Statistical modeling of dependence structures of operational flight data measurements not fulfilling the I.I.D. condition

During flight of civil aircraft, a huge amount of data is recorded. After flight, the data are transferred to ground stations where they are stored and analyzed by the airline. A selection of software packages to manage and process this data, called Flight Data Monitoring (FDM) systems, are available. Since the data are recorded throughout the flight, the records are given as time series. Often, so called measurements or snapshots are calculated from the time series that are singular values per flight that describe organizational, safety, efficiency or maintenance aspects in more detail. Examples for measurements are speed at touchdown and maximal vertical speed during approach. Once measurements are calculated, they can be cumulated from several flights or the whole flight operation and further investigations, e.g. statistical analyses, can be conducted. For several statistical tools such as fitting distributions to data, there are statistical requirements the data have to fulfill. Often, these requirements are not verified, but (consciously or not) assumed to be fulfilled. One common requirement in statistics is that the considered data are independent and identically distributed (I.I.D.). In case the data do not fulfill this requirement, certain statistical methods should not be applied. In this paper, the common statistical requirement I.I.D. together with a statistical test to verify this property specifically for flight data are described. Furthermore, linear marginal models which are statistical tools to transfer non-I.I.D. to I.I.D. data are collected and described. Once the (modified) data fulfill the statistical requirements, the dependence structures of measurements are analyzed. Thereby, the statistical concept of vine copulas is briefly described and applied. The obtained dependence structures can be interpreted and for instance subsequently be used to estimate accident probabilities based on the generation of samples.