Multicomponent error model for mass measurement based size fractionating aerosol samplers

A mass based size fractionating aerosol sampling device such as an impactor has a number of experimental measurement errors that can affect the size distribution determination. These errors are not necessarily additive, such as weighing errors, multiplicative such as airflow errors, or a power function such as bounce. In general, the cumulative errors are a combination of different relational scales and they are likely to have different functional forms across the full range of measurements. A complete theory of errors must consider a diverse set of functional relationships between mass, flow, size distribution, and other non-linear parameters such as entry losses and bounce to estimate the error bounds for a measured size distribution and aerosol concentration. In addition, aerosol exposure measurements are single sample events. The theoretical multi-compartment error model is an extension of the Rocke and Lorenzato model of measurement errors in analytical chemistry and it includes generalized parameters for all empirically meaningful transformations. Although the general theory is complicated, heuristic reductions can be made to reduce the estimation process to a manageable size. The numerical examples of error analysis of a hypothetical impactor show that the measured distribution related error bound estimation process is not difficult to perform.