EVALUATING BIOASSAY UNCERTANITY USING GUM WORKBENCH ® HPS TECHNICAL SEMINAR April 15, 2011 Brian K. Culligan Fellow Scientist Bioassay Laboratory Savannah River Nuclear Solutions Aiken, SC, USA SRNS-STI

2 Introduction  Analytical Laboratories (AL) is adopting the ISO Guide to the Expression of Uncertainty in Measurement (ISO-GUM).  Brief describe the origins of ISO-GUM  Demonstrate GUM Workbench ® software for a typical Bioassay actinide analysis.  Review benefits from ISO-GUM implementation.

3 The Origins of ISO-GUM – What problems does it address? Prior to International Adoption of the ISO-GUM principles: Lack of standardized approach to uncertainty evaluation Intercomparability of results was difficult or impossible Many times significant contributors to measurement uncertainty were ignored (or overlooked) For more see: JCGM 100:2008 NIST: A measurement is complete only when accompanied by a quantitative statement of its uncertainty. The uncertainty is required in order: 1.To decide if the result is adequate for its intended purpose and 2.To ascertain if it is consistent with other similar results

4 The General Law of “Variance Propagation” Let r be calculated as a general function of any number of uncorrelated random variables,

5 Definitions – define our terms Type A measurement uncertainty evaluation: evaluation of a component of measurement uncertainty by a statistical analysis of measured quantity values obtained under defined measurement conditions Type B measurement uncertainty evaluation: evaluation of a component of measurement uncertainty determined by means other than a Type A evaluation Note that the terms Type A and Type B apply to the methods of evaluation rather than to the sources of uncertainty.

6 Type A and B evaluations Methods of evaluations, NOT TYPES OF UNCERTAINTIES (i.e., not ‘random’ or ‘systematic’) ISO-GUM: “The purpose of the A and B classification is to indicate the two different ways of evaluating uncertainty components and is for convenience of discussion only… …the classification is not meant to indicate that there is any difference in the nature of the components resulting from the two types of evaluation… …Both types of evaluation are based on probability distributions and the uncertainty components resulting from either type are quantified by variances or standard deviations”.

7 Modeling Define the measurand and identify all of the input quantities that contribute to the value of the measurand AND its uncertainty Model the measurement by expressing the relationship between the measurand and the input quantities; y=f(x 1,…,x n ) The method procedure is a good place to start modeling. Use experience and technical knowledge to augment the model. THE GOAL HERE: the math should model measurement reality The philosophy of the GUM is to turn to reasonable results…. This holds for the modeling process. The aim should be reasonable. The fact that the model expresses the experience and knowledge of the measurement can be tested by simulation.

8 Actual Reported Results for Example Analysis (U-234)

9 Sample Spectrum

10 MODEL: Bioassay Actinide Analysis (Alpha PHA) Sample Activity Once a sample has been chemically prepared and counted, the AMS software conducts a peak search within the respective ROI's; integrates or sums the number of gross counts within each ROI; and imports the background counts associated with each ROI. The activity concentration associated with each radionuclide is then calculated Act

11 MODEL: Bioassay Actinide Analysis (Alpha PHA) Chemical Recovery Due to the limitations associated with any chemical process, a means of quantifying analyte losses is required. This is achieved by introducing a known concentration of a radioisotope of the analyte into the sample to be analyzed. This “tracer” is used to quantify the chemical losses incurred by the analyte during sample preparation. Being an isotope of the analyte, the tracer exhibits precisely the same chemical characteristics as the analyte.

12 MODEL: Bioassay Actinide Analysis (Alpha PHA) Minimum Detectable Concentration The Minimum Detectable Concentration (MDC) is the amount of a radionuclide in a sample that would be expected to go undetected 5% of the time. Decision Level The Decision Level (DL) is that activity in a sample that would have to be present for us to decide with 95% certainty that activity exists in the sample. MDC

13 MODEL: Entry into GUM Workbench ® Equations are entered into software:

14 GUM Workbench ® – “List of Quantity” View

15 GUM Workbench ® does the calculus for us

16 GUM Workbench ® – Entering “Quantity Data”

17 GUM Workbench ® – Entering “Quantity Data”

18 GUM Workbench ® – Entering “Quantity Data”

19 GUM Workbench ® – Entering “Quantity Data”

20 What is an Uncertainty Budget? An uncertainty budget is a table that lists all input quantities (i.e., their identifiers), their values, their standard uncertainties, and their uncertainty contributions…. The types of methods (i.e., Type A or Type B) used for evaluating the results and the uncertainties are also indicated. The units of measure. The ISO-GUM standard does not suggest any particular format reporting uncertainty budgets (but GUM Workbench ® provides a consistent format). The budget is important since: It makes the calculation of the combined uncertainty transparent. It identifies the dominant components of the combined standard uncertainty. It is a critical aid in conducting interlaboratory evaluations, when required.

21 The Uncertainty Budget (Activity)

22 The Uncertainty Budget (Recovery)

23 The Uncertainty Budget (MDC)

24 The Uncertainty Budget (DL)

25 The Results

26 Merits of the GUM Workbench ®  The GUM Workbench ® requires as inputs only the expected values, standard deviations, and correlation coefficients of state- of-knowledge probability distributions for the input quantities to the model equation.  It yields as output an approximate expected value and standard deviation of a state-of-knowledge probability distribution for the value of the measurand.  Optimization tool – Budget shows primary contributors to total uncertainty.

27 Acknowledgements The information presented in this training package was developed from slides prepared and used by Peter Mason from DOE-NBL for a course conducted at SRS in April, 2010.