Monitoring multivariate aviation safety data by data depth: control charts and threshold systems

Aviation safety analysis is increasingly needed in regulating air traffic and safety, in light of the rapid growth in air traffic density. With the recent advances in computer technology, large amounts of multivariate aviation safety data are now routinely collected in databases. Many existing analysis methods prescribed in those databases and corresponding safety indicators are based on classical statistical analysis, and their applicability is considerably restricted by the requirement of normality. An alternative nonparametric methodology based on data depth is pursued in this paper. For a given multivariate sample, a data depth can be used to measure their depth or outlyingness with respect to the underlying distribution. The measure of depth leads to a center-outward ordering of the sample points. Derived from this ordering, Liu (1995) introduced a simple, yet effective, control chart for monitoring multivariate observations. The control chart is combined here with properly chosen false alarm rates to develop meaningful threshold systems for multivariate aviation safety data for both regulating and monitoring purposes. The developed procedure is applied to the aviation inspection results collected by the Federal Aviation Administration (FAA) inspection system. The threshold system serves as a standard for evaluating the performance of aircraft operators, and provides clear guidelines for identifying unexpected performances and for assigning appropriate corrective actions.