Sampling duration calculations

Routine air quality monitoring produces filter samples that, when analyzed, yield the total amount of the aerosol present in the volume of air drawn by the pump in the monitoring device during the given sampling period. From this we obtain an average concentration of the aerosol for the given duration. The samples are therefore really aggregate samples. A natural question then is "what is the effect of the duration of aggregation on the accuracy and precision of the estimate of the quantity of interest?" The answer depends on a number of factors, such as the quantity that is being estimated: a mean, or an extreme value, or some other quantity; the nature of the measurement error--additive versus multiplicative; the costs of laboratory analyses, and so on. In this paper, we investigate these issues when the interest is in estimating the mean concentration of a specified aerosol species over a fixed time period. In particular, we propose a method for determining a sampling duration that will yield the "best estimate" of the mean concentration for a given cost whenever appropriate statistical assumptions hold.