Root Sum of Squares (RSS) Uncertainty

ERDC TN-DOER-R5

September 2004

For example,

2,3,7,8-TCDD TBP ME = 1.350 * 62.7/100 = 0.847

(9)

Propagated error for each TBP estimation (PEi) is calculated for each of the TBP input

parameters separately and then combined, adaptating the method of Campbell (1982) for

multiple input values.

1. The mean and the lower and upper 95-percent confidence limits (CLLi and CLUi) of each

of the TBP input parameters are used to first calculate TBP at each limit (TBPLi and TBPUi) by

substituting in Equation 1 each input parameter CLLi and CLUi for that parameter and the means

of all other parameters. For 2,3,7,8-TCDD these are:

Parameter

Mean

CLLi

CLUi

TBPLi

TBPUi

BSAF

0.433

0.297

84.5

1.663

-0.061

0.927

-0.191

2.891

0.474

0.091

3.0

2.353

0.261

0.687

0.744

1.957

fOC

0.005

0.002

3.0

2.353

0.001

0.009

5.550

0.769

0.033

0.004

16.0

1.746

0.027

0.039

1.093

1.608

2. Propagated error for each input parameter is calculated as:

PEi = ( (TBPUi TBPLi )2 / 4 )

(10)

3. Overall propagated error is:

PE = ( Σ PEi2 )

(11)

For the 2,3,7,8-TCDD example, the results are:

Parameter

PEi

BSAF

1.5407

2.374

0.6064

0.368

fOC

2.3909

5.716

0.257

0.066

Overall Propagated Error PE

2.920

4. Total error of TBP for each PCDD/F congener or homologue group is:

TE = ( ME2 + PE2 )

(12)

For the 2,3,7,8-TCDD example,

TE = (0.8472 + 2.9202) = 3.040

(13)

The range of uncertainty using the RSS method for the example is 2,3,7,8-TCDD TBP " TE =

1.35 " 3.04, or between < 0.0 and 4.390 pg g-1 (Table 5). The mean measured tissue