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III. QUALITY ASSURANCE AND
MANAGEMENT OF LABORATORY ACTIVITY
IN THE FIELD OF ENVIRONMENTAL
MONITORING AND CONTROL INCLUDING
SONIC AND ELECTROMAGNETIC POLLUTION
Laboratory Exercises
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III. 1. VALIDATION OF TEST METHODS
III.1.1. Theoretical Aspects
Validation means “confirmation by examination and prediction of objective
evidence that the particular requirements for a specified intended use are fulfilled”
(according to ISO 8402:1994).
Method validation means:
-The process of establishing the performance characteristics and limitations of a
method and the identification of the influences, which may change these
characteristics, and to what extent.
 Which analytes can be determined, in which matrices, in the presence
of which interferences?
 Within these conditions what levels of precision and accuracy can be
achieved?
-The process of verifying that a method is fit for a purpose, i.e. for solving a particular
analytical problem.
Verification means “confirmation by examination and prediction of objective
evidence proving that the specified requirements have been fulfilled” (according ISO
8402:1994).
It is necessary to make the difference between validation and verification.
Verification is applied for standardized methods and validation must be made for:
 non-standard methods;
 laboratory - designed / developed methods;
 standard methods used outside their intended purpose;
 standard methods.
Validation studies for analytical methods typically determine the following
parameters:
 detection limit;
 quantification limit;
 working range;
 selectivity;
 sensitivity;
 robustness;
 recovery;
 accuracy;
 precision ;
 repeatability ;
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
reproducibility.
The performance parameters being tested are selected depending on the
analytical requirements and based on the specifications from Table III.1.1.
Table III.1.1. Analytical requirements and the corresponding performance
parameters.
Analytical requirements
- Qualitative or quantitative answer?
For the analyte present in more than one
form, is important the extractable, free or
total analyte?
analyte(s) of interest and the most probable
level (%, g g-1, ng g-1 etc.)?
Level of precision and accuracy, allowed
uncertainty degree.
Possible interferences
Comparison of results with results from other
laboratories?
Comparison of the results with external
specifications?
Related performance parameters
Confirmation
of
identity,
selectivity/specificity,
Limit of detection
Limit of quantification
Recovery
Limit of detection
Limit of quantification
Working range
Recovery
Accuracy
Repeatability
Reproducibility
Selectivity/specificity
robustness
Reproducibility
Accuracy
Reproducibility
Limit of Detection (LoD) means:
the lowest content that can be measured with reasonable statistical certainty;
the lowest concentration of analyte in a sample that can be detected, but not
necessarily quantified under the stated conditions of the test;
the lowest analyte content, if actually present, that can be detected and can be
identified.
Where measurements are made for low concentrations of analyte (trace
analysis) it is important to know what is the lowest concentration of analyte that can
be confidently detected by the method. This problem must be analyzed statistically
and a domain of decision criteria must be proposed.
It is normally sufficient to provide an indication of the level at which detection
becomes problematic.
For quantitative measurements, 10 independent blank samples (a) or 10
independent blank samples fortified at lowest acceptable concentration (b) are
analyzed, measured a single time each, and the mean value and standard deviation
(s) of the blank sample is calculated for each set of measurements.
-
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LoD is expressed as the analyte concentration corresponding to:
a) mean value of the blank sample + 3 s;
b) 0 + 3 s or the mean value of the blank sample + 4.65 s
For qualitative measurements, is sufficient a critical concentration below
which the specificity can not be identified. Thus, for a series of concentration levels
are analyzed blank samples injected with analyte. For each concentration level it is
necessary to make 10 independent repeated measurements and a response curve of %
positive or negative results versus concentration should be constructed. From this
curve can be established, by interpolation, the threshold concentration at which the test
becomes unreliable.
Generally, the LoD, expressed in terms of concentration cL, or the quantity qL,
is derived from the smallest measurement xL, that can be detected with reasonable
certainty for a given analytical procedure. The value of xL is calculated with the
formula:
xL = xbl + k sbl
where : xbl is the mean value of the measurements for the blank sample of reagents; s bl
is the standard deviation of the measurements for the blank sample of reagents ; k is a
numerical factor chosen according to the desired confidence level.
Table III.1.2. Limit of detection
Measurements
Determination/Estimation
Optimum value
-
LIMIT OF DETECTION (LoD)
10 independent blank samples one time measured or
or 10 blank samples fortified at lowest acceptable
concentration , one time measured
LoD = 3s + X
in which:
s = standard deviation for the blank or blank fortified with
an analyte samples
X = measured value or mean measured value
function of tested method type
Limit of Quantification (LoQ), known as Quantifiable Limit means:
the content equal to or greater than the lowest concentration point on the
calibration curve;
the lowest concentration of analyte in a sample that can be determined with
acceptable repeatability and accuracy;
performance characteristics that mark the ability of a chemical measurement
process to adequately quantify an analyte.
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The ability to quantify is generally expressed in terms of the signal or analyte
value that will produce estimates having a specific relative standard deviation (RSD),
commonly 10%. The formula of calculation is:
LoQ = kQσQ
where: - σQ is the standard deviation at that point; kQ is the multiple whose reciprocal
equals the RSD. The IUPAC recommended value for kQ is 10.
The following analyses will be made:
10 independent blank samples measured once each and the standard deviation (s)
is calculated. LoQ is expressed as the concentration of the analyte corresponding
to the a blank sample value + 10s;
fortified aliquots of a blank sample at various analyte concentrations close to the
LoD and the standard deviation (s) of each concentration is calculated. (s) is
represented graphically against concentration and a value to the LoQ is
established by interpolation.
Table III.1.3. Limit of Quantification
LIMIT OF QUANTIFICATION (LoQ)
10 independent blanks one time measured
or
10 blank samples fortified at lowest acceptable
concentration , one time measured
Determination /Estimation LoQ = 10s + X
where:
s = standard deviation for the blank or blank fortified with
an analyte samples
X = measured value
function of tested method type
Optimum value
Measurements
Working Range – the analyte concentration interval or the value for which
the method can be applied is determined. Within the working interval can exist a
linear response interval. Sometimes also a nonlinear response range may be used , in
case of a stable situation and calculation by computer. Generally, linearity studying
involves at least 10 different concentrations / property values. Anywhere, in the
working range, multi - point (preferably 6+) calibration points will be necessary. It is
important to retain that the working range and linearity may be different for different
matrices due to the of interferences if they are not eliminated.
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Table III.1.4. Working range.
Measurements
Determination/Estimation
Optimal value/Interpretation
WORKING RANGE
From the calibrating curve with 6-10 ascending and
equidistant concentrations points
-The lower limit corresponds with LoD or LoQ
- The upper limit is established qualitatively by visual
examination of the linearity domain of the calibrating
curve or by regression coefficient determination
-In some cases can be used non - linear curves
Selectivity (or specificity) means “the ability of a testing method to determine
accurately and specifically the analyte of interest in the presence of other components
in a sample from a matrix, under the stated conditions of the test”.
According to IUPAC Compendium of Chemical Terminology (1987) [14],
selectivity in analysis means:
 for qualitative analyses – “the extent to which other substances interfere with the
determination of a substance according to a given procedure”
 for quantitative analyses – “a term used in conjunction with another substantive
(e.g. constant, coefficient, index, factor, number) for quantitative characterization
of interferences”.
It is necessary to establish the fact that the signal produced at the measurement
stage, or other measured property, which was attributed to the analyte, is only due to
the analyte and not from the presence of something chemically or physically similar or
arising as a coincidence. This is confirmation of identity.
Selectivity / specificity are measures which assess the reliability of measurements in
the presence of interferences.
The selectivity of a method is usually investigated by studying its ability to
measure the analyte of interest in test portions to which specific interferences have
been deliberately introduced.
Thus, firstly:
 analysis of the samples and reference materials by the selected or other
independent methods and use of the results from the confirmatory techniques to
assess the ability of the method to confirm analyte identity and its ability to
measure the analyte separately from other interferences. To which extent the
obtained data are reasonably sufficient to provide enough reliability is then
decided;
 analysis of the samples containing various suspected interferences in the presence
of analytes of interest and determination of the effect of interferences - if the
presence of the interference enhances or inhibits detection or quantification of the
measurands. If the detection or quantification is inhibited by interferences, further
method development will be required.
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Specificity is generally considered to be 100% selectivity.
Sensitivity
Sensitivity is “the slope of the response curve, i.e. the change in instrument
response function of the change in analyte concentration”.
Table III.1.5. Sensitivity.
Measurements
Determination/Estimation
SENSITIVITY
From calibrating curve with 6-10 ascending and
equidistant concentrations points
b= calibrating curve slope
or S = Δ Y/ Δ C
Optimal value
where:
S = sensitivity
Δ Y= absorbance variation
Δ C = concentration variation
-alternates on different concentration ranges
Robustness
The robustness test is used for the analysis of the behavior of an analytic
process when slight changes in the working conditions / operating parameters are
executed or by the evaluation of the effects on the results over a longer period.
Recovery
Recovery is “the fraction of analyte added to a test sample (fortified or
injected sample) before the measurement”. The percentage recovery R% is calculated
with the formula:
R% = [(CF-CU)/CA] x 100
where: - CF is the concentration of the analyte measured in the fortified sample; CU is
the concentration of the analyte measured in the unfortified sample; CA is the
concentration of the analyte added in the fortified sample.
Recovery can be determined analyzing CRM and reporting the concentration
found to the certified value.
Accuracy
Accuracy means “degree of concordance between the results of a test and the
accepted reference value”. The method validation seeks to quantify the accuracy of
the results by assessing systematic and random errors.
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Accuracy has two components: trueness and precision. The trueness of a
method is “the degree of concordance between the mean value obtained between a
large series of results for a test and the accepted reference value”.
Table III.1.6. Robustness.
Measurements
Determination /Estimation
Optimum value/Interpretation
ROBUSTNESS
On 4 sub-samples with the same known concentration
are executed measurements when three factors from the
working procedure are modified. The three factors (A,
B ,C) depend on the tested analysis stage.
For example, in the solvent extraction stage the three
factors can be:
- stirring time for the separation funnel,
- mL of extraction agent,
-temperature of sample to be extracted.
In the GC analysis – the three factors can be:
-chromatographic column length
-carrying gas flow
-working temperature
The parameters could be modified in the range ±10%
or less if major changes will occur. The amplified
factors will be marked (+) and the unchanged or
reduced factors with (–).
The Youden and Steiner scheme will be applied
Experiment
Factors
Result
A
B
C
1
+
+
Y1
+
2
+
Y2
3
+
Y3
+
4
Y4
The effect A = (∑ Y A+ - ∑ Y A- ) /2
Where : ∑ Y A+ is the sum of results Yi where factor A
has positive values
∑ Y A- is the sum of result Yi where factor A
has negative values
The effect B = (∑ Y B+ - ∑ Y B- ) /2
The effect C = (∑ Y C+ - ∑ Y C- ) /2
The effect of modified factor will be established by
applying the t-Student test or a strong modifying effect
will be considered if:
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The effect A ( B, C) > 1.4 s cc
s cc = initial method standard deviation from the control
chart.
The method will be considered robust if these
modifications do not have an important influence on
the theoretical values.
Table III.1.7. Accuracy
Measurements
Determination/Estimation
ACCURACY
10 analyses repeated for a known concentration
sample prepared from a reference material
(standard substance)
Accuracy % = ( X - μ ) x 100
where:
X = the mean of the 10 determinations
μ = the real value of the reference material
(standard substance)
Bias % =
Optimum value/Interpretation
X 

 100
-100%
-the obtained value will be checked using the tstudent test
Trueness is normally expressed in terms of bias and can be established by
using & analyzing Certified Reference Materials (with known concentration value and
confidence interval) or by analyzing the same sample by the method studied and
another standardized method. Than it is necessary to compare the results obtained and
to check if the result obtained by the developed method belongs to the confidence
interval
Precision is “a measure of the concordance degree between the independent
results of a test obtained in the provided conditions and is usually expressed as
function of the standard deviation that describes the distribution of the results”.
The precision is determined after 10 repeated analyses on a sample with
known concentration prepared from a reference material or from standard substance.
Repeatability
Repeatability and reproducibility represent the two measures of precision.
Repeatability (the smallest expected precision) will give information on the
variability of the method when replicates of the same sample are performed, by a
single analyst, on the same equipment, over a short period of time.
Usually repeatability and reproducibility depend on analyte concentration and
should be determined on a number of relevant concentrations levels.
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To determine the repeatability, the same analyst must analyze the same
samples or Reference Materials making 10 determinations, on the same equipment, in
a short timescale. Then the mean and standard deviation at each concentration must be
calculated.
Table III.1.8. Precision.
PRECISION
10 analyses repeated for a known concentration
sample prepared from a reference material
(standard substance)
Measurements
Determination/Estimation
CV ( RSD) % =
s
 100
X
where:
X = mean value of the 10 determinations
s = standard deviation
- depends on the tested method
Optimal value
Table III.1.9. Repeatability.
Measurements
Determination/Estimation
Optimal value
REPEATABILITY
10 analyses repeated for a known concentration
sample prepared from a reference material (standard
substance). The analyses will be achieved in the same
laboratory, by the same analyst, with the same
equipment, with the same method within close time
intervals
r = 2.8 x sr
where:
sr = repeatability standard deviation
-depends on the methods and the laboratory’s level of
proficiency
Reproducibility (the largest expected precision) will give information on the
variability of the method when the same sample is analyzed in different laboratories.,
by different analysts, on different equipment, over a long period of time.
To determine the intra-laboratory reproducibility, different analysts of the
same laboratory must analyze the same samples or Reference Materials making 10
determinations, on different equipment, in an extended timescale. Then the mean and
standard deviation at each concentration must be calculated.
To determine the inter-laboratory reproducibility, different analysts of
different laboratories must analyze the same samples or Reference Materials making
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10 replicates, on different equipment, in an extended timescale. For the interlaboratory reproducibility is necessary to organize a collaborative study.
Table III.1.10. Internal reproducibility.
INTERNAL REPRODUCIBILITY
10 analyses repeated for a known concentration
sample prepared from a reference material
(standard substance). The analyzes will be
conducted in the same laboratory by different
analysts, different equipments, the same
procedure at larger time intervals.
RL = 2.8 x 1.6 x sr = 1.6 x r
Determination/Estimation
where:
sr = repeatability standard deviation
r = repeatability
- depends of the methods and the laboratory’s
Optimal value
level of proficiency
Measurements
Once the validation process is complete it is important to document the
procedures so that the method can be clearly and unambiguously implemented. The
Method Documentation Protocol must contain:
 updates and review;
 title;
 scope;
 definitions;
 principle;
 normative references;
 reagents and materials;
 apparatus and equipment;
 sampling and samples;
 drawing of the calibration curve;
 procedure;
 calculation and expressing of the results including final units, ± uncertainty,
confidence interval.
Usually the Method Documentation Protocol can be created following the
content of a standard method.
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III.1.2. EXAMPLE OF CALCULATION OF VALIDATION
PARAMETERS
To calculate the Limit of Detection (LoD) and Limit of Quantitation (LoQ) for
a visible spectrophotometric developed method applied to the Cr6+ at input.
10 independent blank samples were analyzed, against water and the results
indicated in Table III.1.11 were obtained.
Table III.1.11. Results for LoD and LoQ.
Sample 1
Sample 2
Sample 3
Sample 4
Sample 5
Sample 6
Sample 7
Sample 8
Sample 9
Sample 10
Mean value - X
Standard deviation - s
3s
10s
LoD
LoQ
X + 3s
X +10s
Concentration, g in a 25 mL calibrated flask
0.1159
0.0982
0.0569
0.0645
0.1628
0.1804
0.0902
0.09
0.0452
0.0455
0.02786
0.106515
0.319546
1.065152
g
g/mL
0.457406
0.0169
1.093012
0.0437
Considered values:
LoD = 0.5 g CrO3 in the solution contained in 25 mL calibrated flask or 0.02 g
CrO3/mL solution;
LoQ = 1.1 g CrO3 in the solution contained in 25 mL calibrated flask or
0.044 g CrO3/mL solution.
If the volume of air sampled is 900 liters, the LoD and the LoQ become:
- LoD = mg CrO3 / cubic meter of air
- LoQ = mg CrO3 / cubic meter of air
Calculate the recovery of the method studied above.
The following were used:
- a sample containing 16 g Cr6+ fortified with 4 g Cr6+;
- a sample containing 24 g Cr6+ fortified with 6 g Cr6+;
-
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- a Certified Reference Material (CRM) having the 21.25 g Cr6+/mL as certified
value and a confidence interval between 20.60 – 21.91 g Cr6+/mL
The results obtained are centralized in Table III.1.12 and Table III.1.13.
Table III.1.12 .Recovery from fortified samples.
16 g Cr6+ fortified with
Determinat
ions no.
1
2
3
Mean
0 gCr6+
Absorb
ance
0.2810
0.2806
0.2799
-
4 gCr6+
Concen
tration.
g
16.4587
16.4351
16.3997
16.4312
Absorb
ance
0.3481
0.3423
0.3476
-
24g Cr6+ fortified with
0 g Cr6
Concen
tration.
g
20.4133
20.1246
20.3839
20.3073
Absorb
ance
0.4173
0.4175
0.4165
-
6 g Cr6
Concen
tration.
g
24.4918
24.5035
24.4691
24.4881
Absorb
ance
0.5180
0.5145
0.5169
-
Recovered
quantity
3.88
5.85
R%
96.90
97.52
Concen
tration.
g
30.4267
30.2204
30.3704
30.3392
Table III.1.13. Recovery and trueness from CRM
Determinations no.
1
2
3
4
5
6
7
Mean
R%
Trueness %
Results, in g Cr6+/mL
21.45
21.21
21.18
20.96
20.95
20.97
21.54
21.18
99.67
III.1.3. EXERCISE
To validate the 2,6-ditert-buthyl-phenol gas chromatography determination 10
consecutive determinations were made on a known concentration solution (μ = 0,100
mg/L) prepared from a certified reference material. The obtained values are:
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Sample 1
Sample 2
Sample 3
Sample 4
Sample 5
Sample 6
Sample 7
Sample 8
Sample 9
Sample 10
Concentration, mg/L
0.0952
0.0955
0.0987
0.1010
0.0996
0.0970
0.0970
0.0980
0.0950
0.0925
Using specific methods calculate the accuracy, bias, fidelity and the
repeatability for the proposed method.
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III.2. UNCERTAINTY OF MEASUREMENT
III.2.1. Theoretical Aspects
The word uncertainty means doubt, so, the uncertainty of measurement means
doubt about the validity of a result, as well as doubt regarding the exactness of the
result.
EN ISO/CEI 17025:1999 requires, first of all, to identify the sources of
uncertainty and to build the uncertainty budget.
The uncertainty of the result arises from many different sources, as:
- incomplete definition of the measurand;
- sampling;
- interferences and matrix effects;
- uncertainties of weighing and volumetric equipment;
- calibration of the equipments and reference materials;
- the ability of the analyst.
In estimation of the overall uncertainty, is necessary to take each source of
uncertainty and treat it separately to obtain its contribution. Each of the separate
contributions to uncertainty is referred to as an uncertainty component. If an
uncertainty component is expressed as standard deviation, it is known as standard
uncertainty.
When we combine by the law of propagation of uncertainty, all the
uncertainty components is obtained the combined standard uncertainty.
In analytical chemistry, usually, is reported the expanded uncertainty, obtained from
the combined standard uncertainty multiplied with a coverage factor depending on the
level of confidence.
In uncertainty estimation must be followed the next steps:
Step 1: Specification of the measured value. First of all a clear statement of
what is being measured, including relationship between the measurand and the
parameters, has to be written. The specification information is normally given in the
standard operating procedure (SOP) or another method description.
Step 2: Identify Uncertainty Sources. List the possible sources of uncertainty.
This list will include sources that contribute to the uncertainty of the parameters in the
relationship specified in Step 1, but not only, as well as sources arising from chemical
assumption.
Step 3: Quantify Uncertainty Components. All sources identified in step 2
must be, if possible, estimated. It is important to consider and plan carefully the
experiments and supplemental studies to ensure that all sources of uncertainty are
adequately calculated. The standard uncertainty associated to each source of
uncertainty is obtained.
Step 4: Calculate Total Uncertainty. The individual standard uncertainty of
each source must be combined to obtain the overall uncertainty and then, depending
on confidence level, the expanded combined uncertainty will be calculated.
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Typical sources of uncertainty are:
- sampling;
- storage conditions;
- effects induced by apparatus and equipment;
- reagent purity;
- measurement conditions;
- blank correction;
- operator induced effects;
- random effects.
Uncertainty quantification should be made taking into account:
- the performance characteristics of the method;
- validation studies including collaborative studies;
- in-house development and validation studies;
- proficiency testing data.
Before combination, all uncertainty contributions must be expressed as
standard uncertainties.
Where the uncertainty component was evaluated experimentally from the
dispersion of multiple repeated measurements, it can readily be expressed as a
standard deviation. This will be the case of standard deviation or the standard
deviation of the mean.
Where the uncertainty component was evaluated from previously obtained
data it may be expressed as a standard deviation or is necessary to make the
assumption concerning the nature of distribution: normal, rectangular or triangular. In
rectangular distribution the data must be divided by 31/2 and in the triangular
distribution the data must be divided by 61/2. In a normal distribution, when is
indicated the confidence interval i.e 95%, the data must be divided by 1.96.
Example:
1. A balance reading is ±0.003 mg with 95% confidence interval. The standard
uncertainty will be 0.003 / 1.96.
2. A 100 mL grade A calibrated flask is certified to within ±0.5 mL. The standard
uncertainty will be 0.5 / 31/2 when extreme values are not likely (rectangular
distribution). If extreme values are unlikely the standard uncertainty will be 0.5 /
61/2 (triangular distribution).
3. For a weighing operation is done the standard uncertainty of calibration (ucal=
0.03 mg) and for repeatability is done the standard deviation s = 0.06 mg when
six repeated weighing are made. The combined standard uncertainty uc is equal
with (0.032 + 0.062)1/2. The expanded combined uncertainty Uc taking into
account the Student factor t for 5 degrees of freedom and 95% confidence
interval (t=2.6) is equal with Uc = 2.6 x (0.032 + 0.062)1/2 .
The expanded uncertainty will be reported as “Result: x ± U (units) and we
are obliged to indicate the confidence level or the coverage factor.
Example:
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Nickel: 35.44 ± 0.36 % w/w *
* the reported uncertainty is an expanded uncertainty calculated with a coverage
factor k=3 with a confidence level of approximately 99.7%.
In this case to know the combined standard uncertainty we must to divide the
expanded uncertainty by 3, so the uc = 0.12%
III.2.2. CALCULATION EXAMPLE OF THE MEASUREMENT
UNCERTAINTY
III.2.2.1 In the next example is proposed a methodology for calculation of the
expanded uncertainty in the water analysis for the suspended matter determination
by gravimetric method.
Step 1: Specification of the measured value
Scope
Determination of total suspended matter (TSM) in wastewater.
The procedure used is a method described in STAS 6953-81 at chap.3.
The measurement procedure is described in Figure III.2.1.
Weighing
Filtration
Washing
Drying
Weighing
Result
Fig. III.2.1. Measurement procedure.
Measurand
TSM = (m2 – m1)x 1000/V
where: m2 – the mass of the vessel with residue, in mg; m1 – the mass of the vessel
without residue, in mg; V – volume of analyzed sample in liters; 1000 / conversion
factor from [mL] to [L]
The variables are centralized in Table III.2.1.
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Table III.2.1.
Description
TSM
m2 - m1
V1
Content of TSM, mg /L
Mass of residue, mg
Volume analyzed, mL
X value
Standard
uncertainty u(x)
13
1.3
100.0
2.2
0.22
0.08
Relative
Standard
uncertainty,
u(x)/x
0.1692
0.1692
0.0008
Step 2: Identification of the Uncertainty Sources
The sources of uncertainty are:
a) The weight of residue which is obtained from difference weighing between two
independent measurements. So, for m1 and m2 the sources for each of two
weightings represent the variance and the contribution due to the uncertainty in
the calibration function of the scale. This calibration function has two potential
uncertainty sources: the sensitivity of the balance and the linearity. The sensitivity
can be neglected because the weighing by difference is done on the same balance
over a very narrow range.
The linearity indicated by the manufacture’s information is equal with ± 0.1 mg
without other specifications.
The repeatability is another source. It is indicated by the manufacturer and is
equal with 0.2 mg as standard deviation.
b) For V (volume of wastewater sample) the uncertainty sources are generated by:
- The calibration of the pipette. The manufacturer quotes for a volume of 100
mL ± 0.08 mL at a temperature of 20ºC. The value of the uncertainty is
indicated without a confidence level;
- the repeatability generated by the variations in level filling represent another
source of uncertainty and can be estimated from a repeatability experiment on
a typical example of the pipettes used. A series of ten level filling and
weighing experiments on a typical 100 mL pipette gave a standard uncertainty
of 0.05 mL
- the temperature from the laboratory influences the volume taken because the
calibration was made at a temperature of 20 ºC, whereas the laboratory
temperatures varies between the limit ±4 ºC.
Step 3: Quantify Uncertainty Components
a) m1 and m2
- Because in the manufacturer’s information the linearity is equal with ± 0.1
mg without other specifications. According to the manufacturer the
uncertainty evaluation is done using a rectangular distribution. Hence the
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value for the linearity contribution needs to be divided by 31/2 to give the
component of uncertainty as a standard uncertainty.
0.1/ 31/2 = 0.058 mg.
This component has to be taken into account twice because of the difference
by 8.
- The repeatability indicated as standard deviation has to be taken into account
once because the standard deviation of the differences was directly determined
by difference.
Finally the two components, linearity and repeatability, to give the standard
uncertainty u(m) according to the formula:
u(m) = [(0.22 + 2 x 0.0582)]1/2 = 0.22 mg
b) V
-
-
calibration: Because the value of uncertainty (0.08) is indicated without a
confidence level, the standard uncertainty is calculated assuming a rectangular
distribution, since the actual volume is more likely to be at the extremes than
at the centre of the range. So, the value obtained is 0.08 / 31/2 = 0.046 mL;
repeatability: Because the repeatability gives a standard uncertainty of 0.05
mL, this standard uncertainty can be used directly;
the temperature from the laboratory influences the volume taken for analysis
because the calibration was made at a temperature of 20 ºC, whereas the
laboratory temperatures varies in the limit ±4 ºC. The volume expansion of the
liquid is considerably larger than that of the pipette. The coefficient of volume
expansion for water is 2.1 x 10-4 ºC-1, which leads to a volume variation of:
100 mL x ±4 ºC x 2.1 x 10-4 ºC-1 = ± 0.084 mL.
The standard uncertainty is calculated assuming a rectangular distribution for
the temperature variation i.e. 0.084 / 31/2 = 0.048 mL
The three contributions are combined to obtain the standard uncertainty u (V):
u (V) = ( 0.0462 + 0.052 + 0.0482)1/2 = 0.083 mL ~ 0.08 mL
Step 4: Calculation of the Total Uncertainty
TSM is given by the formula:
TSM = (m2 – m1)x 1000/V
where: m1 - vessel without residue: 23.1540g; m2 - - vessel with residue: 23.1553 g
The residue mass is 0.0013 g = 1.3 mg.
The content of TSM becomes:
TSM = 1.3 x 1000/100 = 13 mg/L
Table III.2.2 indicates the calculated values and associated standard
uncertainty
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Table III.2.2. Calculated values and standard uncertainty
Description
Standard
uncertainty u(x)
0.22
0.08
Value x
Mass of residue (mg)
Volume V (mL)
1.3
100.0
Relative standard
uncertainty u(x)/x
0.1692
0.0080
For this simple multiplicative expression, the uncertainties associated with
each component are combined as follows:
u c (TSM )
 u (m)   u (V ) 
 
 
 
TSM
 m   V 
2
2
0.1692 2  0.0080 2  0.1694
u c (TSM )  TSM  0.1694  13  0.1694  2.20mg / L
However, it is preferable to derive the combined standard uncertainty using
the data given in Table III.2.3.
Table III.2.3. Table for calculation of the uncertainty
A
1
2
3
4
5
6
7
8
9
10
11
12
B
Value
Uncertainty
C
m2 –m1
1.3
0.22
D
V
100.00
0.08
m2 –m1
V
1.3
100.0
1.52
100.00
1.3
100.08
c(TSM)
13
u2
4.8401
15. 2
2.2
4.84
12.99
0.01
0.0001
u(TSM)
2.20
where: C2-D2 = parameter values; C3-D3 = associated uncertainties; B5-B6 = parameter
values; C5 = C2+C3; D6 = D2+D3 ; B8 = the concentration of TSM calculated with the
parameters from B5-B6; C8 = the concentration of TSM calculated with the parameters
from C5-C6; D8 = the concentration of TSM calculated with the parameters from D5-
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D6; C9 = the difference between C8 and B8; D9 = the difference between D8 and B8; C10
= the square of C9; D10 = the square of D9; B10 = the sum of C9 and D9; B12 = the
combined standard uncertainty, square root of B10
The extended uncertainty UTSM is obtained by multiplying the combined
standard uncertainty with a coverage factor of 2 giving UTSM = 2 x 2.20 mg/L= 4.40
mg/L.
III.2.2.2 An acid/base titration
Goal
A solution of (HCl) is standardized against a solution of (NaOH) with
known concentration.
Introduction
This example discusses a sequence of experiments to determine the
concentration of a solution of hydrochloric acid (HCl). In addition, a number of
aspects of the titrimetric technique are highlighted. The HCl solution is titrated against
a solution of (NaOH), which was freshly standardized with potassium hydrogen
phthalate (KHP). The HCl concentration is assumed to be known and of the order of
0.1 mol/L and the end-point of the titration is determined by an automatic titration
system using the shape of the pH-curve. This evaluation gives the measurement
uncertainty in terms of the IS units of measurement.
Step 1: Specification
A detailed description of the measurement procedure is presented in the first
step. It harmonizes a listing of the measurement steps and a mathematical statement of
the measurand.
Procedure
The determination of the concentration of the HCl solution consists of the
following stages (See Figure III.2.2). The separate stages are:
i) The titrimetric standard potassium hydrogen phtalate (KHP) is dried to ensure the
purity quoted in the supplier's certificate. Approximately 0.388 g of the dried
standard are then weighed to achieve a titration volume of 19 mL NaOH.
ii) The KHP titrimetric standard mass is dissolved with approximately »50 mL of
ion free water and then titrated using the NaOH solution. A titration system
controls automatically the addition of NaOH and samples the pH-curve. The
endpoint of the titration is evaluated from the shape of the recorded pH curve.
iii) 15 mL of the HCl solution are transferred by means of a volumetric pipette. The
HCl solution is diluted with de-ionized water to give approximately »50 mL
solution in the titration vessel.
iv) The same automatic titrator performs the measurement of HCl solution
concentration.
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Weighing of KHP
Titration of KHP with NaOH
Transfer of an aliquot of
HCl
Titration of HCl with NaOH
RESULT
Fig. III.2.2. Determination of the concentration of a HCl solution
Calculation:
The measurand is the concentration of the HCl solution. It depends on the
mass of KHP, its purity, its molecular weight, the volumes of NaOH at the end-point
of the two titrations and the aliquot of HCl:
C HCl 
1000  mKHP  PKHP  VT 2
, mol.L-1
VT 1  FKHP  VHCl
cHCl :concentration of the HCl solution [mol/L]
1000 :conversion factor from [mL] to [L]
mKHP :mass of the titrimetric standard KHP, [g]
PKHP :purity of the titrimetric standard KHP, given as mass fraction
VT2 :volume of NaOH solution to titrate HCl [mL]
VT1 :volume of NaOH solution to titrate KHP [mL]
VHCl :volume of HCl titrated with NaOH solution [mL]
Step 2: Identifying and analyzing uncertainty sources
The different uncertainty sources and their influence on the measurand are
best analyzed by visualizing them first in a cause and effect diagram (Figure III.2.3).
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V (T2)
m(KHP)
Influence
Repeatability BIAS
(KHP)
Calibration
Calibration
End Point
Sensitivity
Sensitivity
Temperature
Linearity
Calibration
Repeatability
Repeatability
Linearity
m(tare)
Repeatability
C(HCl)
Repeatability
Repeatability
Calibration
Calibration
Temperature
Temperature
End point
Repeatability/Influences
V(T1)
P(KHP)
F(KHP)
V(HCl)
Fig. III.2.3. Cause – effect diagram
Because a repeatability estimate is available from validation studies for the
procedure as a whole, there is no need to consider all the repeatability contributions
individually. They are therefore grouped into one contribution (shown in the revised
cause-effect diagram from Figure A.2.2.2.2)
V HCl
15 mL of the investigated HCl solution will be transferred by means of a
volumetric pipette. The delivered volume of the HCl from the pipette is subject to the
same three sources of uncertainty as for all the volumetric measuring devices.
- The variability or repeatability of the delivered volume
- The uncertainty in the stated volume of the pipette
- The solution temperature differing from the calibration temperature of the pipette.
Step 3: Quantifying uncertainty components
The goal of this step is to quantify each uncertainty source analyzed in step 2.
Repeatability
The method validation shows a repeatability of 0.1% (expressed as %RSD).
This value can be used directly for the calculation of the combined standard
uncertainty associated with the different repeatability terms.
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m KHP
Calibration/linearity: The balance manufacturer quotes a value of ±0.15 mg
for the linearity contribution. This value represents the maximum difference between
the actual mass on the pan and the reading of the scale. Assuming a rectangular
distribution, the standard uncertainty associated to the linearity contribution is:
0.15
3
0.087mg
The contribution of the linearity has to be accounted for twice, once for the
tare and once for the net mass, leading to an uncertainty u(mKHP) of
u (m KHP )  2  (0.087) 2  u (m KHP )  0.12mg
Note 1: The contribution is applied twice because no assumptions are made
about the shape of the non-linearity. The non-linearity is accordingly treated as a
systematic effect on each weighing, which varies randomLy in magnitude across the
measurement range.
Note 2: Buoyancy correction is not considered because all weighing results are
quoted on the conventional basis for weighing in air [H.19]. The remaining
uncertainties are too small to be considered..
P (KHP)
P (KHP) is given in the supplier's certificate as 100% ±0.05%. The quoted uncertainty
is taken as a rectangular distribution, so that the standard uncertainty u(PKHP) is:
u ( PKHP ) 
0.0005
3
 0.00029
V (T2)
1.
Calibration: The value provided by the manufacturer is (±0.03 mL) and is
approximated to a triangular distribution:
2.
0.03
6
 0.012mL
Temperature: The possible temperature variation is within the limits of ±4°C and
approximated to a rectangular distribution:
15  2.1  10 4  4
3
 0.007 mL
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3.
Change of the end-point of the detection: A change of the determined end-point
of the titration and of the equivalence point due to the atmospheric CO2 can be
avoided by executing the titration in a argon atmosphere. In this case no
uncertainty is.
VT2 is found to be 14.89 mL. Comparing the two contributions of the
uncertainty u(VT2) associated to the volume VT2 is obtained a value of:
u (VT 2 )  0.0122  0.007 2  u (VT 2 )  0.014ml
V (T1)
All contributions except the one for the temperature are the same as for VT2:
0.03
 0.012mL
1.
Calibration:
2.
Temperature: The approximate volume for the titration of 0.3888 g KHP is 19
6
mL NaOH, therefore its uncertainty contribution is :
3.
19  2.1  10 4  4
3
 0.009mL
Change in the end-point of titration: Negligible
VT1 is found to be 18.64 mL with a standard composed uncertainty u(VT1) of:
u(VT 1 )  0.012 2  0.009 2  u(VT 1 )  0.015mL
F (KHP)
The molecular weights and listed uncertainties (from current IUPAC tables)
for the constituent elements of KHP (C8H5O4K) are:
Table III.2.4.
Element
C
H
O
K
molecular
weight
12.0107
1.00794
15.9994
39.0983
Quoted uncertainty
Standard uncertainty
 0.0008
 0.00007
 0.0003
 0.0001
0.00046
0.000040
0.00017
0.000058
For each element, the standard uncertainty is found by treating the IUPAC
quoted uncertainty as forming the boundaries of a rectangular distribution. The
corresponding standard uncertainty is therefore obtained by dividing those values by
3.
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The molar mass for KHP and its standard composed uncertainty are:
FKHP = 8·12.0107+5·1.00794+4·15.9994+39.0983 = 204.2212 g/mol
u ( FKHP )  (8  0.00046) 2  (5  0.00004) 2  (4  0.00017) 2  0.000058 2
 u ( FKHP )  0.0038 g / mol
Note: The single atom contributions are not independent. Therefore, the
uncertainty for the atom contribution is calculated by multiplying the standard
uncertainty of the atomic weight by the number of atoms.
1)
V(HCl)
Calibration: The uncertainty was stated by the manufacturer for a 15 mL pipette
as ±0.02 mL and is approximated with a triangular distribution:
0.02
6
2)
 0.008mL
Temperature: The temperature of the laboratory is within the limits of ±4°C.
Using a rectangular temperature distribution is obtained a standard uncertainty of:
15  2.1  10 4  4
3
 0.007 mL
Combining these contributions is obtained the value of:
u (VHCl )  0.0037 2  0.008 2  0.007 2  u (VT2 )  0.01mL
Step 4: Calculating the combined standard uncertainty
cHCl is given by
c HCl 
1000  mKHP  PKHP  VT 2
VT 1  FKHP  VHCl
All the intermediate values of the two steps are presented in Table III.2.5 .
Table III.2.5. Acid-base titration values and uncertainties
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m KHP
P KHP
VT2
VT1
FKHP
VHCl
Description
Value X
Mass of KHP
Purity of KHP
Volume of NaOH
for HCl titration
Volume of NaOH
for KHP titration
Molar mass of KHP
HCl aliquot for
NaOH titration
0.3888
1.0
0.00013
0.00029
Relative
standard
uncertainty
u(x)/x
0.00033
0.00029
18.89
0.015
0.0010
18.64
0.016
0.00086
204.2212
0.0038
0.000019
15
0.011
0.00073
Standard
Uncertainty
u(x)
Using these values:
cHCl 
1000  0.3888  1.0  14.89
 0.10139mol / lL
18.64  204.2212  15
The uncertainties associated with each component are composed accordingly:
2
2
2
2
2
2
 u (mKHP )   u ( PKHP )   u (VT 2 )   u (VT 1 )   u ( FKHP )   u (VHCl ) 
uc (cHCl )
 
  
  
  
  
  
 
cHCl
 mKHP   PKHP   VT 2   VT 1   FKHP   VHCl 
 0.000312  0.000292  0.000942  0.000802  0.0000192  0.000732  0.001  0.0018
 uc (cHCl )  cHCl  0.0018  0.00018mol / L
A spreadsheet method can be used to simplify the above calculation of the
combined standard uncertainty. The spreadsheet filled in with the appropriate values is
shown in Table III.2.6 , with supplemental explanations.
The sizes of the different contributions can be compared using a histogram.
Figure III.2.4. shows the values of the contributions |u(y,xi)| from Table
III.2.6.
The extended uncertainty U(cHCl) is calculated by multiplying the combined
standard uncertainty by a coverage factor of 2:
U(cHCl) = 0.0018 · 2 = 0.0004 m
The concentration of the HCl solution is: (0.1014 ± 0.0004) mol/L
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Table III.2.6. Table for the calculation of uncertainty
A
B
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
value
uncertainty
m (KHP)
0.3888
P (KHP)
1.0
V (T2)
14.89
V (T1)
18.64
F (KHP) 204.2212
V (HCl)
15
c (HCl)
D
P
(KHP)
1.0
0.00029
0.38893
1.0
14.89
18.64
204.2212
15
0.3888
1.00029
14.89
18.64
204.2212
15
E
V
(T2)
14.89
0.015
F
V
(T1)
18.64
0.016
0.3888
0.3888
1.0
1.0
14.89
14.89
18.64
18.64
204.2212 204.2212
15
15
G
F
(KHP)
204.2212
0.0038
H
V
(HCl)
15
0.011
0.3888
1.0
14.89
18.64
204.2212
15
0.3888
1.0
14.89
18.64
204.2212
15
0.101387 0.101421
0.101417
0.101489 0.101300
0.101385
0.101313
0.000034
0.000029
0.000102
-0.000087
-0.0000019
-0.000074
1.1E-9
8.64E-10
1.043E-8
7.56E-9
3.56E-12
5.52E-9
0.001
0.0015
2.55E-8
u(c(HCl))
C
m
(KHP)
0.3888
0.00013
0.00016
m (KHP)
P (KHP)
V (T2)
V (T1)
F (KHP)
V (HCl)
c (HCl)
0
0.0005
Relative standard uncertainty
Fig. III.2.4. Uncertainties in acid-base titration
III.2.2.3 Determination of the cadmium quantity extracted from the
ceramic walls in acid media by Atomic Absorption Spectrophotometry
Summary
Goal
The amount of released cadmium from the walls of a ceramic vessel is
determined using atomic absorption spectrophotometry. The procedure employed is
based on the empirical method described in the standard BS 6748.
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Measurement procedure
The different stages in determining the amount of cadmium released from the
walls of a ceramic vessel are given in the flow chart. (Figure III.2.5.).
Measurand
r
c0 .VL
.d . f acid . f timp . f temp [mg.dm 2 ]
aV
Identification of the uncertainty sources:
The relevant uncertainty sources are shown in the cause-effect diagram in
Figure III.2.6 .
Quantification of the uncertainty sources:
The sizes of the different contributions are given in Table III.2.7 and their
values are shown diagrammatically in Figure III.2.6 .
Table III.2.7: Uncertainties in the determination of the extracted cadmium.
c0
VL
aV
facid
ftimp
ftemp
r
Description
Value x
Standard
uncertainty u(x)
Content of Cd in the acid
solution that extracted the
metal
Volume of the acid that
extracted (by dissolving)
the metal
Surface area of the vessel
Influence of the acid
concentration
Influence of the time
Influence of temperature
Mass
of
cadmium
extracted by area unit
0.26mg.l-1
0.018mg.l-1
Relative
standard
uncertainty
u(x)/x
0.069
0.332 l
0.0018 l
0.0054
2.37dm2
1.0
0.06dm2
0.0008
0.025
0.008
1.0
1.0
0.036mg.dm-2
0.001
0.06
0.0033 mg.dm-2
0.001
0.06
0.09
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Preparation
Surface
conditioning
Fill with 4%
vol
acetic acid
Metal extraction by dissolving
Preparing of
calibration
standards
Homogenization of
acid solution
AAS
Determination
AAS
Calibration
RESULT
Fig. III.2.5. Metal extraction procedure
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c(0)
Calibration curve
f(acid)
f(time)
f(temperature)
V(L)
Loading
Temperature
Calibration
Reading
Result, r
Length (1)
Length (2)
Area
A(V)
d
Fig. III.2.6. Uncertainty sources for the determination of the cadmium extracted from
the ceramic walls
Example 1: Determination of cadmium quantity extracted from the ceramic
walls in acid media by atomic absorption spectrophotometry..
Step 1: Specification.
The following quote from BS 6748:1986 “Limits of metal extraction from
ceramic wall, glass wall, glass-ceramic wall and enameled wall constitutes the
specification for the measurand.
Reagents:
Water, complying with the requirements of BS 3978.
Acetic acid CH3 COOH, glacial.
Solution of 4% vol. glacial acetic acid in 500 mL water, made up by dilution
of 40 mL glacial acetic acid with water up to 1 L. The solution is freshly prepared
before use.
Standard metal solutions.
(1000 ±1)mg Pb solution in 1 L acetic acid 4% (vol)..
(500 ±0.5)mg Cd solution in 1 L acetic acid 4% (vol).
Apparatus
The atomic absorption spectrophotometer, with a detection limit of at most 0.2
mg/LPb (in 4% v/v acetic acid solution) and 0.02 mg/LCd (in 4% v/v acetic acid
solution).
The laboratory glassware is required to be of at least class B from
boronsilicate incapable of releasing detectable levels of lead or cadmium in 4% acetic
acid solution during the test procedure.
Preparations of samples
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The samples will be washed at 405C in an aqueous solution containing 1
mg/Lof domestic liquid detergent, rinsed with water (as specified above), drained and
wiped dry with clean filter paper. The areas of the samples, which do not contact
foodstuffs in normal use, are covered after washing and drying with a suitable
protective coating.
Procedure
The analytical procedure is illustrated schematically in Figure III.2.7 :
Preparation
Surface
conditioning
Fill with 4%
v/v acetic acid
Metal extraction by dissolving
Prepare calibration
standards
Homogenize
acid solution
AAS
Calibration
AAS
determination
RESULT
Fig. III.2.7. Metal extraction procedure.
The different steps are:
i.
The sample is conditioned to (22±2) °C. Where appropriate (‘category 1’
articles), the surface area of the article is determined.
ii.
The conditioned sample is filled with 4% v/v acid solution to within 1 mm
from the overflow point, measured from the upper rim of the sample, or to
within 6 mm from the extreme edge of a sample with a flat or sloping rim.
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iii.
iv.
v.
i).
ii).
The quantity of 4% v/v acetic acid required or used is recorded to an accuracy
of ±2%
The sample is allowed to stand at (22 ±2) ° for 24 hours (in darkness if
cadmium is determined) with due precaution to prevent evaporation loss.
The extract solution, is homogenized by stirring or by other means, without
loss of solution or abrasion of the surface being tested and a portion is taken
for analysis by AAS.
Analysis
The AAS instrument is set up according to the manufacturer’s instructions
using wavelengths of 217.0 nm for lead determination and 228.8 nm for
cadmium determination with appropriate correction for background absorption
effects.
Provided that absorbance values of the standard metal solutions an of the 4%
v/v acetic acid solution indicate mineral drift, the result may be calculated
from a manually prepared calibration curve (below), or by using the
calibration bracketing technique.
Calculation of results from a manually prepared calibration curve
The concentration c0 of lead or cadmium is calculated using:
c0 
( A0  B0 )
.d [mg.L1 ]
B1
where: c0: concentration of lead or cadmium in the acid solution that extracted the
metal [mg L-1]; A0: absorbance of lead or cadmium in the sample extract; B1: slope of
the calibration curve; B0: intercept of the calibration curve [mg L-1]; D: the factor by
which the sample was diluted
Note: The calibration curve should be chosen to have absorbance values
within the concentration values interval of the sample extract or diluted sample
extract.
Test report
The test report is will to include:
 the nature of the tested article;
 the surface area or volume of the article, as appropriate;
 the amount of lead and/or cadmium in the total quantity of the extracting solution
expressed as milligrams of Pb or Cd per square decimeter of surface area for
category 1 articles or as milligrams of Pb or Cd per liter of the volume for
category 2 or 3 articles.
Note: This extract from BS 6748:1996 is reproduced with the permission of
BSI. Complete copies can be obtained by post from BSI customer services, 389
Chiswick Leigh Road, London W4 4AL England, Tel: +44(0)20899690001.
Step 2: Identifying and analyzing uncertainty sources
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Step 1 describes an ‘empirical method’. If such a method is used within its
defined field of application, the bias of the method is defined as zero. Therefore bias
estimation relates to the laboratory performance and not to the bias intrinsic to the
method. Because no reference material certified for this standardized method is
available, overall control of bias is related to the control of method parameters
influencing the
result. Such influence quantities are time, temperature, mass and volumes, etc.
The concentration of lead or cadmium in the acetic acid is determined by
atomic absorption spectrometry. For the vessels that cannot be filled completely the
empirical method calls for the result to be expressed as mass r (expressed in mg.dm-2)
of Pb or Cd extracted per unit area r is given by:
r
c0 .VL
V .( A  B0 )
.d  L 0
.d
aV
aV .B1
where: r : mass of Cd or Pb extracted per unit area [mg dm-2]; VL : the volume of acid
that extracted the metal [l]; aV : the surface area of the vessel [dm2]; c0: content of lead
or cadmium in the extraction solution [mg l-1]; A0: absorbance of the metal in the
sample extract; B0: intercept of the calibration curve; B1: slope of the calibration curve
d : factor by which the sample was diluted.
The first part of the above equation is used to draft the basic cause and effect
diagram (Figure III.2.8).
Loading
Temperature
Calibration
Reading
Calibration curve
Result, r
1 Length
2 Length
Area
A(V)
d
Fig. III.2.8. Initial cause and effect diagram.
There is no reference material certified for this empirical method with which
to assess the laboratory performance. As a result, all the possible influence quantities,
such as temperature, time of the extraction process of the metal from the ceramic walls
and acid concentration have to be considered. To accommodate the additional
influence quantities the equation is completed by the respective correction factors
leading to:
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r
c0 .VL
.d . f acid . f timp . f temp
aV
These additional factors are also included in the cause and effect diagram
(Figure III.2.9). There they are shown there as effects on c0.
Note: The temperature domain permitted by the standard is a cause of an
uncertainty arising because of incomplete specification of the measurand. Taking the
effect of temperature into account allows estimation of the range of results which
could be reported whilst complying with the empirical method.
Step 3: Quantifying uncertainty sources
The aim of this step is to quantify the uncertainty arising from each of the
previously identified sources. This can be done either by using experimental data or
from well based assumptions.
c(0)
Calibration curve
f(acid)
f(time)
f(temperature)
V(L)
Loading
Temperature
Calibration
Reading
Result, r
Length (1)
Length (2)
Area
A(V)
d
Fig. III.2.9. Uncertainty sources at the determination of the cadmium extracted from
ceramic walls
Dilution factor d: For the current example, no dilution of the acid solution for
the metal extraction is necessary, therefore no uncertainty contribution has to be
accounted for.
Volume VL
Loading: The empirical method requires the vessel to be filled ‘to within 1
mm from the rim’. For a typical drinking or kitchen vessel, 1 mm will represent about
1% of the height of the vessel. Therefore, the vessel will be 99.5 ±0.5% filled (i.e. VL
will be approximately 0.995 ±0.005 of the vessel’s volume).
Temperature:The temperature of the acetic acid solution has to be 22 ±2ºC.
This temperature range leads to an uncertainty in the determined volume, due to a
considerable larger volume expansion of the liquid compared with the vessel. The
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standard uncertainty of a volume of 332 mL, assuming a rectangular temperature
distribution, is
2.1.10 4.332.2
3
 0.08mL
Reading: The volume VL used must be recorded to within 2%. In practice, the
use of a measuring cylinder allows a measuring accuracy of about 1% (i.e. 0.01 VL).
The standard uncertainty is calculated assuming a triangular distribution.
Calibration: The volume is calibrated according to the manufacturer’s
specification within the range of ±2.5 mL for a 500 mL measuring cylinder. The
standard uncertainty is obtained assuming a triangular distribution.
For this example a volume of 332 mL is used and the four uncertainty components are
combined accordingly:
2
2
2
 0.005.332 
 0.01.332   2.5 
2
u (VL )  
  0.08  
  
  1.83mL
6
6   6



Cadmium concentration c0
The amount of released cadmium is calculated using a manually prepared
calibration curve. For this purpose five calibration standards, with a concentration 0.1
mg L-1, 0.3 mg L-1, 0.5 mg L-1, 0.7 mg L-1 and 0.9 mg L-1, were prepared starting from
a 500 ±0.5 mg L-1 cadmium reference standard. The linear fitting procedure used
assumes that the uncertainties of the values on the abscissa are considerably smaller
than the uncertainty on the values on the ordinate. Therefore, the usual uncertainty
calculation procedure for c0 only reflect the uncertainty on the abscissa and not the
uncertainty of the calibration standards, nor the inevitable correlations induced by
successive dilution from the same stock. In this case, however, the uncertainty of the
calibration standards is sufficiently small to be neglected.
The five calibration standards were measured three times each, providing the
following results:
Table III.2.8.
Concentration [mg.L-1]
0.1
0.3
0.5
0.7
1
0.028
0.084
0.135
0.180
2
0.029
0.083
0.131
0.181
3
0.029
0.081
0.133
0.183
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0.9
0.215
0.230
0.216
The calibration straight line is given by the equation:
Aj= ci.B1+B0
where: Aj: the jth absorbance measurement calibration standard; ci:
corresponding concentration of the ith calibration standard; B1: slope of the
straight line; B0: intercept of the straight line.
And the results of the linear fit are:
Table III.2.9.
Value
0.2410
0.0087
B1
B0
Standard deviation
0.0050
0.0029
with a correction coefficient r of 0.997.
The regression straight line is shown in Figure III.2.10.
The residual standard deviation S is 0.005486.
Absorbance
0.25
x
x
0.20
x
x
0.15
x
0.10
x
0.05
0.00
0.0
0.2
0.4
0.6
0.8
1.0
Concentration of Cd[mg/L]
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Fig. III.2.10. Linear fit by the least square method and uncertainty interval for
duplicate determinations.
The actual solution was measured twice, leading to a concentration c0 of 0.26
mg L-1. The calculation of the associated uncertainty u(c0) with the linear fitting
procedure by the method of the least squares is described in detail in Annex E3.
Therefore, only a short description is given here.
u(c0) is given by:
u(c0)=
S
B1
1 1 (c0  c ) 2 0.005486 1 1 (0.26  0.5) 2
 

 
p n
S xx
0.241
2 15
1.2
 u (c0 )  0.018mg.L1
with the residual standard deviation given by:
n
S
[ A
j 1
J
 ( B0  B1 .c j )] 2
n2
 0.005486
and
n
S   (c j  c) 2  1.2
j 1
where: B1 : slope of the calibration curve; p : number of measurements to determine
c0; n : number of measurements for the calibration of the equipment; c0 : determined
cadmium concentration in the acid solution that extracted the metal; c : mean value of
the different calibration solutions used for calibration (n being the number of
measurements); i : index for the number of calibration solutions used for calibration; j
:index for the number of measurements to obtain the calibration curve.
Area aV
Length measurement: The total surface area of the sample vessel was
calculated, from measured dimensions, to be 2.37 dm2. Since the vessel is
approximately cylindrical, but not perfectly regular, measurements are estimated to be
within a 2 mm limit with a 95% confidence level. Typical dimensions are between 1.0
dm and 2.0 dm leading to an estimated dimensional measurement uncertainty of 1 mm
(after dividing the 95% Figure by 1.96). Area measurements typically require two
length measurements, height and width respectively (i.e. 1.45 dm and 1.64 dm)
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Area: Since the vessel has not a perfect geometric shape, there is also an
uncertainty in any area calculation; in this example, this is estimated to contribute an
additional 5% at 95% confidence level.
The uncertainty contribution of the length measurement and area itself are
combined in the usual way.
 0.05.2.37 
u (aV )  0.01  0.01  

 1.96 
 u (aV )  0.06dm 2
2
2
2
Temperature effect ftemp
A number of studies of the effect of temperature on metal release from
ceramic wall have been undertaken(1-5). Generally, the temperature effect is
substantial and a near-exponential increase in metal release with temperature is
observed until limiting values are reached. Only one study has given an indication of
the effects in the range of 20-25°C. From the graphical information presented the
change in metal release with temperature near 25°C is approximately linear, with a
gradient of approximately 5% °C-1. For the ±2°C range, allowed by the empirical
method, this leads to a factor of 1±0.1. Converting this to a standard uncertainty gives,
assuming a rectangular distribution:
II u ( f temp )  0.1 / 3  0.06
Time effect ftime
For a relatively slow process such as the extraction, the amount released will
be approximately proportional to time for small changes in the time. Krinitz and
Franco found a mean change in concentration for a period larger than 6h of extraction
is approximately 1.8 mg L-1, in about 0.3%/h. For a time of (24±0.5)h c0 will therefore
be needed a correction by a factor ftime of 1±(0.5´0.003) =1±0.0015. This is a
rectangular distribution leading to a standard uncertainty:
u(ftimp) = 0.0015/ 3 = 0.001
Acid concentration facid
One study of the effect of acid concentration on lead release showed that
changing concentration from 4 to 5% v/v increased the lead released from a particular
ceramic batch from 92.9 to 101.9 mg L-1, i.e. a change in facid of (101.9- 92.9) /92.9 =
0.097 . 09 close to 0.1. Another study, using a hot release method, showed a
comparable change (50% change in lead extracted on a change from 2 to 6% v/v)3.
Assuming this effect as approximately linear with acid concentration is obtained an
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estimated change in facid of approximately 0.1 per % v/v. In a separate experiment the
concentration and its standard uncertainty have been established using titration with a
standardized NaOH solution (3.996% v/v u = 0.008% v/v). Taking the uncertainty of
0.008% v/v on the acid concentration results an uncertainty for facid of 0.008 . 0.1 =
0.0008. As the uncertainty on the acid concentration is already expressed as a standard
uncertainty, this value can be used directly as the uncertainty associated with facid.
Note: In principle, the uncertainty value would need correcting for the
assumption that the single study above is sufficiently representative of all ceramics.
The present value indicates, however, a reasonable estimate of the magnitude of the
uncertainty.
Table III.2.10. Intermediate values and uncertainties for extracted cadmium analysis
c0
VL
aV
facid
ftimp
ftemp
Description
Value
Standard
uncertainty
u(x)
Content of cadmium in
the acid solution
Volume of acid that
extracted the Cd
Surface area of the
vessel
Influence of the acid
concentration
Influence of the time
Influence of temperature
0.26 mg.L-1
0.018 mg.L-
Relative
standard
uncertainty
u(x)/x
0.069
1
0.332 L
0.018 L
0.054
2.37 dm2
0.06 dm2
0.025
1.0
0.0008
0.0008
1.0
1.0
0.001
0.06
0.001
0.06
Step 4: Calculating the combined standard uncertainty
The amount of cadmium extracted per unit area, is given by:
r
c0 .VL
.d . f acid . f timp . f temp
av
The intermediate values and their standard uncertainties are collected in Table
III.2.10.
Employing those values is obtained:
r
0.26  0.332
.1.0 1.0 1.9  0.036mg.dm 2
2.37
In order to calculate the combined standard uncertainty of a product (as the
one above) the standard uncertainties are used as follows:
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2
 u (c0 )   u (VL   U (aV )   u ( f acid )   u ( f timp )   u ( f temp ) 
uc (r )
 

  
  
  
  
 

 

r
 c0   VL   aV   f acid   f timp   f temp 
2
2
2
2
2
 0.0642  0.00562  0.0252  0.00082  0.0012  0.062  0.095  uc (r )  0.095r  0.0034mg.dm2
The simpler spreadsheet approach to calculate the combined standard
uncertainty is shown in Table A5.3 from below. The description of the method is
indicated in the Annex E. The values of the parameters are entered in the second row
from C2 to H2, and their standard uncertainties in the row below (C3:H3). The
spreadsheet copies the values from C2:H2 into the second column (B5:B10). The
result (r) calculated using these values is given in B12. Cell C5 shows the value of c0
from C2 plus its uncertainty given in C3. The result of the calculation using the values
C5:C10 is given in the cell C12. The columns D and H follow a similar procedure.
Row 13 (C13:H13) shows the differences of the row (C12:H12) minus the value given
in B12. In row 14 (C14:H14) the values of row 13 (C13:H13) are squared and
summed to give the value shown in B14. B16 gives the combined standard
uncertainty, which is the square root of B14. The contribution of the different
parameters and the influence of the dimensions on the measuring uncertainty are
shown in Figure A 5.8, comparing the size of each contribution (C13:H13 from table
III.2.11) with the composed uncertainty (B16).
Table III.2.11. Spreadsheet calculation of uncertainty for the analysis of the
cadmium extracted from the ceramic walls
A
1
2
3
4
5
6
7
8
9
10
11
12
B
value
uncertain
ty
C
c0
0.26
0.018
D
VL
0.332
0.0018
E
aV
2037
0.06
F
facid
1.0
0.0008
G
ftime
1.0
0.001
H
ftemp
1.0
0.06
0.26
0.332
2.37
1.0008
1.0
1.0
1.0
0.26
0.332
2.37
1.0
1.001
1.0
0.26
0.332
2.37
1.0
1.0
1.06
0.036458
0.038607
0.000036
0.002185
1.33 E-9
4.78 E-6
c0
VL
aV
facid
ftime
ftemp
0.26
0.332
2.37
1.0
1.0
1.0
0.278
0.332
2.37
1.0
1.0
1.0
0.26
0.3338
2.37
1.0
1.0
1.0
0.26
0.332
2.43
1.0
1.0
1.0
r
0.036422
0.038943
0.036619
0.002521
0.000197
6.36 E-8
3.90 E-8
0.035
523
0.036 451
0.000899
8.09 E-7 0.000 029
13
u(y,xi)
14
u(y)2
1.199 E-5
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15
16
A
B
uc(r)
0.0034
C
D
E
F
8.49 E-10
G
H
The expanded uncertainty U(r) is obtained by applying an expansion factor of
2
Ur =0.0034 x 2 =0.007mg .dm-2
Thus, the amount of released cadmium measured according to BS 6748:1986
is of:
(0.036 0.007)mg.dm-2
where the stated uncertainty is calculated using an expansion factor of 2.
III. 2.2.4 Quantity of organophosphoric pesticides in bread – extraction and GC.
.
Introduction
This example illustrates the way in which the internal validation data can be
used to quantify the measurement uncertainty.
The aim of the measurement is to determine the amount of an
organophosphoric pesticides residue in bread.
The validation scheme and experiments establish the traceability by
measurements on spiked samples.
It is assumed that the uncertainty due to any difference in response of the
measurement to the spike and the analyte in the sample is small compared with the
total uncertainty on the result.
Step 1: Specification
The specification of the measurand for more extensive analytical
methods is best done by a comprehensive description of the different stages of
the analytical method and by providing the equation for the calculation of the
measurand.
Procedure
The measurement procedure is illustrated schematically in Figure III.2.11. The
separate stages are:
i)
Homogenization: The complete sample is divided into small (approx. 2 cm)
fragments, a random selection is made of about 15 of these, and the subsamples are homogenized. Where extreme inhomogeneity is suspected
proportional sampling is used before blending.
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ii)
iii)
iv)
v)
vi)
vii)
viii)
ix)
Weighing of sub-samples for analysis gives the sample mass msample
Extraction: Quantitative extraction of the analyte with organic solvent,
decanting and drying through sodium sulfate columns (water removal), and
concentration of the extract using a Kedurna -Danish apparatus.
Liquid-liquid extraction: acetonitrile/hexane liquid partition, washing the
acetonitrile extract with hexane, water removal from the hexane layer using a
sodium sulfate column.
Concentration of the washed extract by passing gas through the extract to near
vapor point.
Dilution to standard volume Vop (approx. 2 mL) in a 10 mL graduated tube.
Measurement: Injection and GC measurement of a 5 L extract sample to
obtain the peak intensity Iop.
Preparation of an approximately 5 g/mL standard solution (actual mass
concentration cref).
GC calibration using the prepared standard and injection and GC measurement
of 5 l of the standard to give a reference peak intensity Iref.
Homogenization
Extraction
Washing
Concentration
Preparing the
solution
GC Determination
GC Calibration
Result
Fig. III.2.11. Organophosphoric pesticides analysis
Calculation
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The mass concentration cop in the final sample is given by:
c op  c ref
I op
I ref
g / mL
and the estimate level of pesticide Pop in the sample (mg/kg) is given by:
Pop 
cop  Vop
Re c  m proba
 10 6 mg / kg
which leads to the global equation:
where: Pop :Level of pesticide in the sample [mg/kg]; Iop : Peak intensity of the
extract sample ; cref : Mass concentration of the reference solution [g/mL]; Vop :
Total volume of the extract [mL]; 106 :Conversion factor from g/g to mg/kg ; Iref :Peak
intensity of the reference solution ; Rec :Recovery; msample: Mass of the investigated
sub-sample [g]
Scope
The analytical method is applicable to a small range of chemically similar
pesticides at concentrations between 0.01 and 2 mg/kg with different kinds of bread as
matrix.
Identifying and analyzing uncertainty sources
The identification of all relevant uncertainty sources for such a complex
analytical procedure is best done by drafting a cause and effect diagram. All the
parameters in the equation of the measurand are represented by the main branches of
the diagram. Further factors are then added to the diagram, considering each step in
the analytical procedure (Figure III.2.12), until the contributory factors become
sufficiently weak (insignificant). This leads to the following diagram:
The sample inhomogeneity is not a parameter in the original equation of the
measurand, but it appears to be a significant effect in the analytical procedure. This is
why a new main branch is added in the cause-effect diagram
Finally, the uncertainty branch due to the inhomogeneity of the sample has to be
included in the calculation of the measurand. To show the effect of uncertainties
arising from that source clearly, it is useful to write:
Pop  Fhom
I op  c ref  Vop
I ref  Re c  m proba
 10 6
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where Fhom is a correction factor assumed to be unity in the original calculation. This
makes it clear that the uncertainties of the correction factors must be included in the
estimation of the overall uncertainty. The final expression also shows how the
uncertainty will be applied.
Note: Correction factors: This approximation is quite general and can be valid
for the highlighting of the assumed aspects. In principle, every measurement has
associated with it such correction factors, which are normally assumed as unity. For
example, the uncertainty in cop can be expressed as a standard uncertainty for cop, or as
the standard uncertainty, that represents the uncertainty in a correction factor. In the
latter case, the value is identical to the uncertainty for cop expressed as a relative
standard deviation.
I(op)
V(op)
Calibration (lin)
Precision
Precision
Purity (ref)
m(ref)
Temperature
Temperature Calibration
V(ref)
Calibration
Precision
Calibration
Calibration
Dilution
Precision
Precision
m(gross)
Linearity
Precision
Sensitivitye
Calibration
m(tare)
Calibration
Linearity
Precision
Sensitivity
F(hom)
Recovery
I(ref)
m(sample)
calibration
Precision
Fig. III.2.12. Cause and effect diagram with added main branches for samples nonhomogeneous.
Step 3: Quantifying uncertainty components
The quantification of the different uncertainty components utilizes data from
three major steps from the in-house development and validation studies:
The most feasible estimation of all successive variations of the analytical
process.
The best possible estimation of all the influences (Rec) and their uncertainties.
Quantification of any uncertainty associated with effects incompletely
established from the point of view of the performance studies.
Some rearrangements of the previously identified influences lead to the cause
and effect diagram from Figure III.2.13 that correlates these three major steps.
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c(ref)
I(op)
Calibration
(lin)(2)
I(op)
I(ref)
Purity(ref)
m(ref)
m(ref)
Temperature(2) Calibration
V(ref)
dilution
V(op)
m(sample)
V(op)
)
Temperature(2)
V(ref)
Calibration (2)
Calibration (3)
Calibration (2)
Dilution
m(gross)
Linearity
m(tare)
Calibration (2)
Calibration (3)
F(hom)(3)
Recovery(2)
I(ref)
m(sample)
Linearity
Calibration (2)
Fig. III.2.13. Cause and effect diagram after rearrangement to accommodate the data
of the validation study
1. Precision study
The total successive variations of the analytical procedure performed with a
number of parallel tests for typical organophosphoric pesticides found in different
bread samples. The overall standard deviation s = 0.382
The result of the standard difference (the difference divided by the mean)
provides a measure of the precision variability. To obtain the estimated relative
standard uncertainty for single determinations, the standard deviation of the standard
differences is taken and divided by 2 to correct from a standard deviation of paired
differences to the standard uncertainty for the single values. This gives a value for the
standard uncertainty due to successive variation of the overall analytical process of:
0.382
2
 0.27
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Note. At first sight, it may seem that the parallel (double) tests provide
insufficient degrees of freedom. However, the goal is not to obtain very accurate
numbers for the precision of the analytical process for one specific pesticide in one
special kind of bread. It is more important in this study to test a wide variety of
different materials and sample concentrations of pesticides, giving a representative
selection of typical organophosphoric pesticides. This is done in the most efficient
way by duplicate tests on many materials, providing (for the repeatability estimate)
approximately one degree of freedom for each material studied in duplicate.
2. Interferences study
The interferences of the analytical procedure were investigated during the inhouse validation study using spiked samples. Table III.2.12 centralizes the results of a
long term study of spiked samples of various types.
The relevant line is the "bread" entry line, which shows a mean recovery for forty-two
samples of 90%, with a standard deviation (s) of 28%.
The standard uncertainty was calculated as the standard deviation of the mean:
u (Re c) 
0.28
42
 0.0432
There are three possible cases arising for the value of the recovery Re c :
Re c taking into account that u (Re c) is not significantly different from 1, so no
correction is applied.
Re c taking into account that u (Re c) is significantly different from 1 and a
correction is applied.
Re c taking into account that u (Re c) is significantly different from 1 but a
correction is not applied.
A significance test is used to determine whether the recovery is significantly
different from 1.0.
The statistical test t is calculated using the following equation:
t
1  Re c
u (Re c)

(1  0.9)
 2.315
0.0432
This value is compared with the 2- critical value tcrit, for n–1 degrees of
freedom at a 95% confidence level (where n is the number of results used to estimate
Re c ).
If t  tcrit than Re c is significantly different from 1.
t = 2.31  tcrit,41  2.021
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In this example a correction factor (1/ Re c ) was applied and therefore
Re c is explicitly included in the calculation of the result.
Table III.2.12. Results of duplicate pesticide analysis
Residue
D1 [mg/kg]
Malathion
Malathion
Malathion
Malathion
Malathion
Pirimiphos
Methyl
Chloropyrifos
Methyl
Pirimiphos
Methyl
Chloropyrifos
Methyl
Pirimiphos
Methyl
Chloropyrifos
Methyl
Chloropyrifos
Methyl
Pirimiphos
Methyl
Chloropyrifos
Methyl
Pirimiphos
Methyl
D2 [mg/kg]
1.30
1.30
0.57
0.16
0.65
0.04
1.30
0.90
0.53
0.26
0.58
0.04
Mean
[mg/kg]
1.30
1.10
0.55
0.21
0.62
0.04
Difference
D1-D2
0.00
0.40
0.04
-0.10
0.07
0.00
Difference
/mean
0.000
0.364
0.073
-0.476
0.114
0.000
0.08
0.09
0.085
-0.01
-0.118
0.02
0.02
0.02
0.00
0.000
0.01
0.02
0.015
-0.01
-0.667
0.02
0.01
0.015
0.01
0.667
0.03
0.02
0.025
0.01
0.400
0.04
0.06
0.05
-0.02
-0.400
0.07
0.08
0.75
-0.10
-0.133
0.1
0.01
0.10
0.00
0.000
0.06
0.03
0.045
0.03
0.667
Table III.2.13. Result of the calculation studies for the recovery for pesticides.
Substrate
Residue Type
N1)
Mean2)[%]
PCB
OC
Conc
.[mg kg–1]
10.0
0.65
Waste Oil
Butter
Compound Animal Feed
I
Animal & Vegetable Fats
I
Brassicas 1987
Bread
Rusk
M
M
8
33
84
109
9
12
OC
0.325
100
90
9
OC
0.33
34
102
24
OC
OP
OP
OC
OC
0.32
0.13
0.13
0.325
0.325
32
42
30
8
9
104
90
84
95
92
18
28
27
12
9
2)
s
[%]
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R
W
S
B
OC
OC
OC
OC
0.325
0.325
0.325
0.325
11
25
13
9
89
88
85
84
13
9
19
22
1) The number of experiments carried out
2) The mean and sample standard deviation s are given as recovery percentage.
3. Other sources of uncertainty
The cause and effect diagram in Figure III.2.14 shows which other sources of
uncertainty have to be examined and eventually considered in the calculation of the
measurement uncertainty.
(1) Considered during the variability investigation of the analytical procedure
(2) Considered during the interference study of the analytical procedure
(3) To be considered during the evaluation of the other sources of uncertainty.
c(ref)
I(op)
Calibration
(lin)(2)
I(op)
I(ref)
Purity(ref)
m(ref)
m(ref)
Temperature(2) Calibration
V(ref)
dilution
V(op)
m(sample)
V(op)
)
Temperature(2)
V(ref)
Calibration (2)
Calibration (3)
Calibration (2)
Dilution
m(gross)
Linearity
m(tare)
Calibration (2)
Calibration (3)
F(hom)(3)
Recovery(2)
I(ref)
m(sample)
Linearity
Calibration (2)
Fig. III.2.14. Evaluation of other sources of uncertainty
All balances and the important volumetric glassware are under strict control.
The interference studies take into account the influence of the calibration of the
different volumetric glassware because during the investigation various volumetric
calibrated flasks and pipettes have been used.
The extensive variability studies, which lasted for more than half a year, also
cover influences of the environmental temperature on the result.
The purity of the reference standard is given by the manufacturer as 99.53%
±0.06%. The purity is another potential uncertainty source with a standard uncertainty
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II. AUTOMATIC ANALYTICAL METHODS FOR ENVIRONMENTAL MONITORING AND CONTROL
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of 0.0006/√3 = 0.00035 (rectangular distribution). However, the contribution is too
small to be considered significant.
Another quantity that influences is the nonlinearity of the signal of the examined
organophosphoric pesticides within the given concentration range. The in-house
validation study has proven that this is not the case.
The homogeneity of the sub-samples is the last remaining uncertainty source.
No literature data were available on the distribution of trace organic components in
bread products, despite an extensive literature search (at first sight this is surprising,
but most food analysts consider the existence of homogeneity rather than evaluate
non-homogeneity separately). Thus, it practical to measure homogeneity directly. The
homogeneity contribution has therefore been estimated based on the sampling method
used.
To aid the estimation, a number of feasible scenarios for the pesticide residue
distribution were considered, and a simple binomial distribution was used to calculate
the standard uncertainty for the total included in the analyzed sample. The scenarios,
and the calculated relative standard uncertainties for the amount of pesticide in the
final sample, were:
Residue distributed on the top surface only: 0.58.
Residue distributed near the surface only: 0.20.
Residue distributed through the sample, but reduced in concentration by
evaporative loss or decomposition: 0.05-0.10 (depending on the surface layer).
Scenario (a) was established in specific conditions by proportional sampling
or complete homogenization. It may arise in the case of supplemental additions (whole
seed) to the surface.
Scenario (b) is considered the most unfortunate case. Scenario (c) is
considered the most probable, but cannot be readily distinguished from (b). On this
basis, the value of 0.2 was chosen.
Note: For more details on the inhomogeneity model, see the last section
of this example.
Calculating the combined standard uncertainty
During the in-house validation study of the analytical procedure the
repeatability of the uncertainty and all other uncertainty sources have been thoroughly
investigated. Their values and uncertainties are collected in Table III.2.14.
Table III.2.14. Uncertainties in pesticide analysis
Description
Value x
standard
uncertainty u(x)
Relative standard
uncertainty u(x)/x
Repeatability(1)
1.0
0.27
0.27
Bias (Rec)(2)
0.9
0.043
0.048
Remarks
Duplicate tests
of different
types of
samples
Spiked samples
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Other sources
(Homogeneity)(3)
u ( Pop )
Pop
1.0
0.2
0.2
Estimations
founded on
model pollution
--
--
0.34
Relative
standard
uncertainty
Only the relative value of the combined standard uncertainty can be calculated
because the uncertainty contribution for the entire range of the analyte was evaluated
.
uc
 0.27 2  0.048 2  0.2 2  0.34  u c ( Pop )  0.34  Pop
Pop
The spreadsheet for this case takes the form shown in Table III.2.15.
Table III.2.15. Uncertainty in pesticide analysis
A
1
2
3
4
5
6
7
8
9
10
11
12
13
Repeatability
Interference
Homogeneity
B
value
uncertainty
C
Repeatability
1.0
0.27
D
Bias
0.9
0.043
E
Homogeneity
1.0
0.2
1.0
0.9
1.0
1.27
0.9
1.0
1.0
0.9043
1.0
1.0
0.9
1.2
1.1111
1.4111
0.30
0.09
1.1058
- 0.0053
0.00002
8
1.333
0.222
0.04938
0.1394
ur(Pop)
0.37
The size of the three different contributions can be compared by the histogram
from Figure III.2.15 that shows the relative standard uncertainty.
The repeatability is the largest contribution to the measurement uncertainty.
Since this component is derived from the overall variability in the method, further
experiments might be needed to show where improvements could be made.
However, the uncertainty could be reduced significantly by homogenizing the
whole loaf before taking a sample.
The standard expanded uncertainty U(Pop) is calculated by multiplying the
combined standard uncertainty with a coverage factor of 2 to give:
U(Pop) = 0.34· Pop·2 = 0.68· Pop
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III.2.3. Exercise
Calculate the uncertainty for the preparation of 100 mL cobalt solution 10µg /
mL, from 99.9 % powdered Cobalt. A 100 mL class A calibrated flask has a ±0.1
certified value and the repeatability standard deviation of ±0.0118 mL. A 1000 mL
round bottom flask has a ±0.4 certified value and the repeatability standard deviation
of ±0.0596 mL. A 10 mL bulb pipette has a ±0.02 certified value and the repeatability
standard deviation of ±0.01 mL. The temperature for the preparing of the solution is
20ºC.
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III.3. CONTROL CHARTS
III.3.1. Theoretical Aspects
The control chart provides a graphic method for distinguishing the pattern of
error or variation from the determined error or allowed variation. This implies
systematic checks, e.g. per day or per batch, that must show that the test result remains
reproducible and that the methodology of measuring the analyte is respected.
The control chart is the most used and available analytical control instrument
for the environmental laboratories. The use of the control chart as a routine activity is
also a requirement of most attesting programs. Several types of control charts can be
applied [21, 22], but the most usual types are:
 Control chart of the Mean ( x -chart, Shewhart chart) - for the control of the
accuracy (bias) (Figure III.3.1);
 Control chart of the type recovery rate (R-chart) - for the control of precision
A. An x -chart can be started when a sufficient number of measured values of
the control sample are available. For this, it is recommended to start with at least 20
repeated analyses in a time interval of at least 20 days. The mean, x , and standard
deviation ,s, of a set of result are calculated and then the warning levels (2s) and
control levels (3s) are drawn on each side of the mean value (Figure III.3.2).
The coordinates of the chart are:

Batch number or analysis date – on the abscissa

Concentration or analytical signal – on the ordinate
Each time a result is obtained for the control sample from a set of tested
samples, the result is recorded on the control chart, if a chart was completed a new one
will be started.
The quality control rules were developed to detect the excessive trueness error
and imprecision and the changes and tendencies in the analyses.
Warning rules (if occurring) lead to the further inspection of the data:
 one control result beyond warning limit
Rejection rules – (if occurring) lead to the rejection of the data:
1.
-1 result above action limit;
2.
-2 consecutive results above the same warning limit;
3.
-7 consecutive results by the same side of the mean value;
4.
-10 consecutive results from 11 with the same value;
5.
- when a result is possibly incorrect
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Conc.
(mg/L)
x  3s (LA)
x  2s (LW)
x
x - 2s (LW)
x - 3s (LA)
Date/batch
LW = warning limit
LA = action limit
Fig. III.3.1. Control chart of the Mean ( x -chart)

Rules 1 and 2 appear generally due to mistakes of glassware manipulation,
dilution mistakes or calculations errors.
 Rules 3 and 4 are indicating a systematic error in the process. For finding these
errors are required additional tests on blank sample, by using an independent
standard or through the apparatus calibration.
 Rules 5 is subjective and is based on the capacity oh the analyst to apprise a
possible error. For this aim, the crossed information is useful, in which others
parameters found in the same sample are considered. Also, this type of deviation
could be found after the complaint of the client.
The warning limit is generally exceeded in less than 5% from the cases and
the action limit in 0.3 % from the cases.
If one of the rejection rules was broken the followings measures are to be
taken:
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II. AUTOMATIC ANALYTICAL METHODS FOR ENVIRONMENTAL MONITORING AND CONTROL
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
the analysis is repeated and if the new obtained result is good the analytical
process is continued;


if the result is not good, the cause for the exceeding is investigated;
the result for the lot in which the exceeding was registered are not used until the
cause is found . The results can be used only if the existing calculation error can
be;
 after finding and eliminating the sources of errors the analyses are repeated for
the whole batch or even the analyses from the previous batches, function of the
cause that generated the deviations.
B. The R-chart can be obtained by running duplicate analysis in the same
batch of control samples or test samples.
The differences between the results allow the calculation of R -mean
difference between duplicate samples and SR –standard deviation of the range of all
pairs of duplicates. The parameters R and SR are determined for at least 10 initial pairs
of duplicates. The warning and control line can be drawn at 2s and 3s distances from
the mean of differences. The graph is single–sided so that the lowest observable value
of the difference will be zero (Figure III.3.2).
R
LA
LW
R
Date /batch
LW = warning limit
LA = action limit
Fig. III.3.2. Control chart of the type recovery rate ( R -chart)
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II. AUTOMATIC ANALYTICAL METHODS FOR ENVIRONMENTAL MONITORING AND CONTROL
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Running duplicates of a control sample in each batch is the simplest way of
controlling precision.
A limitation of the use of duplicates of a control sample in every batch is the
simplest way to check the precision.
A disadvantage of this type of precision control is the fact that it does not
reflect completely the analysis precision for the analyzed sample both as function of
the matrix composition and the concentration. The most convenient way to deal with
this problem is to use more than one control sample with different concentrations or to
use test samples instead of control samples.
The quality control rules and the measures to be taken are similar to those of
the Mean Chart, respectively.
Warning rules (if occurs) lead to the further inspection of the data:
 a single control result over the attention limit;
Rejection rules – (if occurring) lead to the rejection of the data
1.
-1 result over the action limit;
2.
-2 consecutive results above the same warning limit;
3.
-7 consecutive results by the same side of the mean value;
4.
-10 consecutive results from 11 with the same value;
5.
-when a result is possibly incorrect.
In the large laboratories, computers generate the control charts automatically.
For the small or medium laboratories is recommended the manual execution of the
chart and where available the computer aided calculation.
III. 3.2. Example of a Control Chart Construction
In the next example is presented the control chart obtained for a control
sample prepared from a Cr6+ Certified Reference Material having a certified value of
21.25 µg/mL.
In Table III.3.1 are presented the results obtained for the repeated
determinations done during the 20 days interval. The calculated values of the
parameters, which are used for the control chart, are registered in the same table.
The calculated data is filled in the control chart filling also the number of the
batch or the date of the analysis – on the abscissa and the concentration or analytical
signal– on the ordinate. The lines which mark the mean of the value, the warning
limits and the action limits are colored differently in order to watch easily the possible
exceeds of the limit values.
In the form from the figure III.3.3 was traced the control chart for a Cr 6+
solution.
Then, for every batch of minimum 20 analyzed samples a control sample with
known concentration was analyzed and the results were written in the chart, together
185
II. AUTOMATIC ANALYTICAL METHODS FOR ENVIRONMENTAL MONITORING AND CONTROL
Laboratory exercises
with the date of the of the testing and identification of the person which made the
analyses.
Table III.3.1. Results of the determinations for the tracing of the control chart
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
xi value
20.76
20.91
21.33
21.34
21.45
21.45
21.61
21.57
21.57
21.57
21.61
21.54
20.97
20.96
21.57
20.92
21.21
21.18
20.96
20.95
_
xi value = 21.2715µg/mL
s = 0.303 µg/mL
2s = 0.606 µg/mL
3s = 0.909 µg/mL
x +2s = 21.877 µg/mL
x +3s = 22.180 µg/mL
x -2s = 20.665 µg/mL
x -3s = 20.362 µg/mL
The obtained results were:
Date
12.04.2004
19.05.2004
29.05.2004
30.06.2004
16.07.2004
24.07.2004
07.08.2004
15.08.2004
29.08.2004
The obtained value µg/mL
21.375
21.601
21.090
20.703
21.375
21.271
21.271
21.601
20.901
With the help of graphical representation can be easily seen which of the
determined values are not in the admissible limits and interventions can be made in the
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II. AUTOMATIC ANALYTICAL METHODS FOR ENVIRONMENTAL MONITORING AND CONTROL
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appropriate time for the redressing of the analytical process.
Fig. III.3.3. The control chart for a Cr6+ solution
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II. AUTOMATIC ANALYTICAL METHODS FOR ENVIRONMENTAL MONITORING AND CONTROL
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III.3.3. Exercise
For drawing the control chart of lead determination by atomic absorption
spectroscopy were performed 20 repeated tests on a standard solution with a content
of 10 mg Pb/L. the following results were obtained:
x1
x2
x3
x4
x5
= 10.07
= 10.09
= 9.94
= 9.98
= 9.91
x6
x7
x8
x9
x10
= 9,83
= 9.92
= 9.61
= 9.79
= 9.72
x11
x12
x13
x14
x15
= 10.09
= 9.92
= 9.94
= 9.72
= 10.07
x16
x17
x18
x19
x20
= 9,98
= 9.91
= 9.61
= 9.79
= 9.83
Using the calculation formulas for mean value ( x ) and for standard deviation ( s ) the
following results were obtained:
n
n
a)
x
x
i 1
n
i
= 9.887
b)
s
 (x
i
 x)2
i 1
n 1
= 0.151
The values for the warning limits x  2 s and the action limits x  3 s
were calculated obtaining the values:
2 s = 0.302 mg/L
3 s = 0.453 mg/L
x + 2s = 10.19 x + 3s = 10.34
x - 2s = 9.58 x - 3s = 9.43

Mark on the control chart (Fig. III.3.4) the lines for the mean value ( x ) , for the
warning limits and for the action limits.
On the control samples with the concentration of 10 mg/L were done
determinations, in time, and the following values were obtained:
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Determination Date
7.01
18.01
21.01
24.01
28.01
03.02
07.02
12.02
17.02
19.02
22.02
01.03
09.03
Determined
Value
9.985
9.813
10.48
10.04
10.01
9.98
9.93
9.91
9.90
9.84
9.97
9.45
9.51
Determination
Date
15.03
19.03
24.03
30.03
07.04
12.04
19.04
25.04
30.04
04.05
10.05
17.05
20.05
Determined Value
9.65
9.98
9.98
9.98
9.98
9.98
9.98
9.98
9.98
9.98
9.98
9.98
9.97
Mention on the chart these values and mention in which cases the analytical
system is out of control being required intervention measures.
1.
2.
3.
4.
5.
6.
References
EURACHEM Guide – The Fitness for Purpose of Analytical Methods. A
Laboratory Guide to Method Validation and Related Topics, First English
Edition, 1998;
EURACHEM Guide - Quantifying Uncertainty in Analytical Measurement,
Second edition, 1999;
NATA 17025, Laboratory assessment worksheet – august, 2000;
W. Funk, V. Dammann, G. Donnevert “Quality Assurance in Analytical
Chemistry”, VCH, 1995;
ISO 7870:1993- Chart Control – General Principles and applications;
ISO 8258-1991- Shewart Chart Control.
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Fig. III.3.4. The control chart.
190