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Annals of Occupational Hygiene Advance Access originally published online on May 22, 2007
Annals of Occupational Hygiene 2007 51(4):397-406; doi:10.1093/annhyg/mem013
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© The Author 2007. Published by Oxford University Press on behalf of the British Occupational Hygiene Society

Upper Limits for Exceedance Probabilities Under the One-Way Random Effects Model

K KRISHNAMOORTHY1,*, THOMAS MATHEW2 and GURUMURTHY RAMACHANDRAN3

1 Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA
2 Department of Mathematics and Statistics, University of Maryland, 1000 Hilltop Circle, Baltimore, MD 21250, USA
3 Division of Environmental Health Sciences, School of Public health, University of Minnesota, MMC 807, 420 Delaware Street SE, Minneapolis, MN 55455, USA

* Author to whom correspondence should be addressed. e-mail: krishna{at}louisiana.edu

In this article, we propose statistical methods for setting upper limits on (i) the probability that the mean exposure of an individual worker exceeds the occupational exposure limit (OEL) and (ii) the probability that the exposure of a worker exceeds the OEL. The proposed method for (i) is obtained using the generalized variable approach, and the one for (ii) is based on an approximate method for constructing one-sided tolerance limits in the one-way random effects model. Even though tolerance limits can be used to assess the proportion of exposure measurements exceeding the OEL, the upper limits on these probabilities are more informative than tolerance limits. The methods are conceptually as well as computationally simple. Two data sets involving industrial exposure data are used to illustrate the methods.

Keywords: between- and within-worker variability • generalized confidence interval • generalized P-value • tolerance interval

Received August 2, 2006; in final form February 19, 2007


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