Upper limits for exceedance probabilities under the one-way random effects model

K. Krishnamoorthy, Thomas Mathew, Gurumurthy Ramachandran

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)397-406
Number of pages10
JournalAnnals of Occupational Hygiene
Issue number4
StatePublished - Jun 2007

Bibliographical note

Funding Information:
Acknowledgements—This research was supported by grant R01-0H03628-01A1 from the National Institute of Occupational Safety and Health (NIOSH). The authors are thankful to Ms. Yanping Xia for providing computational help and SAS code; they are also grateful to two reviewers and assistant editor David Bartley for providing valuable comments and suggestions.


  • Between- and within-worker variability
  • Generalized P-value
  • Generalized confidence interval
  • Tolerance interval


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