“Quasi Nonparametric” Upper Tolerance Limits for Occupational Exposure Evaluations

Abstract

Upper tolerance limits (UTLs) are often used in comparing exposure data sets with an occupational exposure limit (OEL) or other regulatory criterion (RC): if the 95%-95% UTL does not exceed the OEL, one is 95% confident that at most 5% of exposures exceed the OEL, and the comparison “passes.” The largest of 59 observations is a nonparametric (distribution-free) 95%-95% UTL (NPUTL); the chance that this largest value equals or exceeds the actual 95th percentile is at least 95%, regardless of the underlying data distribution. That many observations may seem excessive in clean environments or small studies, though, and one would like to “pass” using UTLs based on fewer observations sufficiently far below the OEL or RC.

“Quasi-nonparametric” UTLs (QNP UTLs) accomplish this. QNP UTLs assign a “pass” so long as one has “59 [values] less than the RC” (the NPUTL itself), “30 less than 1/2 [of the RC],” “21 less than 1/3,” and on down to “8 less than 1/10,” the last matching a rule-of-thumb given in 2006 American Industrial Hygiene Association (AIHA) guidance. They are derived using the conservative, experience-based assumption that the data distribution is lognormal with log-scale standard deviation σ at most 2.0 (geometric standard deviation at most 7.39). Although based on this assumption, their statistical performance is reasonably unaffected or conservative when data come from other distributions often assumed for contaminant concentrations; moreover, their performance is insensitive to analytical variation. This conservative robustness merits the description “quasi-nonparametric.” QNP UTLs are very easy to use. Reporting Limit (RL) issues do not arise. QNP UTLs reduce the numbers of observations needed to support conservative risk management decisions when sampling from compliant working conditions.

Keywords:

• censored data
• exposure limits
• nondetects
• reporting limits
• uncensored data
• upper tolerance limits

ACKNOWLEDGMENTS

QNP UTLs were originally developed by EnviroStat under Subcontract 58459 with National Security Technologies LLC (NSTec), under Contract DE-AC52–06NA25946 with the US DOE at the Nevada National Security Site (NNSA) (formerly the Nevada Test Site). These efforts were encouraged by Danny Field, now with US DOE/NNSA, and Tom Gran of NSTec. Subsequent refinements were supported under Contract 433-46–004 with Mission Support Alliance LLC, a contractor with the US DOE at the Hanford Site. Careful reviews of previous drafts of this article by Karl Agee of Fowler LLC, supporting US DOE at the Hanford Site, have led to a vastly improved exposition of the material and are greatly appreciated.