydisperse test aerosols, and conversion functions that translate volume equivalent diameters into aerodynamic diameters.
The mixed non-random and random uncertainty of the mean sampled aerosol concentration, attributed to calibration uncertainty, is quantified as a fraction of the standard concentration (C std) This uncertainty is calculated for each value of the influencing variable as a root mean square (RMS) across all N standard deviation (SD) aerosol size distributions (A) This measurement is referred to as u CandSampl-Calibr i, in accordance with CEN/TR 13205-3:2014, section 5.4.3.2.
5.5.3.2, give examples of how this is calculated for the polygonal approximation and the curve-fitting methods, respectively, based on the uncertainty of the sizes of the test particles.
Estimation of sampled concentration
The uncertainty in estimating the sampled concentration arises from the accuracy of the model used to describe sampling efficiency The polygonal approximation method accounts for the limitations of polygonal approximation, as well as the uncertainties in concentrations measured by the candidate sampler and sharp-edged probes Conversely, the curve-fitting method considers the uncertainty in estimated regression models and any adjustments made to measured sampling efficiencies due to temporal or spatial variations In both approaches, the uncertainty is quantified through error propagation, illustrating how these uncertainties affect the calculated concentration.
The random uncertainty in the mean sampled aerosol concentration, attributed to model uncertainties, is quantified as a fraction of the standard deviation (C std) This uncertainty is calculated for each value of the influencing variables using a root mean square (RMS) approach across all data points.
The N SD aerosol size distributions are defined by the u CandSampl-ModelCalc i According to CEN/TR 13205-3:2014, sections 5.4.3.3 and 5.5.3.3, examples illustrate the calculation methods for both polygonal approximation and curve-fitting techniques, taking into account the model's uncertainty regarding sampling efficiency.
Bias relative to the sampling convention
The bias variability of the sampled concentration stems from the difference between the average actual sampling efficiency of the candidate sampler and the sampling convention
The non-random uncertainty in the mean sampled aerosol concentration arises from the differences in the average sampling efficiency curves of candidate samplers and the sampling convention This uncertainty, expressed as a fraction of C std, is calculated for each influence variable value as a root mean square (RMS) over all N standard deviation (SD) aerosol size distributions A It is referred to as \( u_{\text{CandSampl-Bias}}^i \) and is determined using Formula (6).
C std is the target sampled relative aerosol concentration;
C i is the mean sampled relative aerosol concentration; c is the candidate sampler correction factor for bias correction;
D A a is mass median aerodynamic diameter of the a th lognormal aerosol size distribution
The number of aerosol size distributions, denoted as N SD, is outlined in Table 2 The standard uncertainty of measurement, represented as u CandSampl-Bias i, accounts for bias (non-random errors) related to the sampling convention of the sampler at the influence variable value ς i.
The bias in aerosol concentration measured by the candidate sampler, denoted as ∆i, is influenced by the aerosol size distribution A and the i-th value of another variable, ςi Additionally, σA a represents the geometric standard deviation of the a-th lognormal aerosol size distribution A.
NOTE Formulae (2) and (3) describe how C i is calculated for the polygonal approximation and the curve-fitting methods, respectively.
Individual sampler variability
Random error uncertainty is determined using the standard deviations of aerosol concentration measured by candidate sampler individuals This calculation requires a complete set of sampling efficiency data from at least six samplers The polygonal approximation method relies on the variability of concentrations among these samplers, while the curve-fitting method focuses on the differences in their sampling efficiency curves In both approaches, the uncertainty in the calculated concentration is derived from the variations in sampling efficiency between the individuals.
NOTE These differences mainly occur for samplers of the respirable and thoracic aerosol fractions with internal penetration that depends on geometry and surface smoothness, e.g cyclones, horizontal elutriators and impactors
The random uncertainty of the mean aerosol concentration, arising from the variability in measured and calculated concentrations, is quantified as a fraction of the standard deviation (C std) This uncertainty is calculated for each value of the influencing variable as a root mean square (RMS) across all N standard deviation aerosol size distributions (A) This measure is referred to as \( u_{CandSampl-Variability} \).
CEN/TR 13205-3:2014, 5.4.3.4 and 5.5.3.4, give examples of how this is calculated for the polygonal approximation and the curve-fitting methods, respectively, based on the measured differences in sampling efficiency.
Excursion from the nominal flow rate
8.4.6.1 Candidate samplers without any coupling between flow rate and internal penetration, e.g samplers for the inhalable aerosol fraction
The impact of flow deviation on the calculated fractional concentration is directly related to the pump's capability to maintain a consistent flow rate, limited by a maximum allowable deviation of ±δ Pump According to EN ISO 13137 standards, the specified value for δ Pump is 0.05.
The random uncertainty in the mean sampled aerosol concentration, attributed to flow rate deviations and aerosol size distribution A, is quantified as a fraction of C std This uncertainty is calculated as a root mean square (RMS) across all N standard deviation aerosol size distributions A for each influence variable Assuming a rectangular distribution, the RMS source of uncertainty, denoted as \( u_{\text{CandSampl-Flow} i} \), is derived from the formula \( u_{\text{CandSampl-Flow} i}^2 = \delta_{\text{Pump}}^2 \).
C std is the target sampled relative aerosol concentration;
C i is the mean sampled relative aerosol concentration, for aerosol size distribution A, at influence variable value ς i ;
D A a is mass median aerodynamic diameter of the a th lognormal aerosol size distribution A;
The number of aerosol size distributions, denoted as N SD, is outlined in Table 2 The standard uncertainty in measurement, represented as u CandSampl-Flow i, arises from deviations in flow rate influenced by the variable value ςi Here, ςi refers to the i-th value of another influencing variable, while σ A a indicates the geometric standard deviation of the a-th lognormal aerosol size distribution A.
8.4.6.2 Candidate samplers with a coupling between flow rate and internal penetration, e.g samplers for the respirable and thoracic aerosol fractions
The effectiveness of samplers for respirable and thoracic sampling is significantly influenced by the sampling flow rate The uncertainty related to deviations from the nominal flow rate is determined by analyzing how errors in flow rate affect the variability in the sampled mass fraction.
The flow excursion effect on sampled concentration arises from two competing influences of flow rate deviations from the nominal rate Firstly, a higher volumetric flow rate leads to an increased mass flow of aerosol entering the sampler Secondly, this increased flow rate typically enhances the separation power of the sampler.
NOTE 1 Examples of samplers that decrease the penetration with increased flow rate are samplers whose separation is based on inertia, e.g cyclones and impactors On the other hand, the penetration of horizontal (or vertical) elutriators (which is based on sedimentation) is increased with increased flow rate
When measuring with a sampler, flow rate deviation consists of two components: the first is the difference from the nominal flow rate, defined by the allowed relative flow rate deviation, ±δ FlowSet, and the second is the pump's ability to maintain a constant flow rate during sampling, limited by the maximum allowed relative flow rate deviation, ±δ Pump According to EN ISO 13137, δ Pump is set at 0.05 If a measurement procedure or sampling protocol demands stricter flow stability, this specified value should be applied for δ Pump in subsequent calculations.
The non-random uncertainty in the mean sampled aerosol concentration, attributed to flow rate deviations and aerosol size distribution A, is quantified as a fraction of C std This uncertainty, denoted as u CandSampl-Flow i, is computed as the root mean square (RMS) across all N standard deviation (SD) aerosol size distributions A, following the calculations outlined in Formulae (8) to (12).
The dependence on the flow rate of the mass that is sampled by the sampler (expressed as a fraction of the mass aspirated into the sampler), m i D A a ,σ A a ,Q
( ), can be expressed according to Formula (8) as m i D A a ,σ A a ,Q
D A a is mass median aerodynamic diameter a of lognormal aerosol size distribution A; m i D A a ,σ A a ,Q
( ) is the mass collected when sampling from the a th lognormal aerosol size distribution
A using flow rate Q (see Formula (10));
Q 0 is the nominal flow rate;
Q is the a flow rate (other than the nominal flow rate) for which the sampling efficiency was determined; qi D A a ,σ A
( a ) is the coefficient expressing the influence of the flow rate on the collected mass (see
Formula (9)); and σ A a is the geometric standard deviation of the a th lognormal aerosol size distribution A qi D A a ,σ A
( a ) is the regression coefficient estimated from the regression model without intercept, see Formula (9): qi D A a ,σ A
The calculation of m i depends on whether the polygonal approximation or the curve-fitting method is used, see Formula (10): m i D A a ,σ A a ,Q
A D ( A ,σ A ,D ) is the distribution function of the lognormal aerosol size distribution A;
D A a is mass median aerodynamic diameter a of lognormal aerosol size distribution A;
E i ( ) Q,D p is the sampling efficiencies at sampler flow rate Q estimated with the polygonal approximation method; est E i ( ) Q,D is the sampling efficiencies at sampler flow rate Q estimated with the curve-fitting methods; m i D A a ,σ A a ,Q
( ) is the mass collected when sampling from the a th lognormal aerosol size distribution
A using flow rate Q (see Formula (10));
Q is the actual flow rate for which the sampling efficiency was determined;
The function \( W_p \) is dependent on the aerosol size distribution \( A \), as detailed in CEN/TR 13205–3:2012, section 5.4.1, which outlines the calculation of \( W_p \) values across the entire summation range Additionally, \( \sigma_{A_a} \) represents the geometric standard deviation of the \( a \)-th lognormal aerosol size distribution For each aerosol size distribution \( a \) and corresponding influence variable value, the uncertainty due to flow deviation, denoted as \( s_{CandSampl-Flow_{ia}} \), can be estimated using Formula (11) as \( s_{CandSampl-Flow_{ia}} \approx q_i D_{A_a, \sigma_A} \).
( ) = C i is calculated according to Formulae (2) and (3) for the polygonal approximation and the curve-fitting methods, respectively qi D A a ,σ A
The coefficient \( a \) indicates how the flow rate affects the collected mass, while \( q_0 \) varies based on whether the sampled concentration is calculated using the actual flow rate (\( Q \) leading to \( q_0 = 0 \)) or the nominal flow rate (\( Q_0 \) leading to \( q_0 = 1 \)) The uncertainty in the sampled concentration, denoted as \( s_{CandSampl-Flow} \), arises from deviations from the nominal flow and initial flow for the \( a \)th aerosol size distribution at the influence variable \( ς_i \) Additionally, \( δ_{FlowSet} \) represents the maximum allowable relative error in setting the flow rate, while \( δ_{Pump} \) indicates the maximum relative change in flow rate permitted due to pump stability.
NOTE 2 It is only for samplers with decreased penetration with increased flow rate that it makes sense to calculate the concentration based on the nominal flow rate u CandSampl-Flow i is finally calculated from Formula (12): u CandSampl-Flow i 2= 1
C std is the target sampled relative aerosol concentration;
The number of aerosol size distributions, denoted as N SD, is outlined in Table 2 The variable s CandSampl-Flow ia is determined using Formula (11), while u CandSampl-Flow i represents the standard measurement uncertainty resulting from flow rate deviations at the influence variable value ς i.
Combined uncertainty (of measurement)
The combined standard uncertainty is made up of two components: the random error, denoted as \$u_{CandSampl-R}^i\$, and the non-random error, represented as \$u_{CandSampl-nR}^i\$ The calculation of these components varies based on the presence or absence of coupling between the flow rate and the internal penetration of the candidate sampler For instance, samplers designed for inhalable aerosol fractions do not exhibit this coupling, while those for respirable and thoracic aerosol fractions do.
8.4.7.2 Candidate sampler without any coupling between the flow rate and internal penetration
In a candidate sampler that operates independently of the flow rate and internal penetration, the total uncertainty can be calculated by summing the variances from both random and non-random sources for each influencing variable According to Formula (13), the uncertainty for the candidate sampler is expressed as: \[u_{\text{CandSampl-R} i}^2 = u_{\text{CandSampl-ModelCalc} i}^2 + u_{\text{CandSampl-Variability} i}^2 + u_{\text{CandSampl-Flow} i}^2\]Additionally, the non-random uncertainty is given by:\[u_{\text{CandSampl-nR} i}^2 = u_{\text{CandSampl-Calibr} i}^2 + u_{\text{CandSampl-Bias} i}^2\]
The candidate sampler's standard uncertainty of measurement is influenced by several factors at the variable value \( \varsigma_i \) These include bias uncertainty (\( u_{\text{CandSampl-Bias} i} \)), calibration uncertainty (\( u_{\text{CandSampl-Calibr} i} \)), flow rate deviation uncertainty (\( u_{\text{CandSampl-Flow} i} \)), model fitting uncertainty (\( u_{\text{CandSampl-ModelCalc} i} \)), combined uncertainty from non-random errors (\( u_{\text{CandSampl-nR} i} \)), combined uncertainty from random errors (\( u_{\text{CandSampl-R} i} \)), and variability among sampler individuals (\( u_{\text{CandSampl-Variability} i} \)).
8.4.7.3 Candidate sampler with a coupling between the flow rate and internal penetration
For a candidate sampler that exhibits a coupling between flow rate and internal penetration, the variances of both random and non-random sources of uncertainty must be calculated for each influence variable This is done using the following formula: \$$u_{\text{CandSampl-R} i}^2 = u_{\text{CandSampl-ModelCalc} i}^2 + u_{\text{CandSampl-Variability} i}^2\$$ Additionally, the non-random uncertainty is expressed as: \$$u_{\text{CandSampl-nR} i}^2 = u_{\text{CandSampl-Calibr} i}^2 + u_{\text{CandSampl-Bias} i}^2 + u_{\text{CandSampl-Flow} i}^2\$$
The candidate sampler's standard uncertainty of measurement is influenced by several factors at the variable value ς i These include bias relative to the sampling convention (u CandSampl-Bias i), calibration uncertainty (u CandSampl-Calibr i), flow rate deviation (u CandSampl-Flow i), and uncertainty from the fitted model (u CandSampl-ModelCalc i) Additionally, the combined uncertainty due to non-random errors is represented as u CandSampl-nR i, while random errors are captured by u CandSampl-R i Lastly, variability among sampler individuals contributes to the standard uncertainty denoted as u CandSampl-Variability i.
8.4.7.4 Combined uncertainty per influence variable value
To calculate the combined uncertainty of measurement for each influence variable value, use Formula (15): \$$u_{\text{CandSampl}, i} = \sqrt{u_{\text{CandSampl-R}, i}^2 + u_{\text{CandSampl-nR}, i}^2}\$$ In this formula, \$u_{\text{CandSampl}, i}\$ represents the candidate sampler's total combined uncertainty due to both random and non-random errors at the influence variable value \$\varsigma_i\$ The term \$u_{\text{CandSampl-nR}, i}\$ accounts for the uncertainty from non-random errors, while \$u_{\text{CandSampl-R}, i}\$ reflects the uncertainty from random errors, both evaluated at the same influence variable value.
8.4.7.5 Distinction between different values of the influence variables
When it is possible to differentiate between various values of influence variables during the sampling or analytical stages, the combined standard uncertainty of the sampler is influenced by the specific value of the influence variable at the time of sampling, such as wind speed.
NOTE This implies that the reported expanded uncertainty will be a function of the distinguishable values of the other influence variables,ς
For these cases the combined standard uncertainty (for example for influence variable value I) can be given by Formula (16) as: u CandSampl =u CandSampl (ς I )=u CandSampl I
I is the value of the enumerating subscript for a selected value of influence variable value, ς;
N IV represents the number of values for the other influencing variables tested The combined standard uncertainty of the candidate sampler, denoted as \( u_{\text{CandSampl}} \), accounts for both random and non-random errors and is essential for calculating the expanded uncertainty, as outlined in Formula (19).
The candidate sampler's combined standard uncertainty, denoted as I, accounts for both random and non-random errors associated with the specific influence variable value \( \varsigma_i \), while \( \varsigma \) represents the values of other influence variables.
Determine also the corresponding combined measurement uncertainties due to random and non-random errors, respectively, at influence variable valueς I , namely u CandSampl-R I andu CandSampl-nR I
8.4.7.6 Non-distinction between different values of the influence variables
When it is impractical to differentiate between various values of influence variables during sampling or analysis, the maximum combined standard uncertainty for any influence variable, such as wind speed, is chosen as the standard uncertainty applicable to all values of that variable.
NOTE This means that the reported expanded uncertainty will be independent of the indistinguishable values of the other influence variables,ς
For these cases the combined standard uncertainty is calculated from Formula (17) as: u CandSampl =max i≤N IV { u CandSampl i } (17) where
N IV represents the number of values for the other influence variables tested The combined standard uncertainty of the candidate sampler, denoted as \( u_{\text{CandSampl}} \), accounts for both random and non-random errors and is essential for calculating the expanded uncertainty, as outlined in Formula (19) Additionally, \( u_{\text{CandSampl}_i} \) refers to the combined standard uncertainty at a specific influence variable value \( \varsigma_i \), while \( \varsigma \) signifies the values of the other influence variables.
The maximum combined standard uncertainty for the candidate sampler occurs at the influence variable value \(i = i_0\), calculated using Formula (18) as \(u_{\text{CandSampl}} = u_{\text{CandSampl } i_0}\) Here, \(i_0\) represents the subscript value of the influence variable that results in the highest combined standard uncertainty The term \(u_{\text{CandSampl}}\) denotes the candidate sampler's combined standard uncertainty, which accounts for both random and non-random errors, essential for determining the expanded uncertainty as outlined in Formula (19) Additionally, \(u_{\text{CandSampl } i_0}\) refers to the combined standard uncertainty specific to the influence variable value \(ς_{i_0}\), while \(ς\) indicates other influence variable values.
Determine also the corresponding combined measurement uncertainties due to random and non-random errors, respectively, at influence variable valueς i0 , namely u CandSampl-R i0 andu CandSampl-nR i0
Expanded uncertainty
The expanded standard uncertainty for the aerosol sampler, U CandSampl , is calculated from the combined standard uncertainty using a coverage factor of 2
U CandSampl is the candidate sampler’s expanded uncertainty (of measurement); and u CandSampl is the candidate sampler’s combined uncertainty (of measurement)
In situations where it is possible to differentiate between various values of influence variables during the sampling or analytical stages, the expanded uncertainty of the sampler is contingent upon the specific value of the influence variable at the time of sampling.
The calculation of the expanded uncertainty for a complete measuring procedure, i.e incorporating also the stages transport, storage, sample preparation and sample analysis, is described in EN 13205-1:2014, Annex A