The workplace protection factor (WPF) for a given respirator wearer shows substantial variability from wearing to wearing; this variability is commonly assumed to be lognormal in nature. Further, when multiple WPFs are measured for each of multiple wearers, the aggregated WPFs appear to follow a lognormal distribution. However, the analysis typically applied to WPF data does not apportion variability within versus between wearers. We present an analytical framework based on a normal random effects model of log-transformed penetration P values (P = 1/WPF). Data from seven studies of negative-pressure air-purifying half-mask respirators, and from two studies of hemlet-and-visor type powered air-purifying respirators were analyzed by the method of maximum likelihood in the context of the Model. More specifically, analyses were performed for long-transformed P values and for logit-transformed P values. Parameter estimates included within-wearer and between-wearer variance components. In general, the within-wearer component dominated the between-wearer component. We also propose a method for establishing an assigned protection factor; APF, that properly accounts for these variance components. Our method provides an APF satisfying two criteria: (1) for a given wearer, an acceptable WPF distribution has no more than 5% of WPFs below the APF value; and (2)for a wearer population, no more than 5% of wearers have unacceptable WPF distributions. The method incorporates an one-sided confidence limit to account for sampling variability. Alternative confidence limits were computed based on large sample variance estimates of random effects model parameters versus a bootstrap method. In general, there was good agreement between the APF values based on log-transformed versus logit-transformed P data, and between APF values based on the large sample variance estimates versus the bootstrap method. Based on large sample variance estimates for the logit-transformed P data from the seven half-mask studies, estimated APFs ranged from 1.4 to 250, with 5/7 studies yielding an APFless than or equal to 5.3. Given these results and related considerations, we recommend that the current half mask APF be reduced from 10 to 5.
