Du Toit Volschenk Radiation Protection Service South African Bureau of Standards May 1997

1. Uncertainty estimation of a Panasonic four-element dosimetry system with a non-continuous dose calculation algorithm Du Toit Volschenk Radiation Protection Service South African Bureau of Standards May 1997

2. Why is uncertainty estimation necessary? • Need to know whether you are reading accurately and precisely over the whole of your required dose range, for all the radiation types required • Accuracy - measured/given • Precision - standard deviation (can you repeat your accurate measurements?) • Identify possible problem areas in measurement capability • Improve measurement capability by addressing problem areas • Accreditation

3. Conventional approach in estimation of uncertainty • Older terminology: random and systematic errors • New terminology: Type A and Type B errors • Propagation of uncertainties • In general, the square of the resultant standard deviation is the sum of the squares of the contributing (non-interdependent) standard deviations:

4. Conventional approach in estimation of uncertainty • Calculate an uncertainty for each radiation type • In general, the uncertainty for each type of radiation will be independent of the given dose, so that only one dose point is needed for each radiation type

5. Basic requirement for any uncertainty study • The system under consideration must be under adequate statistical control (stability of system) • If not, the results of the study will probably point this out, but not necessarily • e.g. if the data used were representative only of a period during which the system was stable

6. Practical problems with conventional approach • General purpose dose calculation algorithms are not always continuous functions, as shown by the following part of an algorithm:

7. Practical problems with conventional approach • There are built-in uncertainties in the decision branches of algorithms, which may not be easily expressed using the conventional approach • If a branching decision is made using an element response ratio, there will be a statistical "fuzziness" in that element ratio, leading to additional uncertainty in reported dose • While it is easy to calculate the uncertainty in the reported result, how can one calculate that same uncertainty taking into consideration the uncertainty in the branching decision?

8. Practical problems with conventional approach • Dose algorithms may significantly affect uncertainties when special checks are carried out, e.g. • Checking for dosimeter overexposure • Anomalous dosimeter element responses • Trying to get information about received doses which the system is incapable of giving

9. Practical problems with conventional approach • Dosimeter element responses are not necessarily linear with dose (e.g. CaSO element responses become supralinear for high doses) • Element 3 of a UD802 dosimeter will be in the supralinear response range for doses higher than about 300 mSv (30 rem), for X-rays of about 20 keV • This necessitates a number of dose points for each radiation type (because the element ratios upon which branching decisions are made will be affected) • High doses require long exposure times • Many dose points + long exposure times = high irradiation cost = money and/or time • High doses may permanently damage dosimeters

10. A solution to the practical problems • Basic assumption: element response variations are independent of given dose • Select one radiation type as reference radiation • Do a full set of irradiations for the reference set, over the whole dose range required • Do subsets of irradiations for the other radiation types • Model the dosimeter element responses of other radiation types on the reference radiation for the full dose range • Information about non-linear element responses will be available from the reference irradiations

11. A solution to the practical problems • Use the conventional approach as far as it can go, then use the results of the conventional approach as input to a numerical uncertainty estimation method • OR • Use measured data as input to a numerical uncertainty estimation method, ignoring the conventional approach altogether

12. Problems with the solution • The source of reference radiation may not be practical for the high doses required • (collimated beam, on phantom, source to phantom distance, exposure time, availability of source)

13. A solution to the problems with the solution • Find a secondary reference source, with a high exposure rate • (irradiation on a phantom not required, source calibration not required) • Establish the relationship between the element responses for the two reference sources • Do irradiations that are difficult on the primary reference source, with the secondary reference source • Correct the dosimeter element responses obtained with the secondary reference source to arrive at the equivalent responses for the primary source

14. Summary of steps in the uncertainty estimation process • Do a set of irradiations over the practical dose range of the primary reference source • Obtain an expression of element response per given dose for each dosimeter element: • Ei(D)=ci.D, where • Ei element response, ci element constant, D given dose • Do a set of irradiations over approximately the same dose range with the secondary reference source • Establish a relationship between the dosimeter element responses for the two reference sources

15. Summary of steps in the uncertainty estimation process • Do a set of irradiations with the secondary reference source in the remainder of the high dose region • Obtain element response functions over the whole dose range: • Ei=fi(D), where • Ei element response, fi element response function, D given dose • Do subsets of irradiations for each of the other radiation types

16. Summary of steps in the uncertainty estimation process • Establish the relationship between the dosimeter element responses for the other radiation types and those for the reference source: • TEi=CT.fi(D), where • TEi element response for radiation type T, CT element constant, fi(D) element response function with dose for reference radiation type • Calculate sets of element responses for the whole dose range, for each radiation type • Carry out a numerical uncertainty estimation using the calculated and measured dosimeter element responses as input to the dose algorithm

17. Results • Primary reference source used: Cs-137 beam irradiator • Secondary reference source used: Williston-Elin internal Cs-137 irradiator • Element response functions for primary reference source, linear element response region: • Ei(D)=ci.D

18. Results

19. Results • Element response functions for secondary reference source: • Ei(t)=ki.t, where • Ei(t) element response function, ki element constant, t irradiation time in seconds • therefore, for each element, • Di(t)= ki / ci . t, where • ci from Ei(D)=ci.D

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22. Results • Element response functions for reference radiation, over whole dose range: • Ei(D) = aiDb = fi(D), where • ai, bi constants, D given dose

23. Results • Element response functions for other radiation types, over whole dose range: • TEi(D) = Tci.fi(D), where • TEi(D) element response function for dose type T, Tci element constant, fi(D) element response function for reference radiation

24. Results • Numerical uncertainty estimation • The standard deviation, si, of each element response value is calculated using the conventional approach for uncertainty estimation • The standard deviation is used together with a numeric generator to simulate the spread in element values that could be expected from numerous measurements: • GEi(D) = n.si + Ei(D), where • n is a random gaussian-distributed number from a gaussian distribution centered around 0 with a standard deviation of 1; • si is the calculated standard deviation for the element; and • Ei(D) the element response value at given dose D • GEi(D) is calculated at least 10000 times, on 486 or higher PC, with math coprocessor

25. Results • Calculation of element standard deviations: • Response expression for LiBO elements: • x1 Raw element reading • x2 Element correction factor • x3 Reader LiBO background • x4 Reader average element reading for calculating batch correction factor • x5 Reader CaSO background • c1 ,c2 ,c3 ,c4 constants

26. Results • Response expression for CaSO elements: • x1 Raw element reading • x2 Element correction factor • x3 Reader CaSO background • x4 Reader average element reading for calculating batch correction factor • k1 ,k2 ,k3 ,k4 constants

27. Results • Using the law of propagation of uncertainties, examples for LiBO: • for x1 : • for x5 :

28. Results • Relative standard deviation values for LiBO elements • Relative standard deviation values for CaSO elements

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40. Results • Results in NVLAP format

41. Additional benefits • Once the test method has been set up, it is easy to: • Test different algorithms for suitability • See what the effect of changes in existing algorithms will be (helping to design more optimised algorithms) • Going through the whole process of creating a testing algorithm to determine uncertainties and testing existing algorithms, certainly helps to understand the processes involved in dose calculation much better • Once the whole process is over, a sense of relaxation sets in for not having to play around with an untold number of fractions, responses, calculation errors, and program bugs anymore!

42. References • American National Standard for Dosimetry - Personnel Dosimetry Performance - Criteria for Testing (HPS N13.11-1993): ANSI, HPS • IEC 1066 - Thermolumincescence dosimetry for personal and environmental monitoring (First Edition 1991-12): International Electrotechnical Commission • NIST Technical Note 1297 (1994 Edition) - Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results: US Department of Commerce, Technology Administration, National Institute of Standards and Technology • Random Number Generators and Simulation, I Deak (Volume 3 in series Methods of Operations Research): Akademiai Kiado, Budapest, 1990 • Required Accuracy and Dose Thresholds in Individual Monitoring, P Christensen, RV Griffith: Radiation Protection Dosimetry, Vol 54, Nos 3/4, pp 279-285 (1994), Nuclear Technology Publishing