1. Speaker: Jung Hwan Kim KRS presentation (May 27. 2016)
Including Below Detection Limit Samples in Decommissioning Soil Sample Analyses
Speaker: Jung Hwan Kim
KRS presentation (May )

2. Contents Introduction Purpose of the research Case study Results
Conclusions
Future work
References

3. Introduction

4. Introduction
Decommissioning is an emerging international issue in the nuclear industry.
Termination of an NPP license, involves releasing the facility from regulatory control for either restricted or unrestricted use in the future.
Current Domestic Research Focuses on;
Development of Clearance Standards
Evaluation of Exposure.

5. Introduction NPP site soil analysis for license termination
There are technical problems for finalizing regulations and standards.
Hot Spots
Observations reported as below the detection limits
Observations reported as below the detection limits are caused by:
Inherent limitations of measurement methods (e.g. detectors)

6. Introduction Conventional methods for analyzing soil sampling data:
Only use values above detection limit (This ignores non-detects)
Replace non-detects with zero
Replace non-detects with half of the detection limit (DL)
Replace non-detects with DL
However, these strategies have limitations:
Statistically biased estimate
Probabilistic Exposure Assessment is unreliable
Predicts a higher dose --- causing higher waste volumes and associated costs

7. Introduction
To resolve these issues Statistical Techniques were used to analyze a case study
Proposed methods for estimating summary statistics (Mean, STD DEV, PCT)
Kaplan-Meier
Regression on Order Statistics (ROS)
Maximum Likelihood Estimation (MLE)
Proposed method for estimating confidence intervals
Bootstrapping
These techniques are used by many researchers in the Environmental Science and Technology area.

8. Introduction – Kaplan-Meier
The Kaplan-Meier method is a nonparametric technique which is the most commonly used for calculating the probability distribution to estimate summary statistics with censored data.
Kaplan-Meier is nonparametric, so it does not assume the data follow a known distribution.
Kaplan-Meier is well-suited for many environmental data sets because it is nonparametric.

9. Introduction – Kaplan-Meier
Consider the following data set:
20, 20, 10, 1, <0.5, <0.5, <25, <2, <2, 1, 100, 30, 3, <3, 2, 1, 3, 5, <10, <0.5
Order this data set in decreasing order (Efron’s bias correction):
100, 30, <25, 20, 20, 10, <10, 5, 3, 3, <3, 2, <2, <2, 1, 1, 1, <0.5, <0.5, 0.5
The probability of each data point is as below:
The probability of getting a data point less than 100 is 19/20=0.95
The probability of getting a data point below 30 is 18/19=0.947
The location of 30 on the PDF is calculated by 0.95*0.947=0.90
The probability of getting a data point below 20 is 15/17=0.882
The location of 20 on the PDF is calculated by 0.90*0.882=0.794

10. Introduction – Kaplan-Meier
Value
Probability
100
0.95 30
0.90 20
0.794 10
0.741 5
0.684 3
0.570 2
0.507 1
0.253
0.5
Table 1. Kaplan-Meier example data
Fig. 1. Kaplan-Meier method example data plot

11. Introduction – ROS
Robust regression on order statistics (ROS) is a semi-parametric method that can be used to estimate summary statistics with censored data. ROS plots the detected values on a probability plot and calculates a linear regression line in order to estimate the parameters.
ROS internally assumes that the underlying population is normal or lognormal. However, the assumption is applied to only the censored data set and not to the full data set.
It is necessary to fit a known distributional model to the detected values on a probability plot.

12. Estimated Concentration
Introduction – ROS
Input Concentration
Probability
Estimated Concentration
3.2
0.972
2.8
0.944
<2
0.815
1.418
0.713
1.143
0.611
0.954
0.509
0.807
0.407
0.683
0.306
0.572
0.204
0.465
0.102
0.349
1.7
0.873
1.5
0.829
Table 2. ROS final data

13. Introduction – MLE
Maximum likelihood estimation (MLE) is a parametric, model-based method that can be used to estimate summary statistics with censored data. Probability plots and other goodness-of-fit techniques should be used to find matching distributions.
Nondetects are distributed in a manner similar to the detected values.
If the assumed model is incorrect, MLE may lead to misleading results.

14. Introduction – Bootstrap
After generating 100 bootstrap samples, it is possible to find the confidence interval for the mean, calculating the difference between the mean of the original sample and the mean of bootstrap samples.
Bootstrap1
Bootstrap100
Original sample
Fig. 2. Schematic matrix of original smaple and bootstrap samples

15. Purpose of the research
“Develop a statistical approach that more accurately estimates the required site decontamination necessary to meet current cleanup criteria and validate that compliance.”
The expected advantages are:
Better Probabilistic Exposure Assessment
More Cost Effective

16. Case study

17. Case study There is a monazite powder manufacturing plant.
Some of the plant facilities and soil were contaminated during the manufacturing process.
Facility soil was decontaminated and soil survey conducted.

18. Case study
The survey consisted of Grid box No.1 and Grid box No.2, each having 30 data points measuring the concentration of U-238 and K-40, in the same area.
In Grid box No.1, 8 data points are below the detection limit for U-238, and 17 for K-40.
Grid box No.1
U-238
K-40
(8/30)
(17/30)
Fig. 3. Schematic diagram of Grid box No.1

19. Case study
In Grid box No.2, 10 data points are below the detection limit for U-238, and 9 for K-40.
Grid box No.2
U-238
K-40
(10/30)
(9/30)
Fig. 4. Schematic diagram of Grid box No.2

20. Results

21. U-238 in Grid box No.1 Mean (Bq/g) STD DEV Pct25 Median Pct75 Ignoring
Mean
(Bq/g)
STD DEV
Pct25
Median
Pct75
Ignoring
0.339
0.212
0.123
0.351
0.534
Zero
0.249
0.236
0.012
0.148
0.460
1/2 DL
0.261
0.223
0.048 DL
0.274
0.211
0.095
MLE(ln)
0.263
0.221
0.065
0.486
ROS(ln)
0.267
0.218
0.085
K-M
0.051
Table 3. Summary statistics using several estimation methods – U-238 in Grid box No.1

22. K-40 in Grid box No.1 Mean (Bq/g) STD DEV Pct25 Median Pct75 Ignoring
Mean
(Bq/g)
STD DEV
Pct25
Median
Pct75
Ignoring
0.092
0.042
0.072
0.094
0.110
Zero
0.040
0.054
0.087
1/2 DL
0.043
0.051
0.006 DL
0.046
0.049
0.012
MLE(ln)
0.003
0.091
ROS(ln)
K-M
0.044
Table 4. Summary statistics using several estimation methods – K-40 in Grid box No.1

23. U-238 in Grid box No.2 Mean (Bq/g) STD DEV Pct25 Median Pct75 Ignoring
Mean
(Bq/g)
STD DEV
Pct25
Median
Pct75
Ignoring
0.492
0.274
0.228
0.408
0.7735
Zero
0.328
0.324
0.242
0.561
1/2 DL
0.346
0.305
0.055 DL
0.364
0.288
0.109
MLE(ln)
0.353
0.299
0.102
0.604
ROS(ln)
0.358
0.294
K-M
0.379
0.277
0.213
0.583
Table 5. Summary statistics using several estimation methods – U-238 in Grid box No.2

24. K-40 in Grid box No.2 Mean (Bq/g) STD DEV Pct25 Median Pct75 Ignoring
Mean
(Bq/g)
STD DEV
Pct25
Median
Pct75
Ignoring
0.092
0.067
0.023
0.108
0.135
Zero
0.064
0.070
0.026
0.124
1/2 DL
0.066
0.069
0.006 DL
0.068
0.013
MLE(ln)
0.011
0.128
ROS(ln)
0.012
K-M
0.127
Table 6. Summary statistics using several estimation methods – K-40 in Grid box No.2

25. Confidence interval using MLE/Bootstrap
Cases
90% confidence interval
for the mean (Bq/g)
95% confidence interval
U-238 in Grid box No.1
(Mean : 0.263)
[0.189, 0.413]
[0.177, 0.450]
K-40 in Grid box No.1
(Mean : 0.043)
[0.025, 0.176]
[0.022,0.233]
U-238 in Grid box No.2
(Mean : 0.353)
[0.256, 0.554]
[0.240, 0.604]
K-40 in Grid box No.2
(Mean : 0.067)
[0.043, 0.142]
[0.039, 0.165]
Table 7. Various confidence intervals for the mean using MLE/Bootstrap

26. Background - RESRAD
RESRAD is a computer model designed to estimate radiation doses and risks from RESidual RADioactive materials.
RESRAD code is used for determining regulatory compliance.
Both the U.S Department of Energy and the U.S. Nuclear Regulatory Commission use 25 mrem/yr as the general limit or constraint for soil cleanup or site decontamination.
RESRAD code has the basic models and parameters, but it can be modified to meet specific need.

27. Background - RESRAD RESRAD code can be used to :
Compute potential annual doses or lifetime risks to workers or members of the public resulting from exposures to residual radioactive material in soil
Support an ALARA analysis or a cost benefit analyses that can help in the cleanup decision-making process.
Fig. 5. Exposure pathways considered in RESRAD

28. Background - RESRAD Assumptions
Farmer scenario (Consider all pathways)
Municipal landfill
Climate data in Daejeon
National nutrition survey
Default value
Did not consider radon and C-14

29. Results Cases Maximum Total Dose (t) (mrem/yr) Maximum Excess
Cancer Risk (t)
Ignoring
29.11 (t=128.3yr)
1.127E-3 (t=100yr)
Zero
13.09 (t=128.4yr)
4.985E-4 (t=100yr)
1/2 DL
14.15 (t=128.4yr)
5.396E-4 (t=100yr) DL
15.99 (t=128.3yr)
6.114E-4 (t=100yr)
MLE
14.13 (t=128.4yr)
5.388E-4 (t=100yr)
Table 8 Maximum Total Dose (t) and Maximum Excess Cancer Risk (t) for the several estimation
methods in Grid box No.1

30. Conclusions
Summary statistics and confidence intervals were compared to conventional methods.
Proposed methods (MLE, ROS, K-M) were performed using the soil samples from the monazite powder manufacturing plant.
The preliminary evaluation shows that the proposed method can be effectively used to provide
Best Estimate Radioactivity levels at decommissioned NPP site.
Estimates of uncertainty in the Mean Values
RESRAD is used to estimate radiation doses and risks in each case.
Cover thickness is calculated to show the difference between the each method.

31. Future work
Get the soil data from real decommissioned NPP and conduct all of the above analyses (Yankee Rowe Finished/software & codes).
Economic analysis of the degree of savings using new methodology.
Develop RESRAD input code that allows the inclusion of non-detects.

32. References
[1] Dennis R. Helsel (2005), Nondetects And Data Analysis: Statistics for censored environmental data, John Wiley & Sons, Inc., Hoboken, New Jersey. [2] Zhao, Y., and H.C. Frey, “Quantification of Uncertainty and Variability for Air Toxic Emission Factor Data Sets Containing Non-Detects,” Annual Meeting of the Air & Waste Management Association, Pittsburgh, PA, June 2003 [3] OECD NEA, Cost Estimation for decommissioning: An International Overview of Cost Elements, Estimation Practices and Reporting Requirements, p. 7, 2010 [4] Orbitech, Development of Radioactivity Inference Method and Acceptance Criteria Based on Statistical Approach for Treatment or Disposal of NORM Waste, Feb 2016 [5] Brookhaven National Laboratory, Assessment of Radionuclide Release from Contaminated Concrete at the Yankee Nuclear Power Station, March 2004 [6] Argonne National Laboratory, Examination of Technetium-99 Dose Assessment Modeling with RESRAD (onsite) and RESRAD-OFFSITE, June 2011 [7] EPA, Data Quality Assessment: Statistical Methods for Practitioners, Feb 2006 [8] KHNP, Decontamination Experiment of Contaminated Soil and its Safety Assessment by Residual Radioactivity, 2004 [9] KINS, Establishment of Management Plan for the Disposal of NORM Wastes and Unsuitable Processed Products, Feb 2015

33. Thank you

34. Appendix

35. Background Instruments & Analysis Program
ORTEC HPGe (GEM P, 60% efficiency) is utilized.
Counting time is 1,800 sec for all the samples.
ORTEC GammaVision 6.01 is used to analyze.

36. Amount of available data
Appendix
Amount of available data
Percent Censored
< 50 observations
> 50 observations
< 50% nondetects
Kaplan-Meier
50 – 80% nondetects
MLE or ROS
MLE
> 80% nondetects
Report only % above a meaningful threshold
May report high sample percentiles (90th, 95th)
Table 8. Recommended methods for estimation of summary statistics

37. Appendix – Kaplan-Meier
The nonparametric Kaplan-Meier (K-M) method has always been considered as a standard method for estimating summary statistics of censored survival data.
Left-censored data must be flipped prior to using the K-M method, the procedures of calculating survival probability are computed in a way that is similar to analyses for right censored data, and the results are re-transformed when calculating estimates(mean, median, and other percentiles).
In this case, the highest observed value would have the lowest rank 1. Let S be the survival probability. The survival probability is a product of incremental probabilities that are the probabilities of "surviving" to the next lowest detected limit, given the number of data at and below that detection limit.
The mean of K-M estimator is evaluated as the area under the K-M survival curve for the flipped data after re-transformation.

38. Appendix – ROS
ROS calculates summary statistics with a regression equation on a probability plot, and is called "regression on order statistics". We used a robust approach to ROS.
Unobserved values are estimated from a regression equation obtained by using observed data. The regression equation is obtained by fitting observed values to the probability plot, and the explanatory variable in the regression is the normal scores of observed values.

39. Appendix – MLE
The parametric Maximum Likelihood Estimator (MLE) assumes a distribution that will closely fit the observed data.

40. Appendix – MDA Calculation
𝑀𝐷𝐶𝑅= 𝑘 2 𝑇 𝑠 +2𝑘 𝐶 𝑏 𝑇 𝑠 + 𝐶 𝑏 𝑇 𝑏
𝑘 : standard score
𝑇 𝑠 : Sample Counting Time
𝑇 𝑏 : Background Counting Time
𝐶 𝑏 : Background Count Rate
𝑀𝐷𝐴= 𝑀𝐷𝐶𝑅 ×𝐹 𝐸 𝑓𝑓 ×𝑉(𝐿)
𝐹 : 4.50×10 −1 pCi/dpm
𝐸 𝑓𝑓 : Counting efficiency
𝑉(𝐿) : Volume of Sample

41. Results Cases Cover thickness Ignoring -> MLE
(29.11->14.13 mrem/yr)
More than 3m
DL -> MLE
(15.99->14.13 mrem/yr)
1/2 DL -> MLE
(14.15->14.13 mrem/yr)
13.5cm
Table 7. Cover thickness calculated to show the difference between the each method

42. Introduction – ROS Calculating the plotting position:
𝑝𝑒 𝑖 = 𝑝𝑒 𝑗+1 + 𝐴 𝑗 𝐴 𝑗 + 𝐵 𝑗 [1− 𝑝𝑒 𝑗+1 ]
𝐴 𝑗 = the number of observations detected between the jth and (j+1)th detection limits
𝐵 𝑗 = the number of observations, censored and uncensored below the jth detection limit
The number of nondetects below the jth detection limit is defined as 𝐶 𝑗 :
𝐶 𝑗 = 𝐵 𝑗 − 𝐵 𝑗−1 − 𝐴 𝑗−1
Calculating the plotting position:
For observed values
𝑝𝑑 𝑖 =(1− 𝑝𝑒 𝑗 )+ 𝑖 𝐴 𝑗 +1 [ 𝑝𝑒 𝑗 − 𝑝𝑒 𝑗+1 ]
For censored observations
𝑝𝑐 𝑖 = 𝑖 𝐶 𝑗 +1 ∗[1− 𝑝𝑒 𝑗 ]

43. Case study
The survey consisted of Grid box No.1 and Grid box No.2, each having 30 data points measuring the concentration of U-238 and K-40, in the same area.
In Grid box No.1, 8 data points are below the detection limit for U-238, and 17 for K-40.
U-238
K-40
MDA
Minimum
(Bq/g)
Maximum
0.0953
0.0118
Grid box No.1
U-238
K-40
(8/30)
(17/30)
Fig. 3. Schematic diagram of Grid box No.1
Table 3. MDA of U-238 and K-40 in Grid box No.1

44. Case study
In Grid box No.2, 10 data points are below the detection limit for U-238, and 9 for K-40.
U-238
K-40
MDA
Minimum
(Bq/g)
0.0111
Maximum
0.109
0.0126
Grid box No.2
U-238
K-40
(10/30)
(9/30)
Fig. 4. Schematic diagram of Grid box No.2
Table 4. MDA of U-238 and K-40 in Grid box No.2