Exceedance Fraction Adjustments with Non-exposure Days

I have read, I believe it’s a Rappaport study, that if you can demonstrate that the exceedance fraction is less than 5%, then the long term average exposure will be less than half of the exposure limit. This is the basis of the 5% exceedance criteria.

With that in mind, if we have an exposure that is occurring once per week, and the exceedance fraction upper estimate is say 25%, can we divide by 5 and still meet the goals of the 5% exceedance fraction criteria?

Because if the exceedance fraction 1 out of 5 days, is 25%, then the long term average exposure on those days may be much higher than half the OEL, but when averaged out with non-exposure days, mathematically it seems the long term average would still be below half the exposure limit.

It seems whether or not we can apply this exceedance fraction division depends on the toxicology of the compound were measuring? Acute vs chronic effects.

I should quote the actual study, its a great read.

S. M. Rappaport , S. Selvin & S. A. Roach (1988) A Strategy for Assessing
Exposures with Reference to Multiple Limits, Applied Industrial Hygiene, 3:11, 310-315, DOI:

Hello Mike,

From what I recall, the paper adressed the fact that the AM of the lognormal distribution of exposures should not depend on measuring time : so the AM of 15 min. measurements should be the same as the AM of 8-hours measurements.

They use that demonstration to say : if the AM of the 8-h is low enough, then this also entails information about exceedance of short term measurements ; hence, for a certain GSD, if the AM is <0.5OEL, then the exceedance of short term exposure will be low.

This was a way of supporting the use of the AM as a risk metric, as beeing useful also for short term exposures.

There was some debate in the late 90s to 2000s about the use of AM compared to OEL instead of P95 for chronic toxicants. My take on the result is that because OELs are so rarely properly described as long term average cumulative burden threshold, most organizations ended up prefering P95 ( AM just below the OEL can correspond to 30% exceedance…so P95 felt more precautionnary).

Hi Jerome,

Thanks so much, that was my takeaway from the study as well, and the application of AM and P95.