Probabilistic Modeling of Variation in Pilot Performance During Flight Training

A probabilistic analysis for the variability of pilot performance was performed to model the variation in pilot performance during flight training from the viewpoint of reliability theory. We summarized flags among all applicants tallied in flight training to a histogram. Various probability distributions were fitted to the histogram using two bootstrap goodness-of-fit tests. We found that a limit of the marginal distribution of Ryu's bivariate exponential distribution gave the best approximation of the histogram. Defining a random variable for the conditional hazard function as the training step was the key interpreting the physical background of the fitted distribution in terms of the growth process during training. Its hazard function showed keeping the number of flags per flight within a few was important. Also, calculating the ratio to the expectation for each training step and visualizing the transition of the cumulative number of flags revealed a concave growth model as the basic process lying in the background. Moreover, fundamental assumptions of software reliability growth model (SRGM) were interpreted in terms of pilot training, and the existence of a stochastic process was discussed. Visualizing personal processes appearing in reality, we found that their shapes were similar to those of SRGM. Therefore, applying SRGM to pilot training data is expected in the future.