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## The EPA 7-Step DQO Process

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**Day 2 DQO Training CourseModule 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)**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**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**Step 7- Optimize Sample Design**Go back to Steps 1- 6 and revisit decisions. Optimal Sample Design No Yes Information INActionsInformation 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**Step 7- Optimize Sample Design**Go back to Steps 1- 6 and revisit decisions. Optimal Sample Design No Yes Information INActionsInformation 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**Step 7- Optimize Sample Design**Go back to Steps 1- 6 and revisit decisions. Optimal Sample Design No Yes Information INActionsInformation 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**Step 7- Optimize Sample Design**Go back to Steps 1- 6 and revisit decisions. Optimal Sample Design No Yes Information INActionsInformation 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**Step 7- Optimize Sample Design**Go back to Steps 1- 6 and revisit decisions. Optimal Sample Design No Yes Information INActionsInformation 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**Types of Designs**• Systematic Grid with random start • Geometric Probability or “Hot Spot” Sampling • Stratified Random • Stratified Simple Random • Stratified Systematic Grid with random start • Simple Random Statistical Methods for Environmental Pollution Monitoring, Richard O. Gilbert, 1987**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**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**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**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**Systematic Grid, Random Start (cont.)**Remember: Start at random location Move in a pre-selected pattern across the site, making measurements at each point**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**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**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**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**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**CS**Stratified Systematic Sampling**Data**• field • onsite methods • traditional laboratory Begin With the Decision in Mind 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**Logic to Assess Distribution and Calculate Number of Samples****Sampling Approaches**• Sampling Approach 1 • Traditional fixed laboratory analyses • Sampling Approach 2 • Field analytical measurements • Computer simulations • Dynamic work plan**Sampling Approach 2**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) 1. Perform field analytical (using driver COPCs)**Approach 2 Sampling & Lab Analyses**k = 3 k = 3 m = 2 Laboratory**Approach 2 Sampling & Lab Analyses (cont.)**• 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 • n = m * k Remember: Sampling Uncertainty is decreased when sampling density is increased**Step 7- Optimize Sample Design**Go back to Steps 1- 6 and revisit decisions. Optimal Sample Design No Yes Information INActionsInformation 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**Step 7- Optimize Sample Design**Go back to Steps 1- 6 and revisit decisions. Optimal Sample Design No Yes Information INActionsInformation 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**Step 7- Optimize Sample Design**Go back to Steps 1- 6 and revisit decisions. Optimal Sample Design No Yes Information INActionsInformation 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**CS**Histogram**CS**Histogram (cont.)**CS**Histogram (cont.)**CS**Histogram (cont.)**Step 7- Optimize Sample Design**Go back to Steps 1- 6 and revisit decisions. Optimal Sample Design No Yes 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 INActionsInformation 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**3 Approaches for Calculating n**• Skewed approach • FAM/DWP approach • Badly skewed or for all distributions use computer simulation approach • e.g., Monte Carlo • Normal approach**Logic to Assess Distribution and Calculate Number of Samples****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**Logic to Assess Distribution and Calculate Number of Samples****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**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**CS**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**Cs-137 in Perimeter Based on Non-Parametric Test**CS**Eu-152 in Perimeter Based on Non-Parametric Test**CS**Pu-239/240 Trench Footprint Non-Parametric Test**CS**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**Step 7- Optimize Sample Design**Go back to Steps 1- 6 and revisit decisions. Optimal Sample Design No Yes Information INActionsInformation 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**Step 7- Optimize Sample Design**Go back to Steps 1- 6 and revisit decisions. Optimal Sample Design No Yes Information INActionsInformation 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**Step 7- Optimize Sample Design**Go back to Steps 1- 6 and revisit decisions. Optimal Sample Design No Yes Information INActionsInformation 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 isa unit sample collection cost and a unit sampleanalytical 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