Download Including Below Detection Limit Samples in

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Including Below Detection Limit Samples
in Decommissioning Soil Sample Analyses
Speaker: Jung Hwan Kim
KRS presentation (May 27. 2016)
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Contents
 Introduction
 Purpose of the research
 Case study
 Results
 Conclusions
 Future work
 References
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Introduction
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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.
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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)
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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
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Introduction
• To resolve these issues Statistical Techniques were used to analyze a
case study
1.
Proposed methods for estimating summary statistics (Mean, STD DEV, PCT)
• Kaplan-Meier
• Regression on Order Statistics (ROS)
• Maximum Likelihood Estimation (MLE)
2.
Proposed method for estimating confidence intervals
• Bootstrapping
• These techniques are used by many researchers in the Environmental
Science and Technology area.
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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.
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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
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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
0
Table 1. Kaplan-Meier example data
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Fig. 1. Kaplan-Meier method example data plot
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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.
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Introduction – ROS
Input Concentration
Probability
Estimated
Concentration
3.2
0.972
3.2
2.8
0.944
2.8
<2
0.815
1.418
<2
0.713
1.143
<2
0.611
0.954
<2
0.509
0.807
<2
0.407
0.683
<2
0.306
0.572
<2
0.204
0.465
<2
0.102
0.349
1.7
0.873
1.7
1.5
0.829
1.5
Table 2. ROS final data
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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.
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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.
Original sample
Bootstrap1
Bootstrap100
Fig. 2. Schematic matrix of original smaple and bootstrap samples
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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
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Case study
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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.
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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
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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
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Results
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U-238 in Grid box No.1
Mean
(Bq/g)
STD DEV
(Bq/g)
Pct25
(Bq/g)
Median
(Bq/g)
Pct75
(Bq/g)
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
0.148
0.460
DL
0.274
0.211
0.095
0.148
0.460
MLE(ln)
0.263
0.221
0.065
0.148
0.486
ROS(ln)
0.267
0.218
0.085
0.148
0.460
K-M
0.263
0.221
0.051
0.148
0.486
Table 3. Summary statistics using several estimation methods – U-238 in Grid box No.1
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K-40 in Grid box No.1
Mean
(Bq/g)
STD DEV
(Bq/g)
Pct25
(Bq/g)
Median
(Bq/g)
Pct75
(Bq/g)
Ignoring
0.092
0.042
0.072
0.094
0.110
Zero
0.040
0.054
0
0
0.087
1/2 DL
0.043
0.051
0.006
0.006
0.087
DL
0.046
0.049
0.012
0.012
0.087
MLE(ln)
0.043
0.051
0.003
0.012
0.091
ROS(ln)
0.046
0.049
0.012
0.012
0.087
K-M
0.054
0.044
0.091
Table 4. Summary statistics using several estimation methods – K-40 in Grid box No.1
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U-238 in Grid box No.2
Mean
(Bq/g)
STD DEV
(Bq/g)
Pct25
(Bq/g)
Median
(Bq/g)
Pct75
(Bq/g)
Ignoring
0.492
0.274
0.228
0.408
0.7735
Zero
0.328
0.324
0
0.242
0.561
1/2 DL
0.346
0.305
0.055
0.242
0.561
DL
0.364
0.288
0.109
0.242
0.561
MLE(ln)
0.353
0.299
0.102
0.242
0.604
ROS(ln)
0.358
0.294
0.109
0.242
0.561
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
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K-40 in Grid box No.2
Mean
(Bq/g)
STD DEV
(Bq/g)
Pct25
(Bq/g)
Median
(Bq/g)
Pct75
(Bq/g)
Ignoring
0.092
0.067
0.023
0.108
0.135
Zero
0.064
0.070
0
0.026
0.124
1/2 DL
0.066
0.069
0.006
0.026
0.124
DL
0.068
0.067
0.013
0.026
0.124
MLE(ln)
0.067
0.068
0.011
0.026
0.128
ROS(ln)
0.067
0.068
0.012
0.026
0.124
K-M
0.068
0.067
0.026
0.127
Table 6. Summary statistics using several estimation methods – K-40 in Grid box No.2
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Confidence interval using MLE/Bootstrap
Cases
90% confidence interval
for the mean (Bq/g)
95% confidence interval
for the mean (Bq/g)
[0.189, 0.413]
[0.177, 0.450]
[0.025, 0.176]
[0.022,0.233]
[0.256, 0.554]
[0.240, 0.604]
[0.043, 0.142]
[0.039, 0.165]
U-238 in Grid box No.1
(Mean : 0.263)
K-40 in Grid box No.1
(Mean : 0.043)
U-238 in Grid box No.2
(Mean : 0.353)
K-40 in Grid box No.2
(Mean : 0.067)
Table 7. Various confidence intervals for the mean using MLE/Bootstrap
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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.
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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
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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
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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
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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.
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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.
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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
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Thank you
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Appendix
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Background
Instruments & Analysis Program
• ORTEC HPGe (GEM-60195-P, 60% efficiency) is utilized.
• Counting time is 1,800 sec for all the samples.
• ORTEC GammaVision 6.01 is used to analyze.
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Appendix
Amount of available data
Percent Censored
< 50 observations
> 50 observations
< 50% nondetects
Kaplan-Meier
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
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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.
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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.
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Appendix – MLE
• The parametric Maximum Likelihood Estimator (MLE) assumes a
distribution that will closely fit the observed data.
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Appendix – MDA Calculation
• 𝑀𝐷𝐶𝑅 =
𝑘2
𝑇𝑠
+ 2𝑘
𝐶𝑏
𝑇𝑠
+
𝐶𝑏
𝑇𝑏
𝑘 : standard score
𝑇𝑠 : Sample Counting Time
𝑇𝑏 : Background Counting Time
𝐶𝑏 : Background Count Rate
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• 𝑀𝐷𝐴 =
𝑀𝐷𝐶𝑅 ×𝐹
𝐸𝑓𝑓 ×𝑉(𝐿)
−1
𝐹 : 4.50 × 10 pCi/dpm
𝐸𝑓𝑓 : Counting efficiency
𝑉(𝐿) : Volume of Sample
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Results
Cases
Cover thickness
Ignoring -> MLE
(29.11->14.13 mrem/yr)
More than 3m
DL -> MLE
(15.99->14.13 mrem/yr)
More than 3m
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
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Introduction – ROS
• 𝑝𝑒𝑖 = 𝑝𝑒𝑗+1 +
𝐴𝑗
𝐴𝑗 +𝐵𝑗
[1 − 𝑝𝑒𝑗+1 ]
𝐴𝑗 = the number of observations detected between the jth and (j+1)th detection limits
𝐵𝑗 = the number of observations, censored and uncensored below the jth detection limit
The number of nondetects below the jth detection limit is defined as 𝐶𝑗 :
𝐶𝑗 = 𝐵𝑗 − 𝐵𝑗−1 − 𝐴𝑗−1
• Calculating the plotting position:
 For observed values
𝑖
𝑝𝑑𝑖 = (1 − 𝑝𝑒𝑗 ) +
[𝑝𝑒𝑗 − 𝑝𝑒𝑗+1 ]
𝐴𝑗 + 1
 For censored observations
𝑖
𝑝𝑐𝑖 =
∗ [1 − 𝑝𝑒𝑗 ]
𝐶𝑗 + 1
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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
(8/30)
K-40
(17/30)
Fig. 3. Schematic diagram of Grid box No.1
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U-238
K-40
MDA
Minimum
(Bq/g)
0.00997
0.00369
MDA
Maximum
(Bq/g)
0.0953
0.0118
Table 3. MDA of U-238 and K-40 in Grid box No.1
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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
(10/30)
K-40
(9/30)
Fig. 4. Schematic diagram of Grid box No.2
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U-238
K-40
MDA
Minimum
(Bq/g)
0.0111
0.00339
MDA
Maximum
(Bq/g)
0.109
0.0126
Table 4. MDA of U-238 and K-40 in Grid box No.2
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