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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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Presentation on theme: "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."— Presentation transcript:

1 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 Course Module 9

2 2 of 83 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

3 3 of 83 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

4 4 of 83 Information INActions 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

5 5 of 83 Information INActions 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 The outputs should provide information on the context of, requirements for, and constraints on data collection design.

6 6 of 83 Information INActions 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 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.

7 7 of 83 Information INActions 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 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.

8 8 of 83 Information INActions 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 Remember: Sampling Uncertainty is decreased when sampling density is increased.

9 9 of 83 Types of Designs n Simple Random Statistical Methods for Environmental Pollution Monitoring, Richard O. Gilbert, 1987 n Systematic Grid with random start n Geometric Probability or Hot Spot Sampling n Stratified Random –Stratified Simple Random –Stratified Systematic Grid with random start

10 10 of 83 Simple Random n Definition- choice of sampling location or time is random n Assumptions –Every portion of the population has equal chance of being sampled n Limitation-may not cover area

11 11 of 83 Simple Random n 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

12 12 of 83 Example - Simple Random Using Coordinates

13 13 of 83 Systematic Grid, Random Start n Definition-taking measurements at locations or times according to spatial or temporal pattern (e.g., equidistant intervals along a line or grid pattern) n Assumptions –Good for estimating means, totals and patterns of contamination –Improved coverage of area

14 14 of 83 Systematic Grid, Random Start (cont.) n Limitations –Biased results can occur if assumed pattern of contamination does not match the actual pattern of contamination –Inaccurate if have serial correlation

15 15 of 83 Remember: Start at random location Move in a pre-selected pattern across the site, making measurements at each point Systematic Grid, Random Start (cont.)

16 16 of 83 Geometric Probability or Hot- Spot Sampling n Uses squares, triangles, or rectangle to determine whether hot spots exist n Finds hot spot, but may not estimate the mean with adequate confidence

17 17 of 83 n Number of samples is calculated based on probability of finding hot area or geometric probability Geometric Probability or Hot- Spot Sampling (cont.) n 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

18 18 of 83 n 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

19 19 of 83 Example Grid for Hot-Spot Sampling

20 20 of 83 Hot-Spot Sampling n 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

21 21 of 83 Stratified Random n Definition-divide population into strata and collect samples in each strata randomly n Attributes –Provides excellent coverage of area –Need process knowledge to create strata –Yields more precise estimate of mean –Typically more efficient then simple random n Limitations –Need process knowledge

22 22 of 83 CS Stratified Systematic Sampling

23 23 of 83 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

24 24 of 83 Logic to Assess Distribution and Calculate Number of Samples

25 25 of 83 Sampling Approaches n Sampling Approach 1 –Traditional fixed laboratory analyses n Sampling Approach 2 –Field analytical measurements –Computer simulations –Dynamic work plan

26 26 of 83 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)

27 27 of 83 Approach 2 Sampling & Lab Analyses k = 3 m = 2 Laboratory

28 28 of 83 Approach 2 Sampling & Lab Analyses (cont.) n n = m * k Remember: Sampling Uncertainty is decreased when sampling density is increased n Select k of specified Mass/diameter 3 –FE² 22.5 * d³ / M (to control sampling error) n Prepare m multi-increment samples for lab analysis n Perform lab analyses on m samples

29 29 of 83 Information INActions 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 1. Statistical Method/Sample Size Formula 2. Cost Function

30 30 of 83 Information INActions 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 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).

31 31 of 83 Information INActions 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 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

32 32 of 83 CS Histogram

33 33 of 83 CS Histogram (cont.)

34 34 of 83 CS Histogram (cont.)

35 35 of 83 CS Histogram (cont.)

36 36 of 83 Information INActions 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 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.

37 37 of 83 3 Approaches for Calculating n n Normal approach n Skewed approach n FAM/DWP approach –Badly skewed or for all distributions use computer simulation approach e.g., Monte Carlo

38 38 of 83 Logic to Assess Distribution and Calculate Number of Samples

39 39 of 83 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 SkewedApproach CS

40 40 of 83 Logic to Assess Distribution and Calculate Number of Samples

41 41 of 83 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

42 42 of 83 Cs-137, Eu-152 n Because there were multiple COPCs with varied standard deviations, action limits and LBGRs, separate tables for varying alpha, beta, and (LBGR) delta were calculated n 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

43 43 of 83 Non-Parametric Test n For the Perimeter data Cs-137 and Eu-152 have the largest variance n For the Trench footprint data, Pu-239/240 and Cs-137 are the only two COCs with action levels n 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

44 44 of 83 Cs-137 in Perimeter Based on Non-Parametric Test CS

45 45 of 83 CS Eu-152 in Perimeter Based on Non-Parametric Test

46 46 of 83 Pu-239/240 Trench Footprint Non-Parametric Test CS

47 47 of 83 Approach 1 Based Sampling Design n 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

48 48 of 83 Information INActions 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 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.

49 49 of 83 Information INActions 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 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.

50 50 of 83 Information INActions 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 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.

51 51 of 83 Information INActions 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 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$).

52 52 of 83 AUSCA$ = USC$ + USA$ 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 Aggregate Unit Sampling and Analysis Cost i=1 n

53 53 of 83 Total Sampling and Analysis Cost CS

54 54 of 83 Information INActions 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 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 budget and uncertainty requirements.

55 55 of 83 CS Areas to be Investigated

56 56 of 83 Remediation Costs n Trench is a rectangle 106 ft (32.3 m) long and 37 ft (11.2 m) wide n 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 ft 2 –Area of Perimeter Zone is 12,180 ft 2 (excluding Trench area) CS

57 57 of 83 n Volume of Trench, -5 to -20 ft, is 1,654 yd 3 Assume $200/yd 3 for Soil Being Disposed –Cost of Excavation $330,800 n Volume of Perimeter Zone, 1.5/1 slope from 20 ft depth, is 4,507 yd 3 (excluding Trench area), Volume of 5 ft of Overburden is 551 yd 3, $100/yd 3 Onsite Use –Cost of Excavation $505,800 Remediation Costs (cont.) CS

58 58 of 83 Design Options and Costs for Radionuclides Approach 1, Based on 2 Strata CS

59 59 of 83 Approach 1 Based Sampling Design n 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

60 60 of 83 Information INActions 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 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.

61 61 of 83 Design - Approaches Approach 2: Dynamic Work Plan (DWP) & Field Analytical Methods (FAMs) n 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 n Manage uncertainty by increasing sample density by using field analytical measurements

62 62 of 83 Approach 2 Sampling Design n 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 CS

63 63 of 83 n 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

64 64 of 83 n 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 CS Approach 2 Sampling Design (cont.)

65 65 of 83 n Utilize in-situ MCA NaI survey of Cs-137 n 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 CS Approach 2 Sampling Design (cont.)

66 66 of 83 n 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 n Choosing alpha=0.05, beta=0.2, delta = 20% of action level –7 samples needed CS Approach 2 Sampling Design (cont.)

67 67 of 83 CS Approach 2 Sampling Design (cont.)

68 68 of 83 CS Approach 2 Sampling Design (cont.)

69 69 of 83 CS Approach 2 Sampling Design (cont.)

70 70 of 83 n 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 Approach 2 Sampling Design (cont.)

71 71 of 83 Approach 2 Was Selected Most Cost-Effective and Best Uncertainty Management

72 72 of 83 n 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

73 73 of 83 n 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 Approach 2 Based Sampling Design (cont.) CS

74 74 of 83 n Design for Radionuclide COC Sample analysis –Preservation will not be necessary –QA plan will be written and reviewed by decision makers before implementation Approach 2 Based Sampling Design (cont.) CS

75 75 of 83 Steps 1- 6 Step 7 Optimal Design Iterative Process

76 76 of 83 Information INActions 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 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)

77 77 of 83 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.

78 78 of 83 Information INActions 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 The output is the most resource-effective design for the study that is expected to achieve the DQOs.

79 79 of 83 Data Quality Assessment n Step 1: Review DQOs and Sampling Design Guidance for Data Quality Assessment, EPA QA/G9, 2000 n Step 2: Conduct Preliminary Data Review n Step 3: Select the Statistical Test n Step 4: Verify the Assumptions of the Test n Step 5: Draw Conclusions From the Data

80 80 of 83 need Statistical Support: To succeed in a systematic planning process for environmental decision making, you need Statistical Support: qualified statisticians environmental data collection designsstatistical data quality assessments One or more qualified statisticians, experienced in environmental data collection designs and statistical data quality assessments of such designs. Summary

81 81 of 83 Summary (cont.) n Going through the 7-Step DQO Process will ensure a defensible and cost effective sampling program n 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

82 82 of 83 Information INActions 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

83 83 of 83 End of Module 9 Thank you


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