Transcript Uncertainty estimation of a Panasonic four

Uncertainty estimation of a Panasonic fourelement dosimetry system with a noncontinuous dose calculation algorithm
Du Toit Volschenk
Radiation Protection Service
South African Bureau of Standards
May 1997
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
2
Conventional approach in estimation of
uncertainty



Older terminology: random and systematic errors
New terminology: Type A and Type B errors
Propagation of uncertainties
S2 



n   f  x1,x2,...,xn  

 

x
i  1

i

2
.S2
i
In general, the square of the resultant standard
deviation is the sum of the squares of the contributing
(non-interdependent) standard deviations:
 ...  S 2n
S 2  S12  S 2
2
3
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
4
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
5
Practical problems with conventional
approach

General purpose dose calculation algorithms are not
always continuous functions, as shown by the
following part of an algorithm:
A = E3/E2
B = E1/E2
RPS Panasonic Algorithm
C = E3/E4
1997-05-02
D = E4/E2
Page 2 of 4
E = E1/E4
F = (E2-E4)/(E1-E4)
B>8 or
(A<1.5 and E>=1.5)
Gamma + Beta
Yes
or
F>NP
Gamma Dose = E4
and
Gamma + Neutron
(E2-E4)>25
No
No
Yes
Photons
Beta + Gamma
Neutron + Gamma
6
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?
7
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
8
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
9
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
10
A solution to the practical problems
E1
E2
Dose calculation
algorithm
E3
f(E1,E2,E3,E4)
Dose
E4

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
11
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)
12
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
13
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
14
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
15
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:
Ei=CT.fi(D), where
T
TE
i


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
16
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
17
Results
Cs on phantom - Element 1 vs given
dose
Corrected
Element
1500
1000
E1 = 1.0048D
R2 = 0.9741
500
0
0
200
400
600
800
1000
1200
Given Dose mrem
18
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
19
Results
WE Irradiator - Element 1 response vs time
3000
2500
Corrected Element
2000
E = 29.591t
R2 = 0.9986
1500
1000
500
0
0
10
20
30
40
50
60
70
80
90
Time s
20
Results
Cs-137 all doses, Element 1 vs Given Dose
10000000
1000000
Corrected Element
100000
E = 1.328D0.9753
R2 = 0.9984
10000
1000
100
10
1
1
10
100
1000
10000
100000
1000000
10000000
Given Dose mrem
21
Results

Element response functions for reference radiation,
over whole dose range:
Ei(D) = aiDb = fi(D), where
ai, bi constants, D given dose
a
b
R2
E1
1.328
0.9753
0.9984
E2
1.0602
0.9986
0.9995
E3
0.9618
1.0094
0.9998
E4
0.946
1.017
0.9999
22
Results

Element response functions for other radiation types,
over whole dose range:
TE (D)
i
TE (D)
i
= Tci.fi(D), where
element response function for dose type T, Tci element constant,
fi(D) element response function for reference radiation
23
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:
GE (D) = n.s + E (D), where
i
i
i
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
GE (D) is calculated at least 10000 times, on 486 or higher PC, with
i
math coprocessor
24
Results

Calculation of element standard deviations:
Response expression for LiBO elements:
 x1


x

c
3
1
x

2
e
. c2 . c3  c4
x

x


4
5


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
25
Results
Response expression for CaSO elements:
 x1


x

k
3
1
x

2
e
. k2 . k3  k4
 x 4  x3 


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
26
Results
Using the law of propagation of uncertainties, examples for LiBO:
for x1 :
for x5 :
c2 . c3
e

x1 x 2 ( x 4  x5 )
e

x5
 x1


x

c

3
1
 x2

 x 4  x5 
2
. c2 . c3
27
Results
Relative standard deviation values for LiBO elements
Variable Element 1
Element 2
x1
0.016
0.020
x2
0.055
0.058
x3
0.428
0.428
x4
0.036 (low) 0.037 (high) 0.036 (low) 0.037 (high)
x5
0.613
0.613
Relative standard deviation values for CaSO elements
Variable Element 3
Element 4
x1
0.013
0.016
x2
0.048
0.049
x3
0.613
0.613
x4
0.036 (low) 0.037 (high) 0.036 (low) 0.037 (high)
28
Results
Uncertainty in measurement - Cs-137
0.2
1.5
0.19
0.18
1.4
0.17
0.16
1.3
0.14
1.2
0.13
0.12
1.1
0.11
0.1
1
0.09
0.08
0.9
0.07
0.06
Relative Measured dose
95% confidence interval
0.15
I Deep
I Skin
REL D
REL S
0.8
0.05
0.04
0.7
0.03
0.02
0.6
0.01
0
1
10
100
1000
10000
100000
0.5
1000000
Given dose mrem
29
Results
Uncertainty in measurement - LG
0.2
1.5
0.19
0.18
1.4
0.17
0.16
1.3
0.14
1.2
0.13
0.12
1.1
0.11
0.1
1
0.09
0.08
0.9
0.07
0.06
Relative Measured dose
95% confidence interval
0.15
I Deep
I Skin
REL D
REL S
0.8
0.05
0.04
0.7
0.03
0.02
0.6
0.01
0
1
10
100
1000
10000
100000
0.5
1000000
Given dose mrem
30
Results
Uncertainty in measurement - LG + Gamma
0.2
1.5
0.19
0.18
1.4
0.17
0.16
1.3
0.14
1.2
0.13
0.12
1.1
0.11
0.1
1
0.09
0.08
0.9
0.07
0.06
Relative Measured dose
95% confidence interval
0.15
I Deep
I Skin
REL D
REL S
0.8
0.05
0.04
0.7
0.03
0.02
0.6
0.01
0
1
10
100
1000
10000
100000
0.5
1000000
Given dose mrem
31
Results
Uncertainty in measurement - LI
0.2
1.5
0.19
0.18
1.4
0.17
0.16
1.3
0.14
1.2
0.13
0.12
1.1
0.11
0.1
1
0.09
0.08
0.9
0.07
0.06
Relative Measured dose
95% confidence interval
0.15
I Deep
I Skin
REL D
REL S
0.8
0.05
0.04
0.7
0.03
0.02
0.6
0.01
0
1
10
100
1000
10000
100000
0.5
1000000
Given dose mrem
32
Results
Uncertainty in measurement - LI + Gamma
0.2
1.5
0.19
0.18
1.4
0.17
0.16
1.3
0.14
1.2
0.13
0.12
1.1
0.11
0.1
1
0.09
0.08
0.9
0.07
0.06
Relative Measured dose
95% confidence interval
0.15
I Deep
I Skin
REL D
REL S
0.8
0.05
0.04
0.7
0.03
0.02
0.6
0.01
0
1
10
100
1000
10000
100000
0.5
1000000
Given dose mrem
33
Results
Uncertainty in measurement - LK
0.19
1.5
0.18
1.4
0.17
0.16
1.3
0.15
1.2
0.13
0.12
1.1
0.11
0.1
1
0.09
0.08
0.9
0.07
0.06
Relative Measured Dose
95% confidence interval
0.14
I Deep
I Skin
REL D
REL S
0.8
0.05
0.04
0.7
0.03
0.02
0.6
0.01
0
1
10
100
1000
10000
100000
0.5
1000000
Given dose mrem
34
Results
Uncertainty in measurement - MFG
0.2
1.5
0.19
0.18
1.4
0.17
0.16
1.3
0.14
1.2
0.13
0.12
1.1
0.11
0.1
1
0.09
0.08
0.9
0.07
0.06
Relative Measured Dose
95% confidence interval
0.15
I Deep
I Skin
REL D
REL S
0.8
0.05
0.04
0.7
0.03
0.02
0.6
0.01
0
1
10
100
1000
10000
100000
0.5
1000000
Given dose mrem
35
Results
Uncertainty in measurement - MFI
0.2
1.5
0.19
0.18
1.4
0.17
0.16
1.3
0.14
1.2
0.13
0.12
1.1
0.11
0.1
1
0.09
0.08
0.9
0.07
0.06
Relative Measured Dose
95% confidence interval
0.15
I Deep
I Skin
REL D
REL S
0.8
0.05
0.04
0.7
0.03
0.02
0.6
0.01
0
1
10
100
1000
10000
100000
0.5
1000000
Given dose mrem
36
Results
0.3
0.29
0.28
0.27
0.26
0.25
0.24
0.23
0.22
0.21
0.2
0.19
0.18
0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
1.5
1.4
1.3
1.2
1.1
1
0.9
Relative Measured Dose
95% confidence interval
Uncertainty in measurement - MID
I Deep
I Skin
REL D
REL S
0.8
0.7
0.6
1
10
100
1000
10000
100000
0.5
1000000
Given dose mrem
37
Results
0.3
0.29
0.28
0.27
0.26
0.25
0.24
0.23
0.22
0.21
0.2
0.19
0.18
0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
1.5
1.4
1.3
1.2
1.1
1
0.9
Relative Measured Dose
95% confidence interval
Uncertainty in measurement - Sr-90/Y-90
I Deep
I Skin
REL S
0.8
0.7
0.6
1
10
100
1000
10000
100000
0.5
1000000
Given dose mrem
38
Results
Uncertainty in measurement - Tl-204
0.2
1.5
0.19
0.18
1.4
0.17
0.16
1.3
0.14
1.2
0.13
0.12
1.1
0.11
0.1
1
0.09
0.08
0.9
0.07
0.06
Relative Measured Dose
95% confidence interval
0.15
I Deep
I Skin
REL S
0.8
0.05
0.04
0.7
0.03
0.02
0.6
0.01
0
1
10
100
1000
10000
100000
0.5
1000000
Given dose mrem
39
Results
Results in NVLAP format
Rad Type
Cs-137
LG
LG+G
LI
LI+G
LK
MFG
MFI
MID
Sr-90/Y-90
Tl-204
Bd
0.07
0.07
-0.01
0.06
-0.02
0.00
0.00
0.00
-0.03
-0.95
-0.99
Sd
0.03
0.01
0.03
0.01
0.01
0.01
0.01
0.00
0.00
0.00
0.00
Deep
0.07
0.07
0.04
0.07
0.02
0.01
0.01
0.01
0.03
0.95
0.99
Bs
0.04
0.07
0.06
0.06
0.06
-0.01
0.00
0.00
-0.02
0.19
0.06
Ss
0.03
0.00
0.01
0.01
0.01
0.01
0.01
0.00
0.00
0.01
0.00
Skin
0.07
0.08
0.07
0.07
0.07
0.02
0.01
0.01
0.02
0.20
0.07
40
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!
41
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
42