title: A new theoretical framework for modeling respiratory protection based on the beta distribution.
abstract: The problem of modeling respiratory protection is well known and has been dealt with extensively in the literature. Often the efficiency of respiratory protection is quantified in terms of penetration, defined as the proportion of an ambient contaminant concentration that penetrates the respiratory protection equipment. Typically, the penetration modeling framework in the literature is based on the assumption that penetration measurements follow the lognormal distribution. However, the analysis in this study leads to the conclusion that the lognormal assumption is not always valid, making it less adequate for analyzing respiratory protection measurements. This work presents a formulation of the problem from first principles, leading to a stochastic differential equation whose solution is the probability density function of the beta distribution. The data of respiratory protection experiments were reexamined, and indeed the beta distribution was found to provide the data a better fit than the lognormal. We conclude with a suggestion for a new theoretical framework for modeling respiratory protection.
authors.affiliation: Applied Math Department, Israel Institute for Biological Research, PO Box 19, Ness-Ziona, 74100 Israel zivk@iibr.gov.il.
authors.forename: Ziv
authors.initials: Z
authors.lastname: Klausner
authors.affiliation: Applied Math Department, Israel Institute for Biological Research, PO Box 19, Ness-Ziona, 74100 Israel.
authors.forename: Eyal
authors.initials: E
authors.lastname: Fattal
mesh_terms: D000393:Air Pollutants / Q000032:analysis*; D006801:Humans; D019570:Inhalation Exposure; D008962:Models, Theoretical; D016273:Occupational Exposure / Q000032:analysis; D012134:Respiratory Protective Devices
chemical_list: D000393:Air Pollutants
keywords: beta distribution; exposure to airborne contaminants; modeling respiratory protection; respirator performance