Estimation of aircraft operations at airports using nontraditional statistical approaches

The FAA annually invests approximately $3B in small commercial and general aviation airports, with additional infrastructure investments appropriated at the state level. Accurate airport operations counts are critical for fair and efficient allocation of federal and state funds for airport development and improvement. Of the 3,331 airports in the United States that constitute the National Plan of Integrated Airport Systems, however, only slightly more than 500 have either full-or part-time air traffic control facilities and associated personnel who are available to manually register those counts. There are several methods used to count aircraft operations at airports lacking full-time personnel; these are generally based on traditional statistical sampling techniques. Sample data is typically obtained by employing short-term contract staff to deploy acoustic and pneumatic counting devices and to provide human observations. The sample sizes associated with these methods are inherently small due to financial constraints. Small sample sizes create difficulties in terms of estimation of the population mean and variance from the sample parameters because the normality assumption of the distribution of the sample means may not hold. Two modifications to the estimation procedure are suggested here. The first employs a Frequentist model based on sampling without replacement from a discrete, finite, uniformly-distributed population. The second involves a Monte Carlo simulation and associated Bayesian hierarchical model using a Poisson likelihood function, which incorporates the inherent Poisson nature of the underlying arrival process and assumes uncertainties in the registration of operations counts. The latter approach is shown to improve substantially the accuracy of both the traditional, unmodified predictor and the Frequentist modification.