Samples from Elevated Surfaces of a Smelter
The Department of Energy (DOE) Chronic Beryllium Disease Prevention Program is concerned with monitoring objects (e.g., equipment, buildings) for beryllium contamination and workers for exposure to beryllium in the workplace.
The SESdata is the results of a survey to evaluate possible beryllium contamination based on 31 surface wipe samples from elevated surfaces (SES) of a smelter at a DOE facility. For equipment that is being evaluated for release to the public, or for non beryllium use, the DOE has established a release limit for removable beryllium contamination of 0.2 μ g/100cm^2.
A data frame with 31 observations on the following 2 variables
beryllium μ g/100cm^2
0 if non-detect; 1 if detected
Statistics of interest are the exceedance fraction and the 95th percentile. The exceedance fraction is an estimate of the percentage of surface area that is expected to exceed the release limit Lp = 0.2 μ g/100cm^2 with p = 0.95. Both the point estimate and the UCL for F exceed Fo = 100 (1-p) = 5%, indicating that the equipment is not acceptable. In fact, at the 95 confidence level at least 19.5% of the surface area exceeds the release limit.
A more detailed description and analysis of this data is given as Example 1 in Section 4 of Frome and Wambach (2005)
Frome, E. L. and Wambach, P. F. (2005), "Statistical Methods and Software for the Analysis of Occupational Exposure Data with Non-Detectable Values," ORNL/TM-2005/52,Oak Ridge National Laboratory, Oak Ridge, TN 37830. Available at: http://www.csm.ornl.gov/esh/aoed/ORNLTM2005-52.pdf
1 2 3 4 5 6 7 8 9
data(SESdata) mle.ses <- unlist(lnorm.ml(SESdata)) # ML for SESdata print(mle.ses[1:4]) # ML estimates of parameters print(mle.ses[5:8]) # Standard errors of ML estimates # Next line produces a lognormal q-q plot with ML line qq.lnorm(plend(SESdata),mle.ses,mle.ses) title("Lognormal Q-Q plot For SESdata Example 1 in ORNLTM2005-52") unlist(efraction.ml(SESdata,gam=0.95,L=0.2)) # MLE of exceedance fraction and CLs unlist(percentile.ml(SESdata,p=0.95,gam=0.95)) # MLE of 95 percentile and CLs
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