Environmental health exposures to airborne chemicals often originate fromchemical mixtures. Environmental health professionals may be interested inassessing exposure to one or more of the chemicals in these mixtures, but often,exposure measurement data are not available, either because measurementswere not collected/assessed for all exposure scenarios of interest or because someof themeasurementswere below the analytical methods' limits of detection (i.e.,censored). In some cases, based on chemical laws, two or more componentsmay have linear relationships with one another, whether in single or multiplemixtures. Although bivariate analyses can be used if the correlation is high, correlationsare often low. To serve this need, this paper develops a multivariateframework for assessing exposure using relationships of the chemicals presentin these mixtures. This framework accounts for censored measurements in allchemicals, allowing us to develop unbiased exposure estimates.We assessed ourmodel's performance against simpler models at a variety of censoring levels andassessed our model's 95% coverage.We applied our model to assess vapor exposurefrom measurements of three chemicals in crude oil taken on the OceanIntervention III during the Deepwater Horizon oil spill response and cleanup.