A.4.4.2 Results for HMX (M2-B)

For the HMX (10 m × 10 m DU) simulations, Tables A-8 through A-10 show the summaries from the evaluated simulations. The coverage, bias, number of increments, and number of ISs are used to create the coverage plot shown in Figure A-14. Figure A-15 shows the panel of t-UCL histograms for all 40 sampling patterns evaluated on the HMX 10 m × 10 m DU.

Table A-8. Discrete summary: HMX decision unit (M2-B)

Grid sampling type Number of increments Chebyshev UCL coverage t-UCL coverage Chebyshev RPD above mean t RPD above mean Chebyshev RPD below mean t RPD below mean
Random 9 97.65 85.55 140.04 69.15 13.56 15.08
Systematic 9 97.40 83.70 138.07 69.42 11.88 15.48
Random 16 99.05 87.00 110.39 51.50 6.36 11.33
Systematic 16 98.75 86.40 108.63 50.69 5.54 13.01
Random 30 99.55 87.45 83.39 37.49 4.61 8.02
Systematic 30 100.00 90.30 82.82 35.91   6.67
Random 100 100.00 92.20 48.01 19.73   4.15
Systematic 100 100.00 92.80 47.63 19.61   4.64

Table A-9. Standard ISM summary: HMX decision unit (M2-B)

Number of ISs Number of increments Chebyshev UCL coverage t-UCL coverage Chebyshev RPD above mean t RPD above mean Chebyshev RPD below mean t RPD below mean
2 16 90.70 93.60 69.45 94.49 9.84 10.13
3 16 96.50 92.20 59.36 41.10 8.33 7.33
4 16 97.55 90.10 52.77 30.81 5.48 6.15
5 16 98.85 91.75 47.53 24.89 2.97 4.66
2 30 90.20 92.75 50.93 68.96 6.64 6.10
3 30 96.15 92.85 40.70 27.96 5.22 5.69
4 30 98.20 94.00 36.95 20.86 3.59 4.59
5 30 98.75 92.35 33.07 17.44 3.89 3.90
2 49 90.30 92.85 39.87 54.62 6.10 6.01
3 49 96.40 92.35 34.71 23.86 4.60 4.47
4 49 97.65 91.90 29.76 16.71 2.97 3.68
5 49 98.95 92.50 26.96 13.85 2.55 3.56
2 100 91.40 93.30 28.15 38.71 4.67 4.69
3 100 96.95 93.60 22.86 15.56 3.77 3.41
4 100 98.65 94.15 20.29 11.39 1.55 2.27
5 100 99.10 94.05 18.50 9.47 2.10 2.24

Table A-10. Grouped ISM summary: HMX decision unit (M2-B)

Number of ISs Number of increments Chebyshev UCL coverage t-UCL coverage Chebyshev RPD above mean t RPD above mean Chebyshev RPD below mean t RPD below mean
2 16 90.85 92.85 70.55 96.55 9.55 8.54
3 16 96.95 93.05 61.46 42.15 6.42 6.05
4 16 99.80 98.95 89.73 47.36 2.40 5.87
5 16 99.15 93.65 52.03 26.73 5.65 5.19
2 30 91.20 94.00 50.99 69.54 6.84 7.05
3 30 98.55 95.95 47.58 32.33 2.99 3.93
4 30 100.00 99.75 87.32 46.18   3.89
5 30 99.45 95.25 38.94 19.40 4.19 3.44
2 49 92.05 95.35 38.57 52.55 5.02 5.78
3 49 98.70 96.75 38.65 26.05 3.67 3.43
4 49 100.00 100.00 83.60 43.78    
5 49 99.90 97.90 33.76 16.12 2.76 2.63
2 100 93.50 95.00 29.49 40.74 5.66 5.22
3 100 99.20 97.15 27.85 19.02 2.88 2.07
4 100 100.00 100.00 81.47 42.85    
5 100 99.75 98.95 26.67 12.83 1.97 2.38

Figure A-14. Plot of the coverage statistics for each of the simulated sampling patterns as applied to the HMX decision unit. (Note: The different sampling patterns are displayed within the plot as well as UCL type).

Figure A-14. Plot of the coverage statistics for each of the simulated sampling patterns as applied to the HMX decision unit.
(Note: The different sampling patterns are displayed within the plot as well as UCL type).

Figure A-15. Panel of histograms of the distribution of t-UCL values for the 2,000 simulations.  (Note: The red line identifies the true mean. The y-axis identifies the percent of 2000 simulations in each bin  and is distorted to show the percentage in the low count bins.)

Figure A-15. Panel of histograms of the distribution of t-UCL values for the 2,000 simulations.
(Note: The red line identifies the true mean. The y-axis identifies the percent of 2000 simulations in each bin
and is distorted to show the percentage in the low count bins.)

This DU has some strong spatial heterogeneity, but the distribution of concentration values is not as skewed or heavily right-tailed with a CV of 1.1. The mean is 0.132 with a standard deviation of 0.146. When three or more replicates are used, the coverage results for the grouped IS patterns were near or above the designed criteria of 95% for all but the IS composed of 16 increments. The standard IS performed reasonably well for the 100-increment standard IS design.

Specific observations from these simulations are noted below and support the consensus points listed in Table A-1:

  • The mean concentration estimates for grouped ISM and standard ISM sampling have the same expectation and distribution (see Figure A-13).
  • The grouped ISM methods have equivalent or greater coverage than standard IS when the same number of ISs and increments are used.
  • The RPD of the UCLs for grouped ISM is generally higher than that of standard IS.
  • Grouped IS, by its definition, provides an improved spatial picture of the concentrations within the site.
  • For these maps, the t-UCL may be expected to yield adequate coverage with 100-increment ISM designs.
  • As few as 30 increments can be used for DUs with less severe heterogeneity and still maintain coverage with a t-UCL.
  • Systematic grid, random grid, or simple random sampling all generally give the same results in terms of coverage, and the use of one or the other can be selected for ease of application (see Figure A-10).
  • In general, the Chebyshev method may be necessary to attain adequate coverage depending on the severity of the heterogeneity.
  • The improvements in coverage are the more pronounced by increasing the number of increments (e.g., 50–100) instead of the number of replicates (e.g., 3–5).