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**Day 2 DQO Training Course Module 9 The EPA 7-Step DQO Process**

Step 7 - Optimize Sample Design Presenters: Mitzi Miller and Al Robinson 3:30 PM - 4:45 PM (75 minutes)

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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 7: Optimize Sample Design**

Step 1: State the Problem Step Objective: Identify the most resource-effective data collection and analysis design that satisfies the DQOs specified in the preceding 6 steps Step 2: Identify Decisions Step 3: Identify Inputs Step 4: Specify Boundaries Step 5: Define Decision Rules Step 6: Specify Error Tolerances Step 7: Optimize Sample Design

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs The outputs should provide information on the context of, requirements for, and constraints on data collection design. For each design option, select needed mathematical expressions Gray Region Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region Based on the DQO outputs from Steps 1-6, for each decision rule develop one or more sample designs to be considered and evaluated in Step 7. Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions For each option, pay close attention to the Step 4 outputs defining the population to be represented with the data: Sample collection method Sample mass size Sample particle size Etc. Gray Region Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region Remember: Sampling Uncertainty is decreased when sampling density is increased. Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Statistical Methods for Environmental Pollution Monitoring,**

Types of Designs Simple Random Systematic Grid with random start Geometric Probability or “Hot Spot” Sampling Stratified Random Stratified Simple Random Stratified Systematic Grid with random start Statistical Methods for Environmental Pollution Monitoring, Richard O. Gilbert, 1987

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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**

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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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**Systematic Grid, Random Start (cont.)**

Remember: Start at random location Move in a pre-selected pattern across the site, making measurements at each point

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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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**Geometric Probability or Hot-Spot Sampling (cont.)**

Number of samples is calculated based on probability of finding hot area or geometric probability 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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**Geometric Probability or Hot-Spot Sampling (cont.)**

Limitations Not appropriate for hot spots that are not elliptical 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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**Stratified Systematic Sampling**

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**Begin With the Decision in Mind**

Data field onsite methods traditional laboratory Contaminant Concentrations in the Spatial Distribution of the Population Population Frequency Distribution Correct Equation for n (Statistical Method) , , , Alternative Sample Designs Optimal Sampling Design How Many Samples do I Need? The end

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**Logic to Assess Distribution and Calculate Number of Samples**

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**Sampling Approaches Sampling Approach 1 Sampling Approach 2**

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) Red, yellow, and green are DQA. Yellow is case where results close to AL

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**Approach 2 Sampling & Lab Analyses**

k = 3 k = 3 m = 2 Laboratory

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**Approach 2 Sampling & Lab Analyses (cont.)**

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 Remember: Sampling Uncertainty is decreased when sampling density is increased

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region Select the optimal sample size that satisfies the DQOs for each data collection design option 1. Statistical Method/Sample Size Formula 2. Cost Function Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region Select the optimal sample size that satisfies the DQOs for each data collection design option 1. Statistical Method/Sample Size Formula Define suggested method(s) for testing the statistical hypothesis and define sample size formula(e) that corresponds to the method(s). Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region Select the optimal sample size that satisfies the DQOs for each data collection design option 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 Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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CS Histogram

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CS Histogram (cont.)

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CS Histogram (cont.)

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CS Histogram (cont.)

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**Step 7- Optimize Sample Design**

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 with their corresponding levels of , , and . Select those sample sizes that have acceptable levels of , , and associated with them. Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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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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**Logic to Assess Distribution and Calculate Number of Samples**

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**Normal Approach Reject the ‘Normal’ Approach and**

CS 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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**Logic to Assess Distribution and Calculate Number of Samples**

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**Design Approaches Approach 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 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

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Non-Parametric Test CS For the Perimeter data Cs-137 and Eu-152 have the largest variance For the Trench footprint data, Pu-239/240 and Cs-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

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**Cs-137 in Perimeter Based on Non-Parametric Test**

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**Eu-152 in Perimeter Based on Non-Parametric Test**

CS

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**Pu-239/240 Trench Footprint Non-Parametric Test**

CS

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**Approach 1 Based Sampling Design**

CS 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

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region 2. Cost Function For each selected sample size, develop a cost function that relates the number of samples to the total cost of sampling and analysis. Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region In order to develop the cost function, the aggregate unit cost per sample must be determined. This is the cost of collecting one sample and conducting all the required analyses for a given decision rule. Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region 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 is a unit sample collection cost and a unit sample analytical cost. Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region 1. Add the unit sample collection cost (USC$) and the unit sample analytical cost (USA$) for each method chosen. 2. Sum each of the above values for all of the analytical methods chosen to get the aggregate unit sample collection and analysis cost (AUSCA$). Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Aggregate Unit Sampling and Analysis Cost**

AUSCA$ = USC$ + USA$ i=1 Where (here): USC$ = Unit Sample Collection Cost USA$ = Unit Sample Analysis Cost AUSCA$ = Aggregate Unit Sample Collection and Analysis Cost n = Number of analytical methods planned

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**Total Sampling and Analysis Cost**

CS

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**Step 7- Optimize Sample Design**

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. Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region Select the optimal sample size that satisfies the DQOs for each data collection design option From the table, select the optimal sample size that meets the project budget and uncertainty requirements. Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Areas to be Investigated**

CS Areas to be Investigated

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Remediation Costs CS 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)

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**Remediation Costs (cont.)**

CS 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

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CS Design Options and Costs for Radionuclides Approach 1, Based on 2 Strata

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**Approach 1 Based Sampling Design**

CS 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

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent If no sample design meets the error tolerances within the budget or consider Approach 2, relax one or more of the constraints or request more funding, etc. Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Design - Approaches Approach 2:**

Dynamic Work Plan (DWP) & Field Analytical Methods (FAMs) Manage uncertainty by increasing sample density by using field analytical measurements 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

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**Approach 2 Sampling Design**

CS 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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**Approach 2 Sampling Design (cont.)**

CS 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

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**Approach 2 Sampling Design (cont.)**

CS 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

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**Approach 2 Sampling Design (cont.)**

CS 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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**Approach 2 Sampling Design (cont.)**

CS 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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**Approach 2 Sampling Design (cont.)**

CS Approach 2 Sampling Design (cont.)

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**Approach 2 Sampling Design (cont.)**

CS

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**Approach 2 Sampling Design (cont.)**

CS Approach 2 Sampling Design (cont.)

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**Approach 2 Sampling Design (cont.)**

CS Approach 2 Sampling Design (cont.) 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

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**Approach 2 Was Selected Most Cost-Effective and Best Uncertainty Management**

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**Approach 2 Based Sampling Design (cont.)**

CS 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

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**Approach 2 Based Sampling Design (cont.)**

CS 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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**Approach 2 Based Sampling Design (cont.)**

CS 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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Iterative Process Steps 1- 6 Step 7 Optimal Design

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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent 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) Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints 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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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances The output is the most resource-effective design for the study that is expected to achieve the DQOs. Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

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**Data Quality Assessment**

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

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Summary To succeed in a systematic planning process for environmental decision making, you need Statistical Support: One or more qualified statisticians, experienced in environmental data collection designs and statistical data quality assessments of such designs.

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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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**Step 7- Optimize Sample Design**

Information IN Actions Information OUT From Previous Step To Next Step Review DQO outputs from Steps 1-6 to be sure they are internally consistent Decision Error Tolerances Develop alternative sample designs For each design option, select needed mathematical expressions Gray Region Select the optimal sample size that satisfies the DQOs for each data collection design option Check if number of samples exceeds project resource constraints Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. No Yes

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End of Module 9 Thank you

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