II · Web viewA Laboratory Guide to Method Validation and Related Topics, First English Edition, 1998; EURACHEM Guide - Quantifying Uncertainty in Analytical Measurement, Second edition,

II. AUTOMATIC ANALYTICAL METHODS FOR ENVIRONMENTAL MONITORING AND CONTROLLaboratory exercises

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 AspectsValidation 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 ; reproducibility.

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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 Related performance parameters- Qualitative or quantitative answer? Confirmation of identity,

selectivity/specificity,Limit of detectionLimit of quantification

For the analyte present in more than one form, is important the extractable, free or total analyte?

Recovery

analyte(s) of interest and the most probable level (%, g g-1, ng g-1 etc.)?

Limit of detectionLimit of quantificationWorking range

Level of precision and accuracy, allowed uncertainty degree.

RecoveryAccuracy Repeatability Reproducibility

Possible interferences Selectivity/specificityComparison of results with results from other laboratories?

robustnessReproducibility

Comparison of the results with external specifications?

AccuracyReproducibility

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. LoD is expressed as the analyte concentration corresponding to:

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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; sbl

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

LIMIT OF DETECTION (LoD)Measurements 10 independent blank samples one time measured or

or 10 blank samples fortified at lowest acceptable concentration , one time measured

Determination/Estimation LoD = 3s + Xin which:s = standard deviation for the blank or blank fortified with an analyte samplesX = measured value or mean measured value

Optimum 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.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:

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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)Measurements 10 independent blanks one time measured

or 10 blank samples fortified at lowest acceptable concentration , one time measured

Determination /Estimation LoQ = 10s + Xwhere:s = standard deviation for the blank or blank fortified with an analyte samplesX = measured value

Optimum value function of tested method type

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.

Table III.1.4. Working range.

WORKING RANGE

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Measurements From the calibrating curve with 6-10 ascending and

equidistant concentrations points Determination/Estimation -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

Optimal value/Interpretation -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.

Specificity is generally considered to be 100% selectivity.Sensitivity

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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.

SENSITIVITYMeasurements From calibrating curve with 6-10 ascending and

equidistant concentrations points Determination/Estimation b= calibrating curve slope

or S = Δ Y/ Δ C

where:S = sensitivityΔ Y= absorbance variationΔ C = concentration variation

Optimal value -alternates on different concentration ranges

RobustnessThe 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.

RecoveryRecovery 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.

AccuracyAccuracy 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.

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”.

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Table III.1.6. Robustness.

ROBUSTNESSMeasurements 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 temperatureThe 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 (–).

Determination /Estimation The Youden and Steiner scheme will be appliedExperiment Factors

A B C

Result

1 + + +

Y1

2 - + -

Y2

3 + - +

Y3

4 - - - Y4The effect A = (∑ Y A+ - ∑ Y A- ) /2Where : ∑ 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- ) /2The effect C = (∑ Y C+ - ∑ Y C- ) /2

Optimum value/Interpretation The effect of modified factor will be established by applying the t-Student test or a strong modifying effect will be considered if: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

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modifications do not have an important influence on the theoretical values.

Table III.1.7. Accuracy

ACCURACYMeasurements 10 analyses repeated for a known concentration

sample prepared from a reference material (standard substance)

Determination/Estimation Accuracy % = ( - μ ) x 100where:

= the mean of the 10 determinations μ = the real value of the reference material (standard substance)

Bias % =

Optimum value/Interpretation -100%-the obtained value will be checked using the t-student 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.

RepeatabilityRepeatability 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.

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.

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Table III.1.8. Precision.

PRECISIONMeasurements 10 analyses repeated for a known concentration

sample prepared from a reference material (standard substance)

Determination/EstimationCV ( RSD) % =

where:= mean value of the 10 determinations

s = standard deviationOptimal value - depends on the tested method

Table III.1.9. Repeatability.

REPEATABILITYMeasurements 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

Determination/Estimation r = 2.8 x sr

where:sr = repeatability standard deviation

Optimal value -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 10 replicates, on different equipment, in an extended timescale. For the inter-laboratory reproducibility is necessary to organize a collaborative study.

Table III.1.10. Internal reproducibility.

INTERNAL REPRODUCIBILITY

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Measurements 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.

Determination/Estimation RL = 2.8 x 1.6 x sr = 1.6 x rwhere:sr = repeatability standard deviationr = repeatability

Optimal value - depends of the methods and the laboratory’s level of proficiency

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.

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.

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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.

Concentration, g in a 25 mL calibrated flaskSample 1 0.1159Sample 2 0.0982Sample 3 0.0569Sample 4 0.0645Sample 5 0.1628Sample 6 0.1804Sample 7 0.0902Sample 8 0.09Sample 9 0.0452Sample 10 0.0455Mean value - X 0.02786Standard deviation - s 0.1065153s 0.31954610s 1.065152

g g/mLLoD X + 3s 0.457406 0.0169 LoQ X +10s 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+;- 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+/mLThe 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 24g Cr6+ fortified with

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Determinations no.

0 gCr6+ 4 gCr6+ 0 g Cr6 6 g Cr6

Absorbance

Concentration. g

Absorbance

Concentration. g

Absorbance

Concentration. g

Absorbance

Concentration. g

1 0.2810 16.4587 0.3481 20.4133 0.4173 24.4918 0.5180 30.42672 0.2806 16.4351 0.3423 20.1246 0.4175 24.5035 0.5145 30.22043 0.2799 16.3997 0.3476 20.3839 0.4165 24.4691 0.5169 30.3704

Mean - 16.4312 - 20.3073 - 24.4881 - 30.3392Recovered quantity 3.88 5.85

R % 96.90 97.52

Table III.1.13. Recovery and trueness from CRM

Determinations no. Results, in g Cr6+/mL1 21.452 21.213 21.184 20.965 20.956 20.977 21.54

Mean 21.18R % 99.67Trueness %

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:

Concentration, mg/LSample 1 0.0952Sample 2 0.0955Sample 3 0.0987Sample 4 0.1010Sample 5 0.0996Sample 6 0.0970

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Sample 7 0.0970Sample 8 0.0980Sample 9 0.0950Sample 10 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 AspectsThe 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:145


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 valueScopeDetermination 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.

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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Weighing

Filtration

Result

Drying

Washing

Weighing

Weighing

Filtration

Result

Drying

Washing

Weighing


Table III.2.1.

Description X value Standard uncertainty u(x)

Relative Standard

uncertainty, u(x)/x

TSM Content of TSM, mg /L 13 2.2 0.1692m2 - m1 Mass of residue, mg 1.3 0.22 0.1692

V1 Volume analyzed, mL 100.0 0.08 0.0008

Step 2: Identification of the Uncertainty SourcesThe 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 Componentsa) 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 mLThe 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 mLStep 4: Calculation of the Total UncertaintyTSM is given by the formula:

TSM = (m2 – m1)x 1000/V

where: m1 - vessel without residue: 23.1540g; m2 - - vessel with residue: 23.1553 gThe residue mass is 0.0013 g = 1.3 mg.The content of TSM becomes:

TSM = 1.3 x 1000/100 = 13 mg/LTable 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 Value x Standard uncertainty u(x)

Relative standard uncertainty u(x)/x

Mass of residue (mg) 1.3 0.22 0.1692Volume V (mL) 100.0 0.08 0.0080

For this simple multiplicative expression, the uncertainties associated with each component are combined as follows:

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 B C D1 m2 –m1 V2 Value 1.3 100.003 Uncertainty 0.22 0.0845 m2 –m1 1.3 1.52 1.36 V 100.0 100.00 100.0878 c(TSM) 13 15. 2 12.999 2.2 0.0110 u2 4.8401 4.84 0.00011112 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-D6; C9 = the difference between C8 and B8; D9 = the difference between D8 and B8; C10 =

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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 titrationGoalA solution of (HCl) is standardized against a solution of (NaOH) with

known concentration. IntroductionThis 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: SpecificationA 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.

ProcedureThe 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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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:

, mol.L-1

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 fractionVT2 :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 sourcesThe 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).

151

Weighing of KHP

Titration of KHP with NaOH

Transfer of an aliquot of HCl

Titration of HCl with NaOH

RESULT

Weighing of KHP

Titration of KHP with NaOH

Transfer of an aliquot of HCl

Titration of HCl with NaOH

RESULT


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 HCl15 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 componentsThe goal of this step is to quantify each uncertainty source analyzed in step 2. RepeatabilityThe 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.

152

C(HCl)

V (T2)

End Point

V(T1)

Temperature

Calibration

Repeatability

RepeatabilityInfluenceBIAS

Calibration

Sensitivity

LinearityRepeatability Repeatability

Calibration

Sensitivity

Linearity

m(KHP)(KHP)

Repeatability

Calibration

Temperature

End point

Repeatability/InfluencesP(KHP) F(KHP) V(HCl)

Repeatability

Calibration

Temperature

m(tare)

C(HCl)

V (T2)

End Point

V(T1)

Temperature

Calibration

Repeatability

RepeatabilityInfluenceBIAS

Calibration

Sensitivity

LinearityRepeatability Repeatability

Calibration

Sensitivity

Linearity

m(KHP)(KHP)

Repeatability

Calibration

Temperature

End point

Repeatability/InfluencesP(KHP) F(KHP) V(HCl)

Repeatability

Calibration

Temperature

m(tare)


m KHPCalibration/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:

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

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:

V (T2)

1. Calibration: The value provided by the manufacturer is (±0.03 mL) and is

approximated to a triangular distribution:

2. Temperature: The possible temperature variation is within the limits of ±4°C and approximated to a rectangular distribution:

153


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 CO 2 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:

V (T1)All contributions except the one for the temperature are the same as for VT2:

1. Calibration:

2. Temperature: The approximate volume for the titration of 0.3888 g KHP is 19

mL NaOH, therefore its uncertainty contribution is :

3. Change in the end-point of titration: NegligibleVT1 is found to be 18.64 mL with a standard composed uncertainty u(VT1) of:

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 molecular weight

Quoted uncertainty Standard uncertainty

C 12.0107 0.0008 0.00046H 1.00794 0.00007 0.000040O 15.9994 0.0003 0.00017K 39.0983 0.0001 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

.The molar mass for KHP and its standard composed uncertainty are:

154


FKHP = 8·12.0107+5·1.00794+4·15.9994+39.0983 = 204.2212 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.

V(HCl)1) Calibration: The uncertainty was stated by the manufacturer for a 15 mL pipette

as ±0.02 mL and is approximated with a triangular distribution:

2) Temperature: The temperature of the laboratory is within the limits of ±4°C. Using a rectangular temperature distribution is obtained a standard uncertainty of:

Combining these contributions is obtained the value of:

Step 4: Calculating the combined standard uncertainty cHCl is given by

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

Description Value X StandardUncertainty

u(x)

Relative standard

uncertainty

155


u(x)/x

m KHP Mass of KHP 0.3888 0.00013 0.00033P KHP Purity of KHP 1.0 0.00029 0.00029

VT2Volume of NaOH for HCl titration 18.89 0.015 0.0010

VT1Volume of NaOH for KHP titration 18.64 0.016 0.00086

FKHP Molar mass of KHP 204.2212 0.0038 0.000019

VHClHCl aliquot for NaOH titration 15 0.011 0.00073

Using these values:

The uncertainties associated with each component are composed accordingly:

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

Table III.2.6. Table for the calculation of uncertainty

156


A B C D E F G H

1 m (KHP)

P (KHP)

V (T2)

V (T1)

F (KHP)

V (HCl)

2 value 0.3888 1.0 14.89 18.64 204.2212 153 uncertainty 0.00013 0.00029 0.015 0.016 0.0038 0.01145 m (KHP) 0.3888 0.38893 0.3888 0.3888 0.3888 0.3888 0.38886 P (KHP) 1.0 1.0 1.00029 1.0 1.0 1.0 1.07 V (T2) 14.89 14.89 14.89 14.89 14.89 14.89 14.898 V (T1) 18.64 18.64 18.64 18.64 18.64 18.64 18.649 F (KHP) 204.2212 204.2212 204.2212 204.2212 204.2212 204.2212 204.221210 V (HCl) 15 15 15 15 15 15 151112 c (HCl) 0.101387 0.101421 0.101417 0.101489 0.101300 0.101385 0.10131313 0.000034 0.000029 0.000102 -0.000087 -0.0000019 -0.00007414 2.55E-8 1.1E-9 8.64E-10 1.043E-8 7.56E-9 3.56E-12 5.52E-91516 u(c(HCl)) 0.00016

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

SummaryGoalThe 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.

Measurement procedure157

0 0.0005 0.001 0.0015 Relative standard uncertainty

m (KHP)

P (KHP)

V (T2)

V (T1)

F (KHP)

V (HCl)

c (HCl)


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

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.

Description Value x Standarduncertainty u(x)

Relative standarduncertainty u(x)/x

c0 Content of Cd in the acid solution that extracted the metal

0.26mg.l-1 0.018mg.l-1 0.069

VL Volume of the acid that extracted (by dissolving) the metal

0.332 l 0.0018 l 0.0054

aV Surface area of the vessel 2.37dm2 0.06dm2 0.025facid Influence of the acid

concentration1.0 0.0008 0.008

ftimp Influence of the time 1.0 0.001 0.001ftemp Influence of temperature 1.0 0.06 0.06r Mass of cadmium

extracted by area unit 0.036mg.dm-2 0.0033 mg.dm-2 0.09

158


Fig. III.2.5. Metal extraction procedure

159

Preparation

Surfaceconditioning

Fill with 4% vol

acetic acid

Metal extraction by dissolving

Homogenization of acid solution

AASDetermination AAS

Calibration

Preparing ofcalibrationstandards

RESULT

Preparation

Surfaceconditioning

Fill with 4% vol

acetic acid


Homogenization of acid solution

AASDetermination AAS

Calibration

Preparing ofcalibrationstandards

RESULT


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 samplesThe samples will be washed at 405C in an aqueous solution containing 1

mg/Lof domestic liquid detergent, rinsed with water (as specified above), drained and 160

Calibration curvef(acid)f(time)

f(temperature)

Length (1)Length (2)

Area

Loading Temperature

CalibrationReading

c(0) V(L)

A(V) d

Result, r


f(temperature)


Area

Loading Temperature

CalibrationReading

c(0) V(L)

A(V) d

Result, r


f(temperature)


Area

Loading Temperature

CalibrationReading

c(0) V(L)

A(V) d

Result, r


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.

ProcedureThe analytical procedure is illustrated schematically in Figure III.2.7 :

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.

iii. The quantity of 4% v/v acetic acid required or used is recorded to an accuracy of ±2%

161

Preparation

Surfaceconditioning

Fill with 4% v/v acetic acid


Homogenize acid solution

AASdetermination

AASCalibration

Prepare calibrationstandards

RESULT

Preparation

Surfaceconditioning

Fill with 4% v/v acetic acid


Homogenize acid solution

AASdetermination

AASCalibration

Prepare calibrationstandards

RESULT


iv. 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.v. 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

i). 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.

ii). 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 curveThe concentration c0 of lead or cadmium is calculated using:

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 reportThe 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 sourcesStep 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

162


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 theresult. 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:

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 curved : 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).

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:

163

Calibration curve

1 Length2 Length

Area

Loading Temperature

CalibrationReading

A(V) d

Result, r

Calibration curve

1 Length2 Length

Area

Loading Temperature

CalibrationReading

A(V) d

Result, r


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 sourcesThe 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.

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

164


f(temperature)


Area

Loading Temperature

CalibrationReading

c(0) V(L)

A(V) d

Result, r


f(temperature)


Area

Loading Temperature

CalibrationReading

c(0) V(L)

A(V) d

Result, r


f(temperature)


Area

Loading Temperature

CalibrationReading

c(0) V(L)

A(V) d

Result, r


standard uncertainty of a volume of 332 mL, assuming a rectangular temperature distribution, is

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:

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] 1 2 30.1 0.028 0.029 0.0290.3 0.084 0.083 0.0810.5 0.135 0.131 0.1330.7 0.180 0.181 0.1830.9 0.215 0.230 0.216

165


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 Standard deviationB1 0.2410 0.0050B0 0.0087 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.

Fig. III.2.10. Linear fit by the least square method and uncertainty interval for duplicate determinations.

166

x

x

x

x

xx

Concentration of Cd[mg/L]

0.25

0.20

0.15

0.10

0.05

0.00

0.0 0.2 0.4 0.6 0.8 1.0

Abs

orba

nce

x

x

x

x

xx

Concentration of Cd[mg/L]

0.25

0.20

0.15

0.10

0.05

0.00

0.0 0.2 0.4 0.6 0.8 1.0

Abs

orba

nce


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)=

with the residual standard deviation given by:

and

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)

167


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.

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

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/ = 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 estimated change in facid of approximately 0.1 per % v/v. In a separate experiment the

168


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

Description Value Standard uncertainty u(x)

Relative standard uncertainty u(x)/x

c0 Content of cadmium in the acid solution

0.26 mg.L-1 0.018 mg.L-

10.069

VL Volume of acid that extracted the Cd

0.332 L 0.018 L 0.054

aV Surface area of the vessel

2.37 dm2 0.06 dm2 0.025

facid Influence of the acid concentration

1.0 0.0008 0.0008

ftimp Influence of the time 1.0 0.001 0.001ftemp Influence of temperature 1.0 0.06 0.06

Step 4: Calculating the combined standard uncertaintyThe amount of cadmium extracted per unit area, is given by:

The intermediate values and their standard uncertainties are collected in Table III.2.10.

Employing those values is obtained:

In order to calculate the combined standard uncertainty of a product (as the one above) the standard uncertainties are used as follows:

169


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 B C D E F G H

1 c0 VL aV facid ftime ftemp

2 value 0.26 0.332 2037 1.0 1.0 1.0

3 uncertainty

0.018 0.0018 0.06 0.0008 0.001 0.06

45 c0 0.26 0.278 0.26 0.26 0.26 0.26 0.26

6 VL 0.332 0.332 0.3338 0.332 0.332 0.332 0.332

7 aV 2.37 2.37 2.37 2.43 2.37 2.37 2.37

8 facid 1.0 1.0 1.0 1.0 1.0008 1.0 1.0

9 ftime 1.0 1.0 1.0 1.0 1.0 1.001 1.0

10 ftemp 1.0 1.0 1.0 1.0 1.0 1.0 1.06

11 1.0

12 r 0.036422 0.038943 0.036619 0.035 523

0.036458 0.038607

13 u(y,xi) 0.002521 0.000197 -0.000899

0.036 451 0.000036 0.002185

14 u(y)2 1.199 E-5 6.36 E-8 3.90 E-8 8.09 E-7 0.000 029 1.33 E-9 4.78 E-6

15 8.49 E-10

16 uc(r) 0.0034

170


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. .

IntroductionThis 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: SpecificationThe 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.

ProcedureThe 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 sub-samples are homogenized. Where extreme inhomogeneity is suspected proportional sampling is used before blending.

ii) Weighing of sub-samples for analysis gives the sample mass msample

iii) 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.

171


iv) Liquid-liquid extraction: acetonitrile/hexane liquid partition, washing the

acetonitrile extract with hexane, water removal from the hexane layer using a sodium sulfate column.

v) Concentration of the washed extract by passing gas through the extract to near vapor point.

vi) Dilution to standard volume Vop (approx. 2 mL) in a 10 mL graduated tube.vii) Measurement: Injection and GC measurement of a 5 L extract sample to

obtain the peak intensity Iop.viii) Preparation of an approximately 5 g/mL standard solution (actual mass

concentration cref).ix) GC calibration using the prepared standard and injection and GC measurement

of 5 l of the standard to give a reference peak intensity Iref.

Fig. III.2.11. Organophosphoric pesticides analysis

CalculationThe mass concentration cop in the final sample is given by:

172

Homogenization

Extraction

Washing

Concentration

GC Determination

Preparing the solution

GC Calibration

Result

Homogenization

Extraction

Washing

Concentration

GC Determination

Preparing the solution

GC Calibration

Result


and the estimate level of pesticide Pop in the sample (mg/kg) is given by:

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]

ScopeThe 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 sourcesThe 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:

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.

173


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.

Fig. III.2.12. Cause and effect diagram with added main branches for samples non-homogeneous.

Step 3: Quantifying uncertainty componentsThe 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.

174

Precision

PrecisionPrecision

Precision

Precision

Precision

m(tare)Linearity

calibrationm(sample)

Calibration

F(hom) Recovery I(ref)

Calibration

m(gross)Linearity

V(op)

Temperature

Calibration

Purity (ref)

CalibrationDilution

V(ref)Temperature Calibration

m(ref)

Calibration (lin)I(op)

Calibration

Sensitivitye

Precision

Precision

Sensitivity

Precision

PrecisionPrecision

Precision

Precision

Precision

m(tare)Linearity

calibrationm(sample)

Calibration

F(hom) Recovery I(ref)

Calibration

m(gross)Linearity

V(op)

Temperature

Calibration

Purity (ref)

CalibrationDilution

V(ref)Temperature Calibration

m(ref)

Calibration (lin)I(op)

Calibration

SensitivityeSensitivitye

PrecisionPrecision

PrecisionPrecision

SensitivitySensitivity


Fig. III.2.13. Cause and effect diagram after rearrangement to accommodate the data of the validation study

1. Precision studyThe 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 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:

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

175

P(op)

m(tare)

Linearity

Calibration (2)m(sample)

Calibration (2)

F(hom)(3) Recovery(2) I(ref)

Calibration (3)

m(gross)

Linearity

V(op))

Temperature(2)

Calibration (2)

c(ref)

Purity(ref)

Calibration (2)Dilution

V(ref)

Temperature(2) Calibration

m(ref)

Calibration (lin)(2)I(op)

Calibration (3)

I(op)

I(ref)

m(ref)

V(ref)

dilution

V(op)m(sample)

m(tare)

Linearity


Calibration (2)


Calibration (3)

m(gross)

Linearity

V(op))

Temperature(2)

Calibration (2)

c(ref)

Purity(ref)


V(ref)


m(ref)


Calibration (3)

I(op)

I(ref)

m(ref)

V(ref)

dilution

V(op)m(sample)


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 studyThe interferences of the analytical procedure were investigated during the in-

house 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:

There are three possible cases arising for the value of the recovery : taking into account that is not significantly different from 1, so no

correction is applied. taking into account that is significantly different from 1 and a

correction is applied. taking into account that 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:

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

). If t tcrit than is significantly different from 1.

t = 2.31 tcrit,41 2.021

In this example a correction factor (1/ ) was applied and therefore is explicitly included in the calculation of the result.

Table III.2.12. Results of duplicate pesticide analysis

Residue D1 [mg/kg] D2 [mg/kg] Mean [mg/kg]

DifferenceD1-D2

Difference/mean

Malathion 1.30 1.30 1.30 0.00 0.000Malathion 1.30 0.90 1.10 0.40 0.364Malathion 0.57 0.53 0.55 0.04 0.073Malathion 0.16 0.26 0.21 -0.10 -0.476Malathion 0.65 0.58 0.62 0.07 0.114

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Pirimiphos Methyl

0.04 0.04 0.04 0.00 0.000

Chloropyrifos Methyl

0.08 0.09 0.085 -0.01 -0.118

Pirimiphos Methyl

0.02 0.02 0.02 0.00 0.000


0.01 0.02 0.015 -0.01 -0.667

Pirimiphos Methyl

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

Pirimiphos Methyl

0.07 0.08 0.75 -0.10 -0.133


0.1 0.01 0.10 0.00 0.000

Pirimiphos Methyl

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 Conc.[mg kg–1] N1) Mean2)[%] s

2) [%]

Waste Oil PCB 10.0 8 84 9Butter OC 0.65 33 109 12

Compound Animal Feed I OC 0.325 100 90 9

Animal & Vegetable Fats I OC 0.33 34 102 24

Brassicas 1987 OC 0.32 32 104 18Bread OP 0.13 42 90 28Rusk OP 0.13 30 84 27

M OC 0.325 8 95 12M OC 0.325 9 92 9

R OC 0.325 11 89 13W OC 0.325 25 88 9S OC 0.325 13 85 19B OC 0.325 9 84 22

1) The number of experiments carried out2) The mean and sample standard deviation s are given as recovery percentage.

3. Other sources of uncertaintyThe 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

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(2) Considered during the interference study of the analytical procedure(3) To be considered during the evaluation of the other sources of uncertainty.

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 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

178

m(tare)

Linearity


Calibration (2)


Calibration (3)

m(gross)

Linearity

V(op))

Temperature(2)

Calibration (2)

c(ref)

Purity(ref)


V(ref)


m(ref)


Calibration (3)

I(op)

I(ref)

m(ref)

V(ref)

dilution

V(op)m(sample)

m(tare)

Linearity


Calibration (2)


Calibration (3)

m(gross)

Linearity

V(op))

Temperature(2)

Calibration (2)

c(ref)

Purity(ref)


V(ref)


m(ref)


Calibration (3)

I(op)

I(ref)

m(ref)

V(ref)

dilution

V(op)m(sample)


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 uncertaintyDuring 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 Remarks

Repeatability(1) 1.0 0.27 0.27

Duplicate tests of different

types of samples

Bias (Rec)(2) 0.9 0.043 0.048 Spiked samples

Other sources(Homogeneity)(3) 1.0 0.2 0.2

Estimations founded on

model pollution

-- -- 0.34Relative 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.

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The spreadsheet for this case takes the form shown in Table III.2.15.

Table III.2.15. Uncertainty in pesticide analysis

A B C D E1 Repeatability Bias Homogeneity2 value 1.0 0.9 1.03 uncertainty 0.27 0.043 0.245 Repeatability 1.0 1.27 1.0 1.06 Interference 0.9 0.9 0.9043 0.97 Homogeneity 1.0 1.0 1.0 1.289 1.1111 1.4111 1.1058 1.333

10 0.30 - 0.0053 0.22211 0.1394 0.09 0.00002

80.04938

1213 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

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 ( -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 -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, , 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

181


Fig. III.3.1. Control chart of the Mean ( -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: 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;

182

LW = warning limitLA = action limit

Date/batch

Conc.(mg/L)

s (LA) x 3

s (LW) x 2

x

s (LW) - x 2

s (LA)- x 3


Date/batch

Conc.(mg/L)

s (LA) x 3

s (LW) x 2

x

s (LW) - x 2

s (LA)- x 3


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 -mean difference between duplicate samples and SR –standard deviation of the range of all pairs of duplicates. The parameters 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).

Fig. III.3.2. Control chart of the type recovery rate ( -chart)

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.

183


R

Date /batch

LA

LW

R


R

Date /batch

LA

LW

R


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 data1. -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 Cr6+

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 with the date of the of the testing and identification of the person which made the analyses.

184


Table III.3.1. Results of the determinations for the tracing of the control chart

Day xi value

_xi value = 21.2715µg/mL

1 20.762 20.913 21.334 21.345 21.456 21.457 21.618 21.579 21.5710 21.5711 21.6112 21.54

s = 0.303 µg/mL2s = 0.606 µg/mL3s = 0.909 µg/mL+2s = 21.877 µg/mL+3s = 22.180 µg/mL-2s = 20.665 µg/mL-3s = 20.362 µg/mL

13 20.9714 20.9615 21.5716 20.9217 21.2118 21.1819 20.9620 20.95

185


The obtained results were:

Date The obtained value µg/mL12.04.2004 21.37519.05.2004 21.60129.05.2004 21.09030.06.2004 20.70316.07.2004 21.37524.07.2004 21.27107.08.2004 21.27115.08.2004 21.60129.08.2004 20.901

186


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 appropriate time for the redressing of the analytical process.

187


Fig. III.3.3. The control chart for a Cr6+ solution

188


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 = 10.07 x6 = 9,83x2 = 10.09 x7 = 9.92x3 = 9.94 x8 = 9.61x4 = 9.98 x9 = 9.79x5 = 9.91 x10 = 9.72

x11 = 10.09 x16 = 9,98x12 = 9.92 x17 = 9.91x13 = 9.94 x18 = 9.61x14 = 9.72 x19 = 9.79x15 = 10.07 x20 = 9.83

Using the calculation formulas for mean value ( ) and for standard deviation ( s ) the following results were obtained:

a)x

x

n

ii

n

1 = 9.887 b)s

x x

n

ii

n

( ) 2

1

1= 0.151

The values for the warning limits 2 s and the action limits 3 s were calculated obtaining the values:

2 s = 0.302 mg/L x + 2s = 10.19 x + 3s = 10.343 s = 0.453 mg/L x - 2s = 9.58 x - 3s = 9.43

Mark on the control chart (Fig. III.3.4) the lines for the mean value ( ) , 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:

189


Determination Date Determined

ValueDetermination

DateDetermined Value

7.01 9.985 15.03 9.6518.01 9.813 19.03 9.9821.01 10.48 24.03 9.9824.01 10.04 30.03 9.9828.01 10.01 07.04 9.9803.02 9.98 12.04 9.9807.02 9.93 19.04 9.9812.02 9.91 25.04 9.9817.02 9.90 30.04 9.9819.02 9.84 04.05 9.9822.02 9.97 10.05 9.9801.03 9.45 17.05 9.9809.03 9.51 20.05 9.97

190


Mention on the chart these values and mention in which cases the analytical system is out of control being required intervention measures.

References1. EURACHEM Guide – The Fitness for Purpose of Analytical Methods. A

Laboratory Guide to Method Validation and Related Topics, First English Edition, 1998;

2. EURACHEM Guide - Quantifying Uncertainty in Analytical Measurement, Second edition, 1999;

3. NATA 17025, Laboratory assessment worksheet – august, 2000;4. W. Funk, V. Dammann, G. Donnevert “Quality Assurance in Analytical

Chemistry”, VCH, 1995;5. ISO 7870:1993- Chart Control – General Principles and applications;6. ISO 8258-1991- Shewart Chart Control.

191


Fig. III.3.4. The control chart.

192

Documents

II · Web viewA Laboratory Guide to Method Validation and Related Topics, First English Edition, 1998; EURACHEM Guide - Quantifying Uncertainty in Analytical Measurement, Second edition,