1. An Introduction to Quality Assurance in Analytical Science Dr Irene Mueller-Harvey Mr Richard Baker Mr Brian Woodget

2. 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) The presentation contains some animation which will be activated automatically (no more than a 2 second delay), by mouse click or by use of the page down key on your keyboard.

3. The Famous Trio: When expressing results of analytical measurements you will need to bear in mind the 3 inter-linking parameters of: VALIDATION TRACEABILITY MEASUREMENT UNCERTAINTY Has the method been validated and it is fit for purpose? Will the results be traceable to an accepted reference standard? How sure will you be of the accuracy of the results obtained?

4. About validation, traceability & measurement uncertainty As you have seen in Part 1 of this presentation, all analytical results have an error associated with them. Measurement uncertainty is an estimate of the potential size of that error and is affected by both the time and effort put into method validation and the traceability of standard reference materials and substances Note: refer to Part 2 of the presentation for a description of method validation and to Part 3 for a description of traceability

5. Measurement Uncertainty (1) Analysis of a sample of soil has shown it to contain 30 + 5 mg/kg of lead Mean result from replicate analyses Estimate of the measurement uncertainty Note: accredited laboratories (ISO 17025) carrying out this analysis would need 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

6. Measurement Uncertainty (2) Sources of uncertainty arise from ALL aspects of the analysis - these could include: Volumetric glassware Calibration standards sampling sample preparation instruments operator skill Potential sources of error

7. Measurement Uncertainty (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 experience An overall estimate of the uncertainty can then be calculated by using accepted procedures. Analytical balance

8. Measurement Uncertainty (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 the UK 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.

9. Measurement uncertainty (4) The uncertainty estimation process can be illustrated diagrammatically: SPECIFICATION - clear statement of what is being measured and the relationship between it and parameters on which it depends IDENTIFY UNCERTAINTY SOURCES - list sources for each part of the process or for each parameter QUANTIFY UNCERTAINTY COMPONENTS - estimate the size of each uncertainty component CONVERT TO STANDARD DEVIATIONS - express error component as a standard deviation CALCULATE THE COMBINED UNCERTAINTY RE-EVALUATE THE PROCESS IF NECESSARY

10. Measurement uncertainty (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.

11. Measurement uncertainty (6) Combined uncertainties Dependent upon the type of analysis carried out, the standard uncertainties may be combined to produce a combined uncertainty [u c (y)] One of three equations may be used, the choice being dependent upon the complexity of the analysis and the relationship between the components parts A model equation must be devised which describes in simple algebraic terms the whole analysis process

12. Measurement uncertainty (7) The rules for estimating combined uncertainties depend upon the model algebraic equation devised to illustrate the analysis process. You only need consider two at the present 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: [u c (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: [u c (y)/y] 2 = [u(a)/a] 2 + [u(b)/b] 2 + [u(c)/c] 2

13. Measurement uncertainty (7a) Example to illustrate a calculation involving rule 1 Suppose that you have four components (a, b, c, d) and you need 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 g c = 46.10 g, u(c) = + 0.08 g d = 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 [u c (T)] 2 = u(a) 2 + u(b) 2 + u(c) 2 + u(d) 2 = 0.01 2 + 0.02 2 + 0.08 2 + 0.02 2 = 0.0073 u c (T) = + 0.085 Thus: T = 125.37 + 0.085

14. Measurement uncertainty (7b) Example to illustrate a calculation involving rule 2 You have performed an acid/base titration to measure the molarity (M) of a solution of HCl, by titration with a standard solution of KOH. The following information is known or was obtained during the titration C KOH = 0.0990 M, [u(C KOH ) = 0.00017] V KOH = 25.54 ml, [u(V KOH ) = 0.032] V HCl = 25.00 ml, [u(V HCl ) = 0.021] The equation for the calculation may be expressed as: C KOH X V KOH C HCl = = 0.1011 V HCl Each of the individual standard uncertainties needs to be expressed as an RSD so for: C KOH = 0.00017/0.0990 = 0.00172 V KOH = 0.032/25.54 = 0.00125 V HCL = 0.021/25.00 = 0.00084 Thus: u c (C HCl ) =[(0.00172) 2 + (0.00125) 2 + (0.00084) 2 ] 1/2 X 0.1011 u c (C HCl ) = [0.0000051] 1/2 X 0.1011 = 0.00226 X 0.1011 = 0.00023 M C HCl = 0.1011 + 0.0002 M

15. Measurement uncertainty (8) Coverage factor In order to give confidence to the value for the combined uncertainty, the calculated value u c (y) is often multiplied by a coverage factor (k). For a 95% level of confidence the value of k is 2 [ See Students t test table] Note: a more complete description of the principles used for calculating uncertainties may be found in: Quantifying Uncertainty in Analytical Measurements, Eurochem, 1995. Quality in the Analytical Laboratory, E. Prichard (Ed), Wiley, 1995, Chapter 6.

16. Reporting results The 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 page The 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.

17. Benevolent Department Well-intentioned Organisation Tel: 01234 567890 Fax: 01234 567891 Test report numberClient Test batch numberRecipient's name Date receivedDate reportedAnalyst Batch description Details of analyses Method 7.3.1 is carried out in accordance with BS EN ISO/IEC 17025 standard Calibration data Comments SignedPrint 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)