Investgaton of Uncertanty Sources n the External Dosmetry Laboratory Specfcaton.1.1. Analyss of uncertantes Methods for calculatng the overall uncertanty from ndvdual measured uncertantes are gven n the socalled GUM ISO gude and other standard. The IAEA Safety Standards Seres RS-G-1.3 requrement n respect of overall uncertantes s based on the so-called trumpet curve on a 95 % level. In the IEC 1066 there s no specfc requrement for the overall uncertanty. However calculatons can be done based on the ISO gude Gude to the expresson of uncertanty n measurement. Compared to the IAEA requrements the IEC 1066 permts a much larger uncertanty (1.77 H m /H t 0,33.). In ths document the RS-G-1.3 s followed. The overall uncertanty of a dosmetrc system s determned from the combned effects of the two types of uncertanty (Type A, random, and Type B, systematc see ISO s Gude to the Expresson of Uncertanty n Measurement ). The standard uncertanty of Type A, U A, s dentfed wth the standard devaton S(x) of a seres of measurements wth observed values x (whch form a random dstrbuton wth mean x ). Type A uncertantes are those whch can, n prncple, be reduced by ncreasng the number of measurements. Typcal sources of Type A uncertanty are: (a) (b) (c) In homogenety of detector senstvty; Varablty of detector readngs due to lmted senstvty and background; and Varablty of detector readngs at zero dose. Type B uncertantes U B are those whch cannot be reduced by repeated measurements. The followng sources are usually consdered to cause uncertantes of Type B: (a) (b) (c) (d) (e) (f) (g) (h) Energy dependence; Drectonal dependence; Non-lnearty of the response; Fadng, dependent on ambent temperature and humdty; Effects due to exposure to lght; Effects due to exposure to types of onzng radaton that are not ntended to be measured by the dosmeter; Effects from mechancal shock; Calbraton errors; and
() Varaton n local natural background. The effects of Type B uncertantes often appear wth a certan probablty dstrbuton and behave lke Type A uncertantes. For example, for rradaton at a certan angle of ncdence, a personal dosmeter wll ncur a systematc error due to ts varaton of response wth angle. However, when the same dosmeter s worn by an ndvdual workng wthn the ndvdual s radaton envronment, t s rradated from a range of angles and the resultng uncertanty behaves more lke one of Type A. It s recommended by ISO that Type B uncertantes should be characterzed by standard devatons S and varances ν, and that Type A and Type B uncertantes should be combned by addton n quadrate to obtan an overall uncertanty. As the total uncertanty ncludes both random (Type A) and systematc (Type B) uncertantes, t s a necessary assumpton n dong ths that there s no group of workers, even f consstng of only a few per cent of the large group, for whom the condtons of the workplace mply that the systematc uncertantes exceed the random uncertantes mentoned above. The combned uncertanty U C may then be expressed n the form: C A B U = U + U (4) To obtan a numercal value for U B, one must evaluate the separate uncertantes U B, for each ndvdual uncertanty. U B can then be obtaned from: U B = U B, (5) By conventon, t s often assumed that Type B uncertantes can be represented by a rectangular probablty densty dstrbuton, from whch the standard uncertanty can be obtaned by: a U B, = (6) 3 where a s the half-range of values that parameter s assumed to take. Eqs (4), (5) and (6) then gve: U c 1 = U A + a 3 (7) The combned standard uncertanty thus stll has the character of a standard devaton. If, n addton, t s beleved to have a Gaussan (normal) probablty densty, then one standard devaton each sde of the mean corresponds to confdence lmts of about 66%. Therefore, t s often necessary to multply the combned standard uncertanty by a sutable factor, called the coverage factor k, to yeld an expanded uncertanty (also known as the overall uncertanty ). Typcal values of the coverage factor would be or 3, correspondng to confdence lmts of approxmately 95% or 99% respectvely. The numercal value taken for the coverage factor should be clearly ndcated.
.1.. Performance crtera The performance crtera presented above should be used for demonstratng complance wth the ICRP s recommendaton on overall accuracy. However, t s recognzed that natonal requrements may make t necessary to adopt other crtera, whch may be more strngent or have more mathematcal rgour, for purposes of accredtaton and. Eq. (4) can be used to determne a sngle value of the overall uncertanty of a dosmetry system that can be used for demonstratng complance wth the ICRP s recommendaton on overall accuracy (.e. an uncertanty nterval of -33% to +50% for doses near the dose lmt). The equaton may also be used to defne the performance crtera necessary to satsfy the ICRP s accuracy crtera. An allowable uncertanty of -33% to +50% of the dose beng measured can be met at the 95% confdence level (correspondng to a coverage factor of 1.96) f: 1.96U 0.5 ( 0.33+ 0. 50) (8) c and, accordngly from Eq. (4): C = A B U U + U 0.1 (9) where U A and U B should be expressed n terms of the performance quotent (H m -H t )/H t, wth H m and H t ndcatng the measured and conventonal true doses respectvely. Thus, the acceptance of a dosmetry system does not mply complance wth specfc crtera for each uncertan parameter separately, but only that the combned effects from the uncertantes are wthn a certan lmt. In practce, the uncertantes caused by the energy and angular dependence of the response of the dosmeter receve more attenton than any other source of error, because the effects from all other uncertanty components are assumed to be much smaller. Therefore, t s convenent to dfferentate between the Type B uncertanty due to the energy and angular dependence, characterzed by the resultant standard devaton U B,(E,α), and the uncertantes due to all other Type B uncertantes, characterzed by the resultant standard devaton U B(0). Usng Eq. (5) gves: B B, ( E, ) U B,(0) U = U α + (10) and furthermore, by usng Eq. (9): A + B,( E, ) B,(0) U U α + U 0.1 (11) From Eq. (11), Δ, the maxmum allowable value for U B(E,α), can be calculated f U A and U B(0) are known. Hence, for doses near the dose lmt: 0.1 U A U B,(0) Δ = (1) For example, f t s assumed that U A = U B,(0) = 0.10, then the maxmum allowable uncertanty for the combned energy and angular response at a 95% confdence level equals ±1.96Δ, and the range (±1.96Δ) equals ±0.30.
To calculate the mean energy response over the four angles 0, 0, 40 and 60, for a truly sotropc radaton feld t would strctly be necessary to weght the results for each angle by the sold angle subtended at the dosmeter. In practce, however, the rradaton condtons are more lkely to be rotatonally symmetrcal, n whch case the responses at each angle should have equal weghtng. Thus, a response curve can be constructed for each type of radaton by calculatng and plottng the average angular response for each energy ε : R ε = 0.5( Rε, 0 + Rε,0 + Rε,40 + Rε, 60) (13) where R ε,α s the response at energy ε and ncdent angle α, obtaned from: ( Hε, α ) m Rε, α = (14) ( H ) ε, α t where (H ε,α ) m s the measured dose and (H ε,α ) t s the conventonal true value. If R ε s assumed to represent the average response at energy ε for the range of angles of ncdence of radaton durng the montorng perod, the values ± R ε 1 may be taken as an ndcaton of the uncertanty of the energy response. From Eq. (11), the allowable lmts ±1.96Δ are evaluated for the combned uncertanty (at the 95% confdence level) related to the combned energy and angular response of the dosmeter. A dosmeter may therefore be consdered to perform satsfactorly f the condton: R 1 1. 96Δ (15) ε s fulflled for all of the rradaton energes prescrbed for the test and the overall performance crtera satsfy equaton (9). It should be recognzed that other approprate approaches to the assessment of the angular response of dosmeters have been adopted by natonal standards laboratores. Identfyng and Analysng Uncertanty Sources Uncertanty Sources The uncertanty sources are presented n the fsh-bone approach n fg.1 for the reader, the dosmeter characterstcs and the dose calculaton algorthms. Quantfyng the uncertanty components Any dosmetrc system has to work properly and relably n any stuaton and envronment n whch they are expected to be used. Physcal and dosmetrc features vary dependng on type of detector or whole dosmetrc system. The dosmetrc system and sources of errors should be known, and errors should be corrected when
necessary. Some correctons can be determned durng a type test. Other correctons must routnely be determned by the user for every measurement. For every dosmetry system, the ndcated value, H, s determned from the ndcaton M (sgnal from the detector, e. g. charge for TLD) and corrected for zero effect and other addtve correctons, M a, and also for multplcatve correctons n and f b, e. g. the ndvdual senstvty n of the detector and amplfcaton of the PM tube n the case of a TLD, see Eq. (16). H = n M c a= 1 M d f a b b= 1 Ths calculaton s performed for every evaluaton of a detector and may be done automatcally, e. g. by the software mplemented n the reader. The ndcated value, H may need further correctons to take nto account the specal condtons durng the measurement. After applyng these further correctons the measured value, H m, should be (n prncple) dentcal to the conventonally true value. The measured value, H m, s determned from the ndcated value, H, by applyng the calbraton factor, N 0, the correcton factor for non-lnear response, k n, the l correcton summands, D p, for addtve nfluence quanttes and the w correcton factors, k q, for multplcatve nfluence quanttes (16) H m = N 0 kn H l = w D p k 1 q= 1 p q (17) The equatons (16) and (17) gve the model functon of the measurement necessary for any determnaton of uncertanty accordng to the ISO Gude to the Expresson of Uncertanty n Measurement () (see gude secton 3.1.6, 3.4.1 and 4.1). In prncple, Eq. (16) and Eq. (17) are not fxed, so a combnaton n one equaton s also possble. For practcal reasons the suggested separaton s useful. In routne measurements and wth all the controls sutably adjusted the calbraton factor and all correcton factors n Eq. (17) are set to unty and the correcton summands are set to zero. The measured value s then equal to the ndcated value. These settngs cause an uncertanty of measurement, whch can be determned from the prevously (e. g. n a type test) measured varaton of the correcton factors (gven as correcton nterval half wdth) and the measured varaton of the correcton summands
TABLE 1: Performance characterstcs for TLD systems (IEC-ISO 1066) and ther contrbuton to the uncertantes. Performance characterstc Type U A (a ) Type U B (a ) Probablty Densty Dstrbuton Remarks Batch homogenety Resdual sgnal Detecton threshold Self Irradaton Lnearty response Energy response Isotropy response 0.045 0.003 0 0 Gaussan (normal) Informaton from 0.019 0.030 0 0 Gaussan (normal) Informaton from 0.004 0.001 0 0 Gaussan (normal) Informaton from 0.004 0.001 0 0 Gaussan (normal) Informaton from 0 0 0.01 0.01 Rectangular Informaton from 0 0 0.08 0.030 Rectangular Informaton from 0 0 0.151 0.056 Rectangular Informaton from 0 0 0.080 0.037 Rectangular Informaton from Fadng 0 0 0.10 Rectangular Informaton from Calbraton 0 0 0.03 Rectangular Informaton provded by SSDL Reproducblty Envronmental Influences Mechancal and electromagnetc dsturbances. 0 0 0.05 Rectangular Estmate by expert judgment no data avalable 0 0 0.05 Rectangular Estmate by expert judgment no data avalable
Calculatng the combned standard uncertanty from table 1. U A C A U = U + U = 0.000 and = 0.006 then U = 0.068 U B B c In equaton (9) the condton s that U C = U A + U B system and the results of dfferent. 0.1 and ths condton s satsfed for the TLD It s often necessary to multply the combned standard uncertanty by a sutable factor, called the coverage factor k, to yeld an expanded uncertanty (also known as the overall uncertanty ). A values of the coverage factor would be correspondng to confdence lmts of approxmately 95%. In ths case the Overall uncertanty would be U = 0.16 representng 1,6 % of the value measured..
Measurement and calculaton procedure. The evaluated value of dose s obtaned from the readout value by applyng 1. background correcton. detector senstvty coeffcent 3. calbraton coeffcent (e.g. the use of 60Co or 137Cs) 4. algorthm (calculaton n terms of dose of nterest and, f applcable, the combnaton of results of more than one detector) For WB dosmeter the dose calculaton s based on a specally developed dose algorthm for H p (10) determnaton: 1. the mean background value s deducted from all readngs. f dose of chp () > 0.7 x dose of chp (), dose of chp () s regstered as Hp(10) 3. f dose of chp () < 0.7 x dose of chp (), dose of chp () multpled by 0.71 s regstered as Hp(10) 4. Based on the specfc calbraton procedure for Harshaw TLD readers the measured dose H m was obtaned as follows: H m = M * ECC / RCF - H m0 (18) where M... TL measurng effect of detector ECC... Indvdual relatve senstvty of detector (Element Correcton Coeffcent) RCF (poston )... Reader Calbraton Factor for readout poston H m0,... Averaged zero dose readng For extremty dosmeter and based on the specfc calbraton procedure for Harshaw TLD readers the measured dose H m was obtaned as follows: H m = M * ECC / RCF - H m0 (19) where M... TL measurng effect of detector ECC... Indvdual relatve senstvty of detector (Element Correcton Coeffcent) RCF (poston )... Reader Calbraton Factor for readout poston H m0,... Averaged zero dose readng Assumng the averaged zero dose readng equal cero, then the equaton (16) and (17) could be smplfed to the followng: ECC H m = M (0) RCF
The uncertanty of H m could be then expressed as: U H Hm m = U M M U ECC RCF + ECC RCF (1) the uncertanty of the second term under the square root of (1) could be expressed as All together would be: ECC U ECC U RCF U ECC = + () RCF ECC RCF RCF U M U ECC ECC U RCF U Hm = Hm + + (3) M RCF ( RCF) RCF Example of the calculaton process s shown below wth a set of data: Parameter Measured data Uncertanty Remarks M 43.84 6.6 From a sngle measurement ECC 0.974 1.005 From a group of measurement RCF 17.5 4.18 From a group of measurement H m.44 0.58 Represent 4 % of the value For ths specfc case the measurement uncertanty due s about 4 % of the measured value.
PERFORMANCE CRITERIA FOR COMBINED ENERGY AND ANGULAR DEPENDENCE AS FUNCTION OF ENERGY Table : Combned energy and angular dependence as functon of energy based on IAEA RS-G-1.3 for Whole Body Dosmeter Mean Energy E n kev R E,α=0 R E,α=30 R E,α=45 R E,α=60 Mean Value R E R E - 1 16 1,114 0,963 0,615 0,93 0,746 0,54 0 1,037 0,96 0,707 0,460 0,783 0,17 4 0,990 0,914 0,784 0,573 0,815 0,185 33 0,68 0,71 0,80 0,700 0,731 0,69 48 0,746 0,70 0,678 0,615 0,690 0,310 65 0,815 0,799 0,750 0,684 0,76 0,38 83 0,878 0,855 0,816 0,741 0,8 0,178 100 0,903 0,887 0,841 0,773 0,851 0,149 118 0,935 0,888 0,857 0,769 0,86 0,138 164 0,96 0,91 0,865 0,799 0,875 0,15 08 0,947 0,918 0,883 0,815 0,891 0,109 50 0,945 0,95 0,900 0,818 0,897 0,103 66 0,98 0,955 0,946 0,901 0,93 0,068 150 1,010 0,998 0,988 0,965 0,990 0,010 The crteron s that R E - 1 shall be less or equal 1,96 * (wth 0,16 1,96* 0,31). From ths crteron t can be seen that the used whole body dosmeter fulfls ths requrement for all energes above 16 kev (N-0). For N-15 there are only data avalable for 0 and 30. Table 3 : Combned energy and angular dependence as functon of energy based on AEA RS-G-1.3 for DXT- RAD 707H extremty dosmeter. Mean Energy E n kev R E,α=0 R E,α=30 R E,α=45 R E,α=60 Mean Value R E R E - 1 1 0,70 0,70 0,64 0,5 0,641 0,359 16 0,85 0,84 0,80 0,67 0,790 0,10 0 0,93 0,93 0,9 0,83 0,906 0,094 4 0,99 0,98 0,99 0,93 0,969 0,031 33 1,0 1,08 1,05 1,03 1,045 0,045 48 1,06 1,04 1,03 1,03 1,039 0,039 65 0,89 0,90 0,88 0,88 0,888 0,11 83 0,80 0,79 0,80 0,81 0,801 0,199 100 0,76 0,76 0,76 0,76 0,758 0,4 118 0,77 0,75 0,75 0,75 0,756 0,44 164 0,79 0,78 0,78 0,80 0,787 0,13 08 0,83 0,83 0,79 0,8 0,818 0,18 50 0,85 0,84 0,85 0,83 0,840 0,160 66 0,88 0,87 0,88 0,86 0,870 0,130 150 0,94 0,9 0,89 0,88 0,907 0,093
The crteron s that R E - 1 shall be less or equal 1,96 * (wth 0,16 1,96* 0,31). From ths crteron t can be seen that the used extremty dosmeter fulfls ths requrement except for the radaton type N-15. Table 4 : Combned energy and angular dependence as functon of energy based on IAEA RS-G-1.3 for Whole Body Dosmeter for neutron radaton Qualty Mean Energy E n MeV R E,α=0 R E,α=30 R E,α=45 R E,α=60 R E,α=75 Mean Value R E R E - 1 5Cf_b.4 1.08 1.0 0.95 0.90 1.05 1.00 0.00 5Cf_m. 1.16 1.10 0.98 0.87 0.9 1.00 0.00 The crteron s that R E - 1 shall be less or equal 1,96 * (wth 0,16 1,96* 0,31). From ths crteron t can be seen that the used whole body dosmeter fulfls ths requrement for all energes studed. Table 5: Combned energy and angular dependence as functon of energy based on IAEA RS-G-1.3 for extremty dosmeter for beta radaton. Qualty Mean Energy E n MeV R E,α=0 R E,α=30 R E,α=45 R E,α=60 R E,α=75 Mean Value R E R E - 1 Sr-90/Y- 90.7 1.306 1.070 0.74 0.441 0.359 0.780 0.0 Kr-85 0.687 0.66 0.48 0.365 0.69 0.44 0.397 0.603 Pm-147 0.3 0.494 0.451 0.394 0.381 0.494 0.443 0.557 The crteron s that R E - 1 shall be less or equal 1,96 * (wth 0,16 1,96* 0,31). From ths crteron t can be seen that the used extremty dosmeter fulfls ths requrement only for Sr-90 when usng the suppler recommended calbraton wth Cs-137. For the other lower energes, the system wll be calbrated wth beta sources nstead.
Reader Calbraton R elatve hum dty SSDL S tablty o f P M T nose,h V, Temperature and Reference Lght Gas heatng/coolng Ambent temperature Gas purty Electrcal dsturbances M echancal dsturbances Bact homogenty D etecto n thresho ld Self rradaton Resdual sgnal Energy response Angular Response Lnearty Zero dose readng Fadng R epro ducblty ECC Hp(d) Reader Calbraton Factor Dosmeter W earng poston Dose Calculaton Fg. 1. Sources of uncertantes n the TL dosmetry system.