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The EPA 7-Step DQO Process
Step 7 - Optimize Sample Design
(70 minutes)
Presenter:
Sebastian Tindall
Day 2 DQO Training CourseModule 7
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Terminal Course Objective
To be able to use the output from the previous DQO Process steps to select sampling and analysis designs and understand design alternatives presented to you for a specific project
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Step Objective:Identify the most resourceeffective data collectionand analysis design thatsatisfies the DQOsspecified in the preceding 6steps
Step 7: Optimize Sample Design
Step 4: Specify Boundaries
Step 2: Identify Decisions
Step 3: Identify Inputs
Step 1: State the Problem
Step 5: Define Decision Rules
Step 6: Specify Error Tolerances
Step 7: Optimize Sample Design
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Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designs
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Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designsThe outputs should provideinformation on the contextof, requirements for, and constraints on data collectiondesign.
Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
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Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designs
Based on the DQO outputs from Steps 1-6, for each decision rule develop one or more sample designs to be considered and evaluated inStep 7.
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Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designs
For each option, pay close attention to the Step 4 outputs defining the population to be representedwith the data:• Sample collection method• Sample mass size• Sample particle size• Etc.
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Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designs
Remember:Sampling Uncertainty is decreasedwhen sampling density is increased.
Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
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Types of Designs
Simple Random
Statistical Methods for Environmental Pollution Monitoring, Richard O. Gilbert, 1987
Systematic Grid with random start Geometric Probability or “Hot Spot” Sampling Stratified Random
– Stratified Simple Random– Stratified Systematic Grid with random start
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Simple Random
Definition- choice of sampling location or time is random
Assumptions– Every portion of the population has equal
chance of being sampled Limitation-may not cover area
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Simple Random
To generate a simple random design:– Either grid the site - set up equal lateral
triangles or equal side rectangles and number each grid, use a random number generator to pick the grids from which to collect samples
– Randomly select x, y, z coordinates, go to the random coordinates and collect samples
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Example - Simple Random Using Coordinates
- A Random ly Selected Sam pling Location
- Denotes random length & width Coordinates walked-off bysam pling team
N168'
14
7'
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Systematic Grid, Random Start
Definition-taking measurements at locations or times according to spatial or temporal pattern (e.g., equidistant intervals along a line or grid pattern)
Assumptions– Good for estimating means, totals and patterns of
contamination– Improved coverage of area
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Systematic Grid, Random Start (cont.)
Limitations– Biased results can occur if assumed pattern of
contamination does not match the actual pattern of contamination
– Inaccurate if have serial correlation NPDES outfall
– Periodic recurring release; time dependent Groundwater:
– seasonal recurrence; water-level dependence
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- Equally Spaced SamplingLocations
Nc
- Randomly Selected StartingLocation
Hot spot
Remember:Start at random locationMove in a pre-selected pattern across the site, making measurements at each point
Systematic Grid, Random Start (cont.)
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Geometric Probability or Hot-Spot Sampling
Uses squares, triangles, or rectangles to determine whether hot spots exist
Finds hot spot, but may not estimate the mean with adequate confidence
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Number of samples is calculated based on probability of finding hot area or geometric probability
Geometric Probability or Hot-Spot Sampling (cont.)
Assumptions– Target hot spot has circular or elliptical shape
– Samples are taken on square, rectangular or triangular grid
– Definition of what concentration/activity defines hot spot is unambiguous
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Limitations– Not appropriate for hot spots that are not elliptical
Geometric Probability or Hot-Spot Sampling (cont.)
– Not appropriate if cannot define what is hot or the likely size of hot spot
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Example Grid for Hot-Spot Sampling
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In order to use this approach the decision makers MUST – Define the size of the hot spot they wish to find– Provide rationale for specifying that size.– Define what constitutes HOT (e.g., what
concentration is HOT)– Define the effect of that HOT spot on achieving
the release criteria
Geometric Probability or Hot-Spot Sampling (cont.)
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Stratified Random
Definition-divide population into strata and collect samples in each strata randomly
Attributes– Provides excellent coverage of area– Need process knowledge to create strata– Yields more precise estimate of mean– Typically more efficient then simple random
Limitations– Need process knowledge
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Example - Stratified SimpleRandom
Strata 1
Strata 2
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Sampling Approaches
Sampling Approach 1– Simple Random
– Traditional fixed laboratory analyses
Sampling Approach 2– Systematic Grid
– Field analytical measurements
– Computer simulations
– Dynamic work plan
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Approach 1 Sample DesignCS
Plan View
Former PadLocation
RunoffZone
0 50 100 150 ft0 15 30 46 m
BufferZone
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Design ApproachesApproach 1
Collect samples using Simple Random design.
Use predominantly fixed traditional laboratory analyses and specify the method specific details at the beginning of DQO and do not change measurement objectives as more information is obtained
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Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designs
1. Statistical Method/Sample Size Formula2. Cost Function
Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
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Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designs
1. Statistical Method/Sample Size FormulaDefine suggested method(s) for testing the statistical hypothesis and define sample size formula(e) that corresponds to the method(s).
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Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designs
Perform a preliminary DQA:• Generate frequency distribution histogram(s) for each population• Select one or more statistical methods that will address the PSQs• List the assumptions for choosing these statistical methods• List the appropriate formula for calculating the number of
samples, n
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HistogramCS
0
1
2
3
0 7 14 21 28 35
Pb Concentration (mg/kg)
Fre
qu
en
cy
0
1
2
3
4
0 85 95 105 115
U Concentration
Fre
qu
en
cy0
1
2
3
4
0 1.7 3.4 5.1 6.8
TPH Concentration
Fre
qu
en
cy
0
1
2
3
0 0.8 1.6 2.4 3.2
Arochlor 1260
Fre
qu
en
cy
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3 Approaches for Calculating n
Normal approach Skewed approach FAM/DWP approach
– Badly skewed or for all distributions use computer simulation approach
• e.g., Monte Carlo
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How Many Samples do I Need?
Begin With the Decision in Mind
Optimal Sampling Design
Alternative Sample Designs
, , , Correct Equation for n (Statistical Method)
Population Frequency Distribution
Contaminant Concentrations in the Spatial Distribution of the Population
The end
Data• field• onsite
methods• traditional
laboratory
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Logic to Assess Distribution and Calculate Number of Samples
SkewedCalculate the number of
samples based on skeweddistributions (e.g.,
nonparametric tests suchas WSR or WRS)
Is frequencydistribution fromeach populationsymmetrical orapproximatelysymmetrical?
SymmetricalUse equations based onsymmetrical distribution.
Option 1 Option 2
Badly SkewedBadly skewed or for any
distribution, use computersimulations
(e.g.,Monte Carlo) to performcalculations to estimate the
number of samples
Yes
No
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Normal Approach
Due to using only five samples for initial distribution assessment, one cannot infer a ‘normal’ frequency distribution
Reject the ‘Normal’ Approach and Examine ‘Non-Normal’or ‘Skewed’ Approach
CS
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Logic to Assess Distribution and Calculate Number of Samples
SkewedCalculate the number of
samples based on skeweddistributions (e.g.,
nonparametric tests suchas WSR or WRS)
Is frequencydistribution fromeach populationsymmetrical orapproximatelysymmetrical?
SymmetricalUse equations based onsymmetrical distribution.
Option 1 Option 2
Badly SkewedBadly skewed or for any
distribution, use computersimulations
(e.g.,Monte Carlo) to performcalculations to estimate the
number of samples
Yes
No
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Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designs
Using the formulae appropriate to these methods, calculate the number of samples required, varying , for a given .Repeat the same process using new s.
Review all of calculated sample sizes and along withtheir corresponding levels of , , and .
Select those sample sizes that have acceptable levels of , , and associated with them.
Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
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Pb, U, TPH (DRO/GRO) Because there were multiple COPCs with
varied standard deviations, action limits and LBGRs, separate tables for varying alpha, beta, and (LBGR) delta were calculated
For the U, Pb, and TPH, the largest number of samples for a given alpha, beta and delta are presented in the following table
CS
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Pb, U, TPH Based on Non-Parametric Test CSS a m p l e S i z e s B a s e d o n V a r y i n g E r r o r T o l e r a n c e s a n d L B G R
L e a d , U r a n i u m , a n d T P H
M i s t a k e n l y C o n c l u d i n g < A c t i o n L e v e l
s = 1 0 . 5 ( U ) = 0 . 0 1 = 0 . 0 5 = 0 . 1 0
S a m p l e s i z e f o r m u l a : 2)(
)(16.1
12
2
2211
Sn
W i d t h o f t h e G r a y R e g i o n , ( ) = 2 4 0 – 2 2 9 . 5 = 1 0 . 5 ( t o t a l e r r o r e s t i m a t e )
= 0 . 1 0 1 9 1 2 9
= 0 . 2 0 1 5 9 7
Mis
tak
enly
Con
clu
din
g>
Act
ion
Lev
el
= 0 . 3 0 1 3 8 5
W i d t h o f t h e G r a y R e g i o n , ( ) = 2 4 0 – 1 9 2 = 4 8 ( 2 0 % o f a c t i o n l e v e l )
= 0 . 1 0 4 3 2
= 0 . 2 0 4 2 2
Mis
tak
enly
Con
clu
din
g>
Act
ion
Lev
el
= 0 . 3 0 4 2 2
W i d t h o f t h e G r a y R e g i o n , ( ) = 2 4 0 – 1 2 0 = 1 2 0 ( 5 0 % o f a c t i o n l e v e l )
= 0 . 1 0 4 2 2
= 0 . 2 0 4 2 1
Mis
tak
enly
Con
clu
din
g>
Act
ion
Lev
el
= 0 . 3 0 4 2 1
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Aroclor 1260- Non-Parametric Test
For PCBs, the Aroclor 1260 has the greatest variance and using the standard deviation results in a wide gray region
The following table presents the variation of alpha, beta and deltas for Aroclor 1260
CS
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Aroclor 1260- Non-Parametric Test CSS a m p l e S i z e s B a s e d o n V a r y i n g E r r o r T o l e r a n c e s a n d L B G R
P C B s ( b a s e d o n A r o c l o r 1 2 6 0 )
M i s t a k e n l y C o n c l u d i n g < A c t i o n L e v e l
s = 0 . 8 8 ( A - 1 2 6 0 ) = 0 . 0 1 = 0 . 0 5 = 0 . 1 0
S a m p l e s i z e f o r m u l a : 2)(
)(16.1
12
2
2211
Sn
W i d t h o f t h e G r a y R e g i o n , ( ) = 1 – 0 . 1 2 = 0 . 8 8 ( t o t a l e r r o r e s t i m a t e ) a
= 0 . 1 0 1 9 1 2 9
= 0 . 2 0 1 5 9 7
Mis
tak
enly
Con
clu
din
g>
Act
ion
Lev
el
= 0 . 3 0 1 3 8 5
W i d t h o f t h e G r a y R e g i o n , ( ) = 1 – 0 . 8 0 = 0 . 2 0 ( 2 0 % o f a c t i o n l i m i t )
= 0 . 1 0 2 9 6 1 9 4 1 4 9
= 0 . 2 0 2 2 9 1 4 1 1 0 3
Mis
tak
enly
Con
clu
din
g>
Act
ion
Lev
el
= 0 . 3 0 1 8 6 1 0 8 7 5
W i d t h o f t h e G r a y R e g i o n , ( ) = 1 - 0 . 5 0 = 0 . 5 0 ( 5 0 % o f a c t i o n l i m i t )
= 0 . 1 0 5 0 3 3 2 5
= 0 . 2 0 4 0 2 4 1 8
Mis
tak
enly
Con
clu
din
g>
Act
ion
Lev
el
= 0 . 3 0 3 3 1 9 1 3
a T h e t o t a l e r r o r e s t i m a t e f o r s u b s u r f a c e c o n c e n t r a t i o n s e x c e e d s t h e a c t i o n l i m i t , t h u s i n a p p r o p r i a t e l y m o v i n g t h e L B G R b e l o w z e r o . O n l y t h e s u r f a c e c o n c e n t r a t i o n e r r o r e s t i m a t e i s c o n s i d e r e d h e r e f o r t h a t r e a s o n .
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Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designs
2. Cost FunctionFor each selected sample size, develop a costfunction that relates the number of samples to the total cost of sampling and analysis.
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Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designs
In order to develop the cost function, the aggregate unit cost persample must be determined. This is the cost of collecting one sample and conducting all the required analyses for a given decision rule.
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AUSCA$ = USC$ + USA$i Where (here):USC$ = Unit Sample Collection CostUSA$ = Unit Sample Analysis CostAUSCA$ = Aggregate Unit Sample Collection and Analysis Costj = Number of analytical methods planned
Aggregate Unit Sampling and Analysis Cost
i=1
j
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CSApproach 1 Sampling Design (cont.) Surface Soils S&A Costs
Lab Analytical Cost Without PCBs
Unit Sample Analysis Cost
Pb by ICP/AES $35U by ICP/AES $65TPH (GRO) by GC $65TPH (DRO) by GC $85
Total USA$ $250
Unit Sample Collection Cost $50AUSCA$ = USC$ + total USA$ $300
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CSApproach 1 Sampling Design (cont) Sub-surface Soils S&A Costs
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CSApproach 1 Sampling Design (cont.)
Surface Soils
Lab Analytical Costs for PCBs by GCPolychlorinated biphenyls 150.00$
Total USA$ 150.00$ Unit Sample Collection Cost 50.00$ AUSCA$ = USC$ + total USA$ 200.00$
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CSApproach 1 Sampling Design (cont.)
Sub-surface Soils
Lab Analytical Costs for PCBs by GCPolychlorinated biphenyls 150.00$
Total USA$ 150.00$ Unit Sample Collection Cost 100.00$ AUSCA$ = USC$ + total USA$ 250.00$
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Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designs
Merge the selected sample size outputs with the Aggregate Unit Sample Collection and Analysis cost output.
This results in a table that shows the product of each selected sample size and the AUSCA$.
This table is used to present the project managers and decision makers with a range of analytical costs and the resulting uncertainties.
From the table, select the optimal sample size that meets the project budgetand uncertainty requirements.
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SHOW EXCEL File
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Approach 1 Based Sampling Design Design for Pb, U, TPH
– Alpha = 0.05; Beta = 0.2; Delta = total error
– The decision makers agreed on collection of 9 surface samples for Pb, U and TPH (GRO & DRO) from each of the two surface strata, for a total of 18 samples using a stratified random design
– For the sub-surface, 9 borings/probes will be made in each of the two subsurface stratum at random locations; one sample will be collected at a random depth down to 10 feet from each boring, to assess migration through the vadose zone, for a total of 18 samples
Design for PCBs– Alpha = 0.05; Beta = 0.20; Delta = 0.50 (50% of the AL)
– The decision makers agreed on collection of 24 surface samples from each of the two surface strata; total of 48 samples using a stratified random design
– For the sub-surface, 24 borings/probes will be collected from each of the two subsurface stratum at random locations, collected at a random depth down to 10 feet for a total of 48 samples
CS
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Approach 1 Sample Locations(Surface Strata)
CS
Plan View
Former PadLocation
RunoffZone
0 50 100 150 ft0 15 30 46 m
BufferZone
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CSApproach 1 Sampling Design (cont.)
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Remediation Costs*CS
*Does not include layback area
DR#
Description/Depth Area(ft2)
Volume(yd3)
Cost*
1a Pad & Run-off Zone, 0-6” 12,272 227 $45,4001b Buffer Zone (excluding
Pad and Run-off area), 0-6”42,884 794 $158,800
2a Pad & Run-off Zone,6”-10”
12,272 4,318 $863,600
2b Buffer Zone (excludingPad and Run-off area),6”-10”
42,884 15,089 $3,017,800
* Assume $200 per yd3 for all COPCs
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Approach 1 Based Sampling Design Compare Approach 1 costs versus remediation
costs – Approach 1 S&A costs
• $11,700 (Pb, U, TPH) + $21,600 (PCBs) = $33,300
– Remediation costs• Cost to remediate surface soil under footprint of pad and
buffer area: $204,200• Cost to remediate subsurface soil under footprint of pad and
buffer area: $3,881,400
CS
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Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designsIf no sample design meets the error tolerances within the budget: relax one or more of the constraints or request more funding, etc.
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Design ApproachesApproach 2: Dynamic Work Plan (DWP) & Field Analytical Methods (FAMs)
Use DWP to allow more field decisions to meet the measurement objectives and allow the objectives to be refined in the field using DWP
Manage uncertainty by increasing sample density by using field analytical measurements
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Approach 2 Sampling Design Phase 1: Pb, U, TPH, PCBs
– Perform field analysis of the four strata on-site using XRF (Pb & U), on-site GC (TPH), and Immunoassay (PCBs) methods. Take into account the chance of false positives at the low detection levels
– This will produce a worse-case distributions that will be used to calculate the number of confirmatory samples for laboratory analysis for the surface and below grade strata
CS
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Phase 1: Pb, U, TPH, PCBs– Provide detailed SOPs for performance of FAMs: XRF,
GC, & Immunoassay analysis– Divide both surface strata into triangular grids– Use systematic sampling, w/random start (RS), to locate
sample points; sample in center of each grid Pad & Run-off zone
CSM expects contamination more likely here 10 ft equilateral triangle: 43.35 ft2
Pad + Run-off zone = 12,272 ft2
283 sample points
Buffer area: Also 283 sample points CSM expects contamination less likely here Thus, grid triangle has larger area
Approach 2 Sampling Design (cont.)CS
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Phase 1: Pb, U, TPH, PCBs– Sub-surface strata: Pad & Run-off zone
Use Direct Push Technology (DPT) to collect Push at all surface sample points > ALs Minimum sample locations: 40 (+ 10 >ALs) = ~50 Collect sub-surface samples every 3 feet 50 X 3 = 150 sub-surface samples in this strata Use systematic sampling, w/random start (RS), to locate sample
points
– Buffer area CSM expects contamination less likely here Thus, fewer sample points Same >ALs rationale as above 50 X 3 = 150 sub-surface samples in Buffer area Use systematic sampling, w/RS, to locate sample points
Approach 2 Sampling Design (cont.)CS
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Stratified Systematic Grid with Random Start(Surface Strata)
CS
Not to scaleSquares will be adjusted according to Step 7 design
NFootprint ofConcrete Pad(Stratum 1)
Runoff Zone(Stratum 1)
Buffer Zone(Stratum 2)
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Phase 2: Pb, U, TPH, PCBs– Evaluate the FAM results and construct FDs for each COPC
– Using Monte Carlo method, evaluate the alpha, beta and delta and resulting n based on the XRF, on-site GC, and Immunoassay data and select a value (worst case) for n to confirm the FAM data, using traditional laboratory analysis for each of the four strata
– For this Case Study, we will assume that number came out to be 9 per strata or 36 confirmatory lab samples
CSApproach 2 Sampling Design (cont.)
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CSApproach 2 Sampling Design (cont.)
Surface Soils SC&SA Costs
U by Field XRF $1.5Pb by Field XRF $1.5TPH (GRO) on-site GC $25TPH (DRO) on-site GC $25
PCBs by IMA kits $50
Total USA$ $103
Unit Sample Collection Cost $25AUSCA$ = USC$ + total USA$ $128
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CSApproach 2 Sampling Design (cont)
Sub-surface Soils SC&SA Costs
U by Field XRF $1.5Pb by Field XRF $1.5TPH (GRO) on-site GC $25TPH (DRO) on-site GC $25
PCBs by IMA kits $50
Total USA$ $103
Unit Sample Collection Cost $50AUSCA$ = USC$ + total USA$ $153
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CSApproach 2 Sampling Design (cont.)
COPC (Method) Number of Samples, n AUSCA$Total SC&SA Cost
U and Pb (XRF); TPH (On-site GC); PCBs (IMA kits); Surface Soils (strata 1 & 2) 566 $128 $72,448U and Pb (XRF); TPH (On-site GC); PCBs (IMA kits); Sub-Surface Soils (strata 1&2) 300 $153 $45,900Total $118,348
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CS
Number of Samples, n AUSCA$
Total Sampling and Analytical Cost
Subtotal - Onsite $118,348Pb, U, TPH, PCBs -Surface 18 $250 $4,500Pb, U, TPH, PCBs - Suburface 18 $275 $4,950Subtotal - Lab $9,450
Total Costs On-site and Lab Methods $127,798
Confirmatory Traditional Laboratory Analyses Costs
Approach 2 Sampling Design (cont.)
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Evaluate costs of Approach 2 vs. remediation costs– Sampling and analysis (S&A) costs $127,798– Original budget for S&A $45,000
– Remediation cost• Cost to remediate surface soil under footprint of pad and
buffer area: $204,200• Cost to remediate subsurface soil under footprint of pad
and buffer area: $3,881,400
CSApproach 2 Sampling Design (cont.)
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CS
Approach
# Samples, n On-Site
(Surface / Sub-surface)
# Samples, n Off-Site
(Surface / Sub-surface)
Total Sampling and Analytical Cost
1 none 66/66 $33,3002 566/300 18/18 $127,798
Comparison Costs
Remediation Costs:•Surface - $204,200•Sub-surface - $3,881,400
Approach 2 Sampling Design (cont.)
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A Visual Decision Strategy
S ta rt G e tD a ta
C h e ckD a ta
Fit D a ta
PD F D oH yp oth es is
Te s t
C le a nD irty
Ne e dM o reD a ta
S to pD a ta
G e tS a m ple
S ize
G e tS am pl i n gLocati on s
V ES A
n
V S P
x , y
V is u a l D Q A V is u a l F it V is u a l Te s t
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Approach 2b Sampling & Lab Analyses
Remember:Sampling Uncertainty is decreasedwhen sampling density is increased
n = m * k Select k of specified Mass/diameter3
– FE² 22.5 * d³ / M (to control sampling error)
Prepare m multi-increment samples for lab analysis Perform lab analyses on m samples
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n = m * k
k = 3k = 3
m = 2
Laboratory
Collect “n” samples
Group into “k”
Combine “k”into “m”composites
Remember;we want the
AVERAGEover theDecision Unit
Approach 2b Sampling & Lab Analyses
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Approach 2b Sampling Design Phase 2b: Pb, U, TPH, PCBs
– Let n = 283 (for each Surface strata); n = 150 (for each Sub-surface strata)
– Select appropriate values for m and k, based on cost and managing uncertainty
k = 3 (Surface); k = 3 (Sub-surface); add $5 to SC cost m = 94 (each Surface strata); Total = 188 Surface samples m = 50 (each Sub-surface strata); Total = 100 Sub-surface samples
– Perform field analysis of the four strata on-site using XRF (Pb & U), on-site GC (TPH), and Immunoassay (PCBs) methods.
– Again, this will produce worse-case distributions that will be used to evaluate and errors and to calculate the number of confirmatory samples for laboratory analysis for the surface and below grade strata; Still assume 36 total
CS
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Stratified Systematic Grid with Random Start(Surface Strata)
CS
Not to scaleSquares will be adjusted according to Step 7 design
NFootprint ofConcrete Pad(Stratum 1)
Runoff Zone(Stratum 1)
Buffer Zone(Stratum 2)
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CSApproach 2b Sampling Design (cont.)
SC Costs: Surface 564 30 $16,920U and Pb (XRF); TPH (On-site GC); PCBs (IMA kits); Surface Soils (strata 1 & 2) 188 $103 $19,364
SC Costs: Sub-Surface 300 $55 $16,500U and Pb (XRF); TPH (On-site GC); PCBs (IMA kits); Sub-Surface Soils (strata 1&2) 100 $128 $12,800Total $65,584
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CS
Number of Samples, n AUSCA$
Total Sampling and Analytical Cost
Subtotal - Onsite $65,584Pb, U, TPH, PCBs -Surface 18 $250 $4,500Pb, U, TPH, PCBs - Suburface 18 $275 $4,950Subtotal - Lab $9,450
Total Costs On-site and Lab Methods $75,034
Confirmatory Traditional Laboratory Analyses Costs
Approach 2b Sampling Design (cont.)
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Evaluate costs of Approach 2b vs. remediation costs– Sampling and analysis (S&A) costs $75,034– Original budget for S&A $45,000
– Remediation cost• Cost to remediate surface soil under footprint of pad and
buffer area: $204,200• Cost to remediate subsurface soil under footprint of pad
and buffer area: $3,881,400
CSApproach 2b Sampling Design (cont.)
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CS
Approach
# Samples, n On-Site
(Surface / Sub-surface)
# Samples, n Off-Site
(Surface / Sub-surface)
Total Sampling and Analytical Cost
1 none 66/66 $33,3002 566/300 18/18 $127,7983 188/100 18/18 $75,034
Remediation Costs:•Surface - $204,200•Sub-surface - $3,881,400
Approach 2b Sampling Design (cont.)
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CS
Approach 2b Was SelectedMost Cost-Effective
andBest Management of Uncertainty
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Measure both gasoline & diesel range fractions (GRO/DRO)
Ship & process all samples in one batch to decrease cost.
QC defined per SW 846 [1 MS/MSD, 1 method blank, 1 equipment blank (if equipment is reused), 1 trip blank for GRO only].
Cool GRO/DRO to 4°C, +/- 2°C. QAP written and approved before implementation.
CSQC and Analysis DetailsUsed in All Approaches
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Steps 1- 6
Step 7
Optimal Design
Iterative Process
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Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designs
Justification for a judgmental sampling design• Timeframe• Qualitative consequences of an inadequate sampling
design (low, moderate, severe)• Re-sampling access after decision has been made
(accessible or inaccessible)
Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
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WARNING!!If a judgmental design is selected in lieu of a statistical design the
following disclaimer must be stated in the DQO Summary Report:
“Results from a judgmental sampling design can only be used to make decisions about the locations from which the samples were taken and cannot be generalized or extrapolated to any other facility or population, and error analysis cannot be performed on the resulting data. Thus, using judgmental designs prohibits any assessment of uncertainty in the decisions.”
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Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designsThe output is the most resource-effective design forthe study that is expected toachieve the DQOs.
Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
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Data Quality Assessment
Guidance for Data Quality Assessment,EPA QA/G9, 2000
Step 1: Review DQOs and Sampling Design Step 2: Conduct Preliminary Data Review Step 3: Select the Statistical Test Step 4: Verify the Assumptions of the Test Step 5: Draw Conclusions From the Data
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To succeed in a systematic planning process for environmental decision making, you need need Statistical Support:Statistical Support:
One or more qualified statisticiansqualified statisticians, experienced in environmental data collection designsenvironmental data collection designs and statistical statistical data quality assessmentsdata quality assessments of such designs.
Summary
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Summary (cont.) Going through the 7-Step DQO Process will
ensure a defensible and cost effective sampling program
In order for the 7-Step DQO Process to be effective: – Senior management MUST provide support
– Inputs must be based on comprehensive scoping and maximum participation/contributions by decision makers
– Sample design must be based on the severity of the consequences of decision error
– Uncertainty must be identified and quantified
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Information IN Actions Information OUT
From Previous Step To Next Step
Select the optimal sample size that satisfies the DQOs for each data collection design option
For each design option, select needed mathematical expressions
Check if number of samples exceeds project resource constraints
Decision Error Tolerances
Gray Region
Review DQO outputs from Steps 1-6 to be sure they are internally consistent
Step 7- Optimize Sample Design
Develop alternative sample designs
Optimal Sample Design
Go back to Steps 1- 6 and revisit decisions. Yes
No
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End of Module 7
Thank you
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