implementing department  
author  
starting material  
limit value [mg/m³]    
period of validation  
charging method  
method description  
number of tested concentrations  

Uncertainty associated with sampling, sample storage and transportation

 

Uncertainty associated with sampled air volume

pump flow stability [%]  
sampling time [min]
number of measurements of the flow rate, n
The uncertainty of flow rate calibration and the uncertainty of the flow meter indication are entered in the following two input fields. Examples of values for these uncertainties are listed in EN 482, Appendix B, Table B1. This table can be accessed by clicking on the info button next to the input fields.
calibration of the flow meter u(fc) [%]  
uncertainty of the flow rate reading u(fr) [%]  
sampling time u(t) [%]  
pump flow u(pfs) [%]  
u(sampled air volume) [%]

Uncertainty associated with sampling efficiency

If the sample volume for sampling of gases and vapours is kept well below the experimentally established breakthrough volume, the sampling efficiency is assumed to be 100% and the uncertainty of the sampling efficiency does not need to be taken into account. (see EN 482, annex B, B 3.1)
u(sampling efficiency) [%] 0,0

Uncertainty associated with sample storage and transportation

The calculation is based on the results of the storage test for two different concentrations (0.1 LV and 2 LV) with 6 replicate samples in each case. (LV: limit value)

concentration [mg/m³]
recovery at the beginning of storage [%]
recovery at the end of storage [%]
If the recoveries of the storage test concur with the results from the other recovery tests during validation, storage has no effect on the measurement result. The results of the storage test are then disregarded in the calculation of measurement uncertainty.


 
Δ r difference between the mean results of the replicate samples analysed at the beginning and at the end of the storage test
u(sample storage and transportation) [%] 0,00


Sum of random components of uncertainties of sampling, sample storage and transportation




Sum of non-random components of uncertainties of sampling, sample storage and transportation




Sum of random and non-random components of uncertainties of sampling, sample storage and transportation



Uncertainty of the analysis

 

Uncertainty associated with the method recovery

The calculation is based on the results of the recovery test for three different concentrations at a relative humidity of 50% and a temperature of 20°C. At least 6 samples have to be tested per concentration. Before calculating the measurement uncertainty, the user must check whether the mean value derived from the recoveries is permissible from one concentration in each case. The user must also define the limits from which recovery r is included in the calculation of the analysis result. E.g. The user decides that the mean recoveries in the range of 95% ≤ r ≤ 105% are disregarded in the calculation of the result. If the experimentally determined recoveries are within this range, the uncertainty is calculated in accordance with the following relationship. For mean recoveries of less than 95% or greater than 105%, the analysis result is corrected accordingly. The correction uncertainty is then calculated using the following relationship but without the term Bm/k because the bias has already been included in the calculation of the result by virtue of the recovery deviating significantly from 100%.


with
see EN 1076, equation B.6
umb the relative standard uncertainty associated with the method bias, in %
Bm the bias of the mean results from the reference concentration, in %
k the coverage factor used in the calculation of the expanded uncertainty, k = 2
Kv,rm the coefficient of variation of the replicate samples collected from a test atmosphere, in %
n number of replicate samples of a concentration of the recovery test; n must be at least 6.
urc   the relative standard uncertainty of the reference concentration of the test atmosphere, in %
r mean recovery of a concentration of the recovery test in %
inclusion of the recovery in the calculation of the analysis result
lower limit [%]
upper limit [%]
concentration [mg/m³]
K v,rm [%]
n
u rc [%]  
r [%]
B m [%]
u mb [%]  

Uncertainty associated with the effect of humidity

The calculation is based on the recoveries rh of sampling tests for a high concentration (e.g. 2 LV) and a low one (e.g. 0.1 LV), obtained in each case at relative humidities of 20% and 80%. 6 samplers are charged for each combination of concentration and humidity.
see EN 1076, equation B.7
uh the relative standard uncertainty associated with the effect of relative humidity on the recovery in %
Δ h the highest of the differences between the mean results of replicate samples collected from test atmospheres at relative humidities of 80 % and 20 %, in %
concentration [mg/m³]
relative humidity [%]
rh [%]
If the recoveries of this sampling test concur with the results of the other recovery tests during validation, humidity has no effect on the measurement result. The results of this test are then disregarded in the calculation of measurement uncertainty.

uh [%] 0,00

Uncertainty associated with the effect of temperature

The calculation is based on the recoveries rT of sampling tests obtained in each case at 10°C and 40°C with a concentration of 2 LV. 6 samplers are charged for each temperature.
see EN 1076, equation B.8
uT the relative standard uncertainty associated with the effect of temperature on the recovery in %
Δ T the difference between the mean results of replicate samples collected from test atmospheres at temperatures of 40 °C and 10 °C, in %
concentration [mg/m³]
temperature [°C]
rT [%]
If the recoveries of this sampling test concur with the results of the other recovery tests during validation, temperature has no effect on the measurement result. The results of this test are then disregarded in the calculation of measurement uncertainty.

u T [%] 0,00

The uncertainty component of the method precision

Method precision can be calculated from the results of at least 6 replicate samples per concentration, collected from test atmosphere with approximately 0,1 LV, 1 LV and 2 LV at a relative humidity of 50 % and a temperature of 20 ºC.

with
see EN 1076,equation B.9   see EN 1076,equation B.11
ump the relative standard uncertainty associated with the method precision, in %
Kv,m the coefficient of variation of the means, in %
n the number of replicate samples per concentration, n must be at least 6 and an equal number for all concentrations
Kvp,r the pooled coefficient of variation of the replicate samples, in %
Kv,1-3 the coefficient of variation of the means for a single concentration, in %
concentration [mg/m³]
mean recovery [%]
K v,1-3 [%]
n       
K v,m [%]    
K vp,r [%]    
u mp [%]    

The uncertainty components associated with the concentration of the calibration solutions

The uncertainty associated with the concentration of the calibration solutions depends on the purity of the starting material and on all the volume measurements during the production of the calibration solution. Weighing errors are considered negligible and are disregarded. If a relative deviation (in %) is entered in the following table, it is converted into a standard uncertainty for calculation of the measurement uncertainty, assuming a rectangular distribution. If the relative standard deviation of an uncertainty component is known, it is entered and can be included on the basis of the following relationship in the calculation of the uncertainty associated with the concentration of the calibration solutions.
see EN 1076, equation B.12
ucc the relative standard uncertainty associated with the concentrations of the calibration solutions, in %
um the relative standard uncertainty of the mass of pure compound weighed, in %
Kv,fi coefficient of variation of the flask used to prepare the calibration solutions, in %
Kv,pi coefficient of variation of the micropipette used to prepare the calibration solutions, in %
Kv,syi coefficient of variation of the syringe used to prepare the calibration solutions, in %
Bmax,fi the maximum bias of the flask used to prepare the calibration solutions, in %
Bmax,pi the maximum bias of the micropipette used to prepare the calibration solutions, in %
Bmax,syi the maximum bias of the syringe used to prepare the calibration solutions, in %

General note
In the first column of the following table in the fields under "volume measuring devices" in the pulldown menu, the volume measuring devices that were used in the production of the calibration solutions can be selected.

Notes on the random and non-random deviations
If the standard values are adopted for the calculation, a relatively unfavourable value is calculated for the uncertainty associated with the concentration of the calibration solutions. If this value is of a magnitude accepted by the user, the precise calculation of the random and non-random deviations of the employed volume measuring devices can be dispensed with.

Measuring flasks and cylinders, volumetric pipette
Random deviation: Input of an estimated value for the maximum, relative deviation that is to be expected during filling.
Non-random deviation: Input of the relative tolerance of the measuring device employed or of the standard values 0.5% for measuring flasks, 1.5% for measuring cylinders and 0.5% for volumetric pipettes. The numerical values for the absolute tolerance can be found in laboratory catalogues, for example. All the quoted values for the random and non-random deviations have to be converted into standard uncertainties by dividing them by √3.

Piston-driven micropipettes
Random deviation: Input of the coefficient of variation from the pipette's calibration certificate (CV value), standard value 0.4%.
Non-random deviation: Input of the measurement bias of the pipette employed from the calibration certificate (es-value, inaccuracy), or input of the standard value of 1.0%. The numerical values for the absolute tolerance can be found in laboratory catalogues, for example. The quoted values for non-random deviation must be converted into standard uncertainties by dividing them by √3.

Microlitre syringes
Random deviation: Input of the coefficient of variation (CV value), otherwise the standard value 1.0%.
Non-random deviation: Input of the measurement bias of the syringe employed (es-value, accuracy), or the standard value 1.0%. The quoted values for non-random deviation must be converted into standard uncertainties by dividing them by √3.

Dispenser
Random deviation: Input of the coefficient of variation (CV value), otherwise the standard value 0.5%.
Non-random deviation: Input of the measurement bias of the dispenser employed (correctness, es-value, accuracy), or the standard value 1.0%. The quoted values for non-random deviation must be converted into standard uncertainties by dividing them by √3.

Purity of the starting material
Random deviation: Uncertainty to which the content of the starting material is subject. If there is no information on the random deviation of the content, the value 0.2 is applied for contents greater than/equal to 99% and the value 0.6 for contents between 96 and 99%. These are estimated values for the relative standard deviation.
Non-random deviation: The user decides the deviation from 100% from which this is included in the calculation of the concentration.

deviation [%] standard uncertainty [%]
  random non-random random non-random
volume measuring devices                
purity of the starting material  
u cc [%] 0,00

Uncertainty component associated with the calibration function

The random uncertainty component associated with the calibration function can be calculated from parameters obtained by the least-squares linear regression. 2% is a reasonable estimate of the random uncertainty component associated with the calibration function and can be used in most cases (see EN 1076, B.6.4).
V x0 [%]

Uncertainty associated with instrument response drift

Methods and laboratory operating procedures generally specify a maximum instrument response drift that is permitted before recalibration (often monitored by repeat analysis of a calibration solution). It is necessary to take this non-random uncertainty component into consideration.
see EN 1076, equation B.14
u dr relative standard uncertainty associated with instrument response drift in %
d max the maximum instrument response drift permitted in the method or laboratory operating procedure, in %
d max [%]
u dr [%]

Calculation of the uncertainty of the analysis

concentration [mg/m³]    for data input
recovery, umb [%]    for data input
humidity, uh [%]    for data input 0,00
temperature, uT [%]    for data input 0,00
precision, ump [%]    for data input
concentration of the calibration solutions, ucc [%] for data input 0,00
calibration function, Vx0 [%]    for data input
instrument response drift, udr [%]    for data input
 
u a uncertainty of the analysis, in %
u a,i components of the uncertainty of the analysis, in %
The analysis uncertainty is only calculated when all the data required for calculation of the components of uncertainty have been entered. If data are missing, an "!" appears in the field below for the result of analysis uncertainty. In this case, it is essential to identify the colour-highlighted fields in the table above in which a numerical value is missing and to repeat the input.

concentration [mg/m³]
uncertainty of the analysis, ua [%] ! ! !

Combined standard uncertainty

 

Combined standard uncertainty

 
U [%] combined standard uncertainty, in %
k coverage factor, k=2 (see EN 482, chapter 6)
concentration [mg/m³]
expanded uncertainty, U [%]


Note on interpretation of the result
According to DIN EN 482 (April 2012), the relative expanded measurement uncertainty U of methods for measuring chemical agents is subject to the following requirements:
Short-time measurement: 0.5-fold to twice the limit value, U ≤ 50%
Long-time measurement: 0.1-fold to < 0.5-fold the limit value, U ≤ 50%
Long-time measurement: 0.5-fold to twice the limit value, U ≤ 30%

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