1 of 83 The EPA 7-Step DQO Process Step 7 - Optimize Sample Design 3:30 PM - 4:45 PM (75 minutes) Presenters: Mitzi Miller and Al Robinson Day 2 DQO Training.

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The EPA 7-Step DQO Process

Step 7 - Optimize Sample Design

3:30 PM - 4:45 PM (75 minutes)

Presenters:

Mitzi Miller and Al Robinson

Day 2 DQO Training CourseModule 9

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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 resource-effective data collection and analysis design that satisfies the DQOs specified in the preceding 6 steps

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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Gray Region



No



Develop alternative sample designsThe outputs should provideinformation on the contextof, requirements for, and constraints on data collectiondesign.

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Gray Region



No




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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Gray Region



No




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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Gray Region



No




Remember:Sampling Uncertainty is decreasedwhen sampling density is increased.

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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

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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 rectangle 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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Hot-Spot Sampling

In order to use this approach the decision makers MUST – Define the size of the hot spot they wish to find – Define what constitutes HOT (e.g., what

concentration is HOT)– Define the effect of that HOT spot on achieving

the release criteria

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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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CS

Stratified Systematic Sampling

Process

Process

Side Slope Soils (Stratum 1)

Bottom of theexcavation

-20 ft(Stratum 2)

10 10020 8030 7040 60500

OriginalTrenchProfile

ft

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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 from eachpopulation normal or

approximatelynormal?

NormalUse equations based on

normal 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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Sampling Approaches

Sampling Approach 1– Traditional fixed laboratory analyses

Sampling Approach 2– Field analytical measurements

– Computer simulations

– Dynamic work plan

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Sampling Approach 2

1. Perform field analytical (using driver COPCs) 2. Define separate populations (pseudo-homogeneous strata)

3. Estimate the distribution(s) based on field/historical data

4. If reasonably normal, use Equation 6.6 (parametric test)

5. If not, use either non-parametric tests or go on to #6

6. Perform simulations on the estimated distribution(s) to determine the number of multi-increment samples (n) required for lab analyses for each strata,varying , , and

7. Collect n samples, and evaluate m and k and perform lab analysis

8. Perform a red/yellow/green sequential test of data from the labs samples

9. Collect and/or analyze more increments (m) if in yellow region

10. Make the decision(s) when in the red/green region

11. Perform formal, overall DQA to confirm decision(s)

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Approach 2 Sampling & Lab Analyses

k = 3k = 3

m = 2

Laboratory

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Approach 2 Sampling & Lab Analyses (cont.)

n = m * k

Remember:Sampling Uncertainty is decreasedwhen sampling density is increased

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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Gray Region



No




1. Statistical Method/Sample Size Formula2. Cost Function

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Gray Region



No




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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Gray Region



No




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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CS

Histogram

0123456789

10

0 0.1 0.2 0.3 0.4 0.5

Perimeter Co-60 Concentration (pCi/g)

Fre

qu

en

cy

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CS

Histogram (cont.)

0123456789

10

Perimeter Cs-137 Concentration (pCi/g)

Freq

uenc

y

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CS

Histogram (cont.)

0123456789

10

0 2 4 6 8 10 12 14

Perimeter Eu-152 Concentration (pCi/g)

Fre

qu

en

cy

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Histogram (cont.)

0

1

23

4

5

6

0 1 2 3 4 5 6

Perimeter Sr-90 Concentration (pCi/g)

Fre

qu

en

cy

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Gray Region



No




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.

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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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Option 1 Option 2




number of samples

Yes

No

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Normal Approach

Due to using only 12 RI/FS samples for initial distribution assessment, one cannot infer a ‘normal’ frequency distribution

Reject the ‘Normal’ Approach and Examine ‘Non-Normal’or ‘Skewed’Approach

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Option 1 Option 2




number of samples

Yes

No

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Design ApproachesApproach 1

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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Cs-137, Eu-152

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 Cs-137, Eu-152 (in the perimeter samples), the number of samples for a given alpha, beta and delta are presented in the following table

CS

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Non-Parametric Test

For the Perimeter data Cs-137 and Eu-152 have the largest variance

For the Trench footprint data, Pu-239/240 andCs-137 are the only two COCs with action levels

The following table presents the variation of alpha, beta and deltas for – Cs-137 and Eu-152 in the Perimeter

– Pu-239/240 in the Trench Footprint

CS

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Cs-137 in Perimeter 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

C s - 1 3 7 , A L = 6 . 2 p C i / g

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

= 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 :

W i d t h o f t h e G r a y R e g i o n , ( ) = 4 . 3 1 ( S D o f R I / F S d a t 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 , ( ) = 5 0 % o f A c t i o n L e v e l

= 0 . 1 0 3 1 2 0 1 5

= 0 . 2 0 2 5 1 5 1 1

Mis

tak

enly

Con

clu

din

g>

Act

ion

Lev

el

= 0 . 3 0 2 1 1 2 8


= 0 . 1 0 1 8 6 1 2 2 9 3

= 0 . 2 0 1 4 4 8 9 6 5

Mis

tak

enly

Con

clu

din

g>

Act

ion

Lev

el

= 0 . 3 0 1 1 7 6 8 4 7

212

211

2

5.016.1

ZZZ

n

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CSEu-152 in Perimeter Based on Non-Parametric TestS 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

E u - 1 5 2 , A L = 3 . 3 p C i / g


= 0 . 0 1 = 0 . 0 5 = 0 . 1 0


W i d t h o f t h e G r a y R e g i o n , ( ) = 3 . 6 1 5 ( S D o f R I / F S d a t a ) a

= 0 . 1 0 N / A N / A N / A

= 0 . 2 0 N / A N / A N / A

Mis

tak

enly

Con

clu

din

g>

Act

ion

Lev

el

= 0 . 3 0 N / A N / A N / A


= 0 . 1 0 7 6 5 0 3 8

= 0 . 2 0 6 0 3 6 2 7

Mis

tak

enly

Con

clu

din

g>

Act

ion

Lev

el

= 0 . 3 0 4 9 2 8 2 0


= 0 . 1 0 4 5 7 3 0 0 2 3 0

= 0 . 2 0 3 5 3 2 1 7 1 5 8

Mis

tak

enly

Con

clu

din

g>

Act

ion

Lev

el

= 0 . 3 0 2 8 6 1 6 6 1 1 5

( a ) T h e d e l t a i s g r e a t e r t h a n t h e A L , s o n o s a m p l e n u m b e r s c a l c u l a t e d .

212

211

2

5.016.1

ZZZ

n

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Pu-239/240 Trench Footprint Non-Parametric TestS 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 u - 2 3 9 / 2 4 0 , A L = 7 1 8 , 0 0 0 p C i / g


= 0 . 0 1 = 0 . 0 5 = 0 . 1 0


W i d t h o f t h e G r a y R e g i o n , ( ) = 0 . 7 9 5 ( S D o f R I / F S d a t 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


= 0 . 1 0 4 2 1

= 0 . 2 0 4 2 1

Mis

tak

enly

Con

clu

din

g>

Act

ion

Lev

el

= 0 . 3 0 4 2 1


= 0 . 1 0 4 2 1

= 0 . 2 0 4 2 1

Mis

tak

enly

Con

clu

din

g>

Act

ion

Lev

el

= 0 . 3 0 4 2 1

212

211

2

5.016.1

ZZZ

n

CS

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Approach 1 Based Sampling Design Design for Radionuclide COCs in Perimeter Soil

– Alpha = 0.05 & Beta = 0.20; Delta = 20% of AL

– The number of samples in the Perimeter soil was driven by the Eu-152 data as taken from preceding table

• The decision makers agreed on collection of 217 surface samples from the Perimeter side-slope soils when excavation was complete

– The number of samples in the Trench footprint was the same for either the Pu-239/240 or Cs-137

CS

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Gray Region



No




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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Gray Region



No




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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Gray Region



No




These costs include:• The unit sample collection cost• The unit field analysis cost• The unit laboratory analysis cost

For each analytical method selected in Step 3, there isa unit sample collection cost and a unit sampleanalytical cost.

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Gray Region



No




1. Add the unit sample collection cost (USC$) and the unitsample analytical cost (USA$) for each method chosen.

2. Sum each of the above values for all of the analyticalmethods chosen to get the aggregate unit sample collection and analysis cost (AUSCA$).

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AUSCA$ = USC$ + USA$ Where (here):USC$ = Unit Sample Collection CostUSA$ = Unit Sample Analysis CostAUSCA$ = Aggregate Unit Sample Collection and Analysis Costn = Number of analytical methods planned

Aggregate Unit Sampling and Analysis Cost

i=1

n

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Total Sampling and Analysis CostAnalytical Methods Unit Sample Analysis Cost ($)

Low Medium HighCs-137, Co-60, Eu-152,154,155 (HPGE) 230.00$ 290.00$ 400.00$

Sr-90 185.00$ 230.00$ 325.00$

Pu-239/240 (AEA) 275.00$ 345.00$ 480.00$

Total USA$ 690.00$ 865.00$ 1,205.00$ Unit Sample Collection Cost 70.00$ 80.00$ 90.00$ AUSCA$ = USC$ + total USA$ 760.00$ 945.00$ 1,295.00$

CS

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Gray Region



No




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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CSAreas to be Investigated

Process

10 10020 8030 7040 60500

Process

About 30 ft of layback toaccomodate 1.5/1 slope

from 20 ft down

29.4 mor 97 ft

11.2 mor 37 ft

50.25 m, 166 ft

32.3 m, 106 ft

Original Trench ProfileArea to be left at -20 ft

Plan View

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Remediation Costs

Trench is a rectangle 106 ft (32.3 m) long and 37 ft (11.2 m) wide

Estimated working zone with trench centered within is 166 ft (50.3 m) by 97 ft (29.4 m)– Area of Trench is 3,922 ft2

– Area of Perimeter Zone is 12,180 ft2 (excluding Trench area)

CS

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Volume of Trench, -5 to -20 ft, is 1,654 yd3

Assume $200/yd3 for Soil Being Disposed – Cost of Excavation $330,800

Volume of Perimeter Zone, 1.5/1 slope from 20 ft depth, is 4,507 yd3 (excluding Trench area), Volume of 5 ft of Overburden is 551 yd3,

$100/yd3 Onsite Use– Cost of Excavation $505,800

Remediation Costs (cont.)CS

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Design Options and Costs for RadionuclidesApproach 1, Based on 2 Strata

CS

Radionuclides Traditional Radiochemistry Methods

DR # Alpha BetaWidth of Gray Region

(UBGR-LBGR)Number* of Samples, n AUSCA$

Total Sampling and Analytical

Cost

1, 2 0.01 0.1 0.2 AL 461 $945 $435,6450.05 0.2 0.2 AL 219 $945 $206,9550.1 0.3 0.2 AL 116 $945 $109,620

1, 2 0.01 0.1 0.5 AL 80 $945 $75,6000.05 0.2 0.5 AL 38 $945 $35,9100.1 0.3 0.5 AL 21 $945 $19,845

*n is from slides #44 and #45

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Approach 1 Based Sampling Design Compare Approach 1 S&A costs versus

remediation costs – Approach 1 S&A costs = $206,955 – Remediation costs = $836,600

• Cost to remediate surface soil around perimeter of trench: $330,800

• Cost to remediate subsurface soil under footprint of trench: $505,800

– Total Analytical + Remediation costs = $1,044,000

CS

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Gray Region



No




If no sample design meets the error tolerances within the budget orconsider Approach 2, 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 dynamic work plans

Manage uncertainty by increasing sample density by using field analytical measurements

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Approach 2 Sampling Design Phase 1: Cs-137 FAM

– Establish cost of FAM– Provide detailed SOP for performance of in-situ

Cs-137 surveys– Choose a grid size/shape– Following completion of excavation, perform NaI

survey for Cs-137• Will produce a representative distribution used to

calculate the number of samples for laboratory verification analysis for the perimeter side-slope soils after excavation

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Phase 1: Cs-137

– Approach 2 will not be applied to the floor of the excavation

• Current RI/FS data for the floor of the excavation in the trench shows site is far below the AL

– RIFS data estimate 2 samples needed• Using LBGR of 80% of AL• Alpha=0.05, Beta = 0.2

– Present this information along with the recommended designs to the decision makers for review and approval

Approach 2 Sampling Design (cont.)CS

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Phase 2: Cs-137

– Evaluate the FAM results • Evaluate distribution for Cs-137 data

– Using the appropriate statistics, • Calculate the mean and standard deviation • Select appropriate alpha, beta, and delta values, and

estimate the resulting n based on the Cs-137 data

– Collect n samples to confirm the FAM data • Using traditional laboratory analysis per SW-846 or

other appropriate methods listed in Step 3

CSApproach 2 Sampling Design (cont.)

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Utilize in-situ MCA NaI survey of Cs-137 Established a 5 ft square grid over the

perimeter side-slope soils after excavation– 5 ft grid chosen based on professional judgement– Approximately 122 nodes (approximately half a

day to perform)– Used a random start and performed 30 sec.

counts at each node of the grid


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Data from similar site– Data showed a non-normal distribution– Calculated mean of 0.28 pCi/g– Calculated standard deviation of 1.02 pCi/g

Choosing alpha=0.05, beta=0.2, delta = 20% of action level– 7 samples needed


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Basis for Above Analysis CostsNaI

2 person and equipment per day $2,000.00# analyses/day 444cost/sample 4.50$

On-Site Analytical Cost Without PCBs

Unit Sample Analysis Cost

NaI In-situ measurement $4.50

Total USA$ $4.50

Unit Sample Collection Cost NA

AUSCA$ = USC$ + total USA$ $4.50

CS

Approach 2 Sampling Design (cont.)

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Method Number of Samples, n AUSCA$

Total Sampling and Analytical Cost

NaI In-situ 122 $4.5 $549Total $549

On-Site Analyses Costs


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CS


Number of Samples, n AUSCA$

Total Sampling and Analytical Cost

Subtotal from NaI 122 4.5 $549Radionuclides Traditional Laboratory Methods 7 $945 $6,615Total Costs On-site and Lab Methods $7,164

Confirmatory Traditional Laboratory Analyses Costs

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Evaluate costs of Approach 2 vs. Approach 1 and remediation costs– Approach 2 S&A costs = $7,164– Approach 1 S&A costs = $206,955– Original budget for S&A = $50,000

– Remediation costs = $836,600• Cost to remediate surface soil around perimeter of trench:

$330,800• Cost to remediate subsurface soil under footprint of

trench: $505,800

CS


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Approach 2 Was SelectedMost Cost-Effective

andBest Uncertainty Management

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Analysis for Radionuclide COCs– Methods to analyze all of the COCs in soil

samples are available– All samples will be shipped and processed as

one batch to decrease QC cost

Approach 2 Based Sampling Design (cont.)

CS

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Design for Radionuclide COCs– For each batch, QC will include, as appropriate

1 LCS, 1 method blank, 1 equipment blank (if field equipment is reused between collection of each sample).

– Step 3 of the DQO lists the QC measurement criteria


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Design for Radionuclide COC Sample analysis– Preservation will not be necessary– QA plan will be written and reviewed by

decision makers before implementation


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Steps 1- 6

Step 7

Optimal Design

Iterative Process

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Gray Region



No




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)

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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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Gray Region



No



Develop alternative sample designsThe output is the most resource-effective design forthe study that is expected toachieve the DQOs.

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Data Quality Assessment Step 1: Review DQOs and Sampling Design

Guidance for Data Quality Assessment,EPA QA/G9, 2000

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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Gray Region



No




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End of Module 9

Thank you

1 of 83 The EPA 7-Step DQO Process Step 7 - Optimize Sample Design 3:30 PM - 4:45 PM (75 minutes) Presenters: Mitzi Miller and Al Robinson Day 2 DQO Training.

Documents

sample design step

sample design slide

steps step

previous step

decisions step

step dqo process step

consistent step

simple random design