An Introduction to Quality Assurance in Analytical

ScienceDr Irene Mueller-Harvey

Mr Richard Baker

Mr Brian Woodget

University of Reading

Part 5 - Expression of Results

Contents:• Validation, traceability and measurement uncertainty (slides 3,4)• The ‘what’, ‘why’ and ‘how’ of measurement uncertainty (slides 5-15)• Reporting results (slide 16,17)

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The Famous Trio:

When expressing results of analytical measurements youwill need to bear in mind the 3 inter-linking parameters of:

VALIDATION

TRACEABILITY

MEASUREMENTUNCERTAINTY

Has the method been validatedand it is fit for

purpose?

Will the resultsbe traceable

to an acceptedreferencestandard?

How sure will yoube of the accuracy

of the resultsobtained?

About validation, traceability & measurement uncertainty

As you have seen in Part 1 of this presentation, allanalytical results have an error associated with them.Measurement uncertainty is an estimate of the potentialsize of that error and is affected by both the time andeffort put into method validation and the traceability of standard reference materials and substances

Note: refer to Part 2 of the presentation for a descriptionof method validation and to Part 3 for a description

of traceability

Measurement Uncertainty (1)

Analysis of a sample of soil has shown it to contain 30 + 5 mg/kg of lead

Mean result fromreplicate analyses

Estimate of themeasurement

uncertainty

Note: accredited laboratories (ISO 17025) carrying out this analysis wouldneed to be aware of the levels of uncertainty but would not necessarily have to

present this data unless asked. So the result could well be presented as 30 mg/kg

You need to consider from where the uncertainty is likely to arise

Measurement Uncertainty (2)

Sources of uncertainty arise from ALL aspects of the analysis -these could include:

Volumetricglassware

Calibration standards sampling

samplepreparation

instrumentsoperatorskill

Potential sources of error

MeasurementUncertainty (3)

To estimate the measure of overall uncertainty, errors likely to occur in all aspects of the analysis need to be taken into account in the form of individual standard deviations (SD). Data may be obtained from:• manufacturers of equipment and reagents (e.g. balances, volumetric glassware, standard reagents etc) • data from method validation• estimates from the literature or from previous experienceAn overall estimate of the uncertainty can then be calculated

by using accepted procedures.

Analyticalbalance

MeasurementUncertainty (3a)

The accuracy of an analytical balance is fundamental to all of the procedures carried out within an analytical laboratory. The balance should be capable of weighing accurately to + 0.1 mg and is the starting point for most measurements (sample weight, preparation of standards, method validation etc.)

The balance must be calibrated periodically against weights traceable to theUK standard held at the National Physical Laboratory (NPL), and checked

at least every day against a set of weights held in the laboratory, specifically for this purpose. All calibration data must be stored.

Measurementuncertainty (4)

The uncertainty estimation process can be illustrateddiagrammatically:

SPECIFICATION - clearstatement of what is being

measured and the relationshipbetween it and parameters on

which it depends

IDENTIFY UNCERTAINTYSOURCES - list sources foreach part of the process or

for each parameter

QUANTIFY UNCERTAINTYCOMPONENTS - estimate the

size of each uncertainty component

CONVERT TO STANDARDDEVIATIONS - express error

component as a standard deviation

CALCULATE THE COMBINED UNCERTAINTY

RE-EVALUATE THE PROCESSIF NECESSARY

Measurementuncertainty (5) Standard uncertainties

A measure of the SD of an uncertainty component [u(y)] - may be calculated from:

• experimental data• accuracy guaranteed by a piece of equipment

– e.g. balance accurate to + 0.1 mg @ 95% confidence which may be converted to a SD– pipette guaranteed to deliver 25 + 0.2 ml. Although no confidence level has been stated, SD may again be calculated.

Measurementuncertainty (6)Combined uncertainties

Dependent upon the type of analysis carried out, thestandard uncertainties may be combined to producea combined uncertainty [uc(y)]

One of three equations may be used, the choice beingdependent upon the complexity of the analysis and therelationship between the components parts

A model equation must be devised which describes in simplealgebraic terms the whole analysis process

Measurementuncertainty (7)

The rules for estimating combined uncertainties dependupon the model algebraic equation devised to illustrate

the analysis process. You only need consider two at thepresent time:

Rule 1 - for models involving only a sum or difference of quantities eg. For y = a + b + c, the combined uncertainty is given by:

[uc(y)]2 = u(a)2 + u(b)2 + u(c)2

Rule 2 - for models involving only a product or a quotient eg:For y = a.b.c or y = a/(b.c) , the combined uncertainty is given by:

[uc(y)/y]2 = [u(a)/a]2 + [u(b)/b]2 + [u(c)/c]2

Measurementuncertainty (7a)

Example to illustrate a calculation involving rule 1

Suppose that you have four components (a, b, c, d) and youneed to know their combined mass and the uncertainty associated with this mass. The following information is available:a = 27.81 g, u(a) = + 0.01 g;b = 32.45 g, u(b) = + 0.02 gc = 46.10 g, u(c) = + 0.08 gd = 19.01 g, u(d) = + 0.02 g

Total mass (T) is given by:T = a + b + c + d = 27.81 + 32.45 + 46.10 + 19.01 = 125.37

[uc(T)]2 = u(a)2 + u(b)2 + u(c)2 + u(d)2

= 0.012 + 0.022 + 0.082 + 0.022

= 0.0073uc(T) = + 0.085

Thus: T = 125.37 + 0.085

Measurementuncertainty (7b)

Example to illustrate a calculation involving rule 2

You have performed an acid/basetitration to measure the molarity (M) of a solution of HCl, by titration with astandard solution of KOH. Thefollowing information is known or was obtained during the titration

CKOH = 0.0990 M, [u(CKOH) = 0.00017]VKOH = 25.54 ml, [u(VKOH) = 0.032]VHCl = 25.00 ml, [u(VHCl) = 0.021]

The equation for the calculationmay be expressed as:

CKOH X VKOHCHCl = = 0.1011 VHCl

Each of the individual standarduncertainties needs to be expressed as an RSD so for:

CKOH = 0.00017/0.0990 = 0.00172

VKOH = 0.032/25.54 = 0.00125

VHCL = 0.021/25.00 = 0.00084

Thus:

uc(CHCl) =[(0.00172)2+ (0.00125)2

+ (0.00084)2]1/2 X 0.1011uc(CHCl) = [0.0000051]1/2 X 0.1011 = 0.00226 X 0.1011 = 0.00023 M

CHCl = 0.1011 + 0.0002 M

Measurementuncertainty (8)

Coverage factor

In order to give confidence to the value for the combineduncertainty, the calculated value uc(y) is often multipliedby a coverage factor (k). For a 95% level of confidence the value of k is 2 [ See Student’s ‘t’ test table]

Note: a more complete description of the principles used for calculatinguncertainties may be found in:“Quantifying Uncertainty in Analytical Measurements”, Eurochem, 1995.“Quality in the Analytical Laboratory”, E. Prichard (Ed), Wiley, 1995, Chapter 6.

Reporting resultsThe test report of an accredited laboratory must conform to the requirements of the accreditation body - usually the report must clearly identify-

- the laboratory- the client- the samples- the date they were received- the method of analysis- the analyst- the date of the report- the unique Test Report no. on every pageThe report format must ensure that there can be no confusion

over which results refer to which samples and it should give any information about the condition of the samples that may have affected the test results.

Benevolent Department

Well-intentioned Organisation

Tel: 01234 567890

Fax: 01234 567891

Test report number Client

Test batch number Recipient's name

Date received Date reported Analyst

Batch description

Details of analyses

Method 7.3.1 is carried out in accordance with BS EN ISO/IEC 17025 standard

Calibration data

Comments

Signed Print name

(authorised signatory)

A UKAS accredited testing laboratory No. £$%&

Amiable Laboratory

mc218 A Client

02/01/02 09/01/02 C.

T02 JAN 002

208 Raw milks

XYZAB

Fat, Protein, Lactose by Milk-o-scan (FAL method 7.3.1)

Typical calibration range for milk samples: Fat: 1.6 - 6.6 % Protein: 2.6 - 4.0 % Lactose: 3.8 - 5.0 %

8 missing samples 51,99,100,135,138,145,164,189

.

£$%&

TEST REPORT HEADER

For Accredited

Tests

(example for demonstration only)