Reliability Based Aircraft Structural Design Pays Even with Limited Statistical Data

Probabilistic structural design tends to apply higher safety factors to inexpensive or light-weight components, because it is a more efficient way to achieve a desired level of safety. We show that even with limited knowledge about stress probability distributions we can increase the safety of an airplane by following this paradigm. This is accomplished by a small perturbation of the deterministic design that maximizes safety for the same weight. The structural optimization for safety of a representative system composed of a wing, a horizontal tail and a vertical tail is used to demonstrate the paradigm. We find that moving small amount of material from the wing to the tails leads to substantially increased structural safety. Since aircraft companies often apply additional safety factors beyond those mandated by the Federal Aviation Administration (FAA), this opens the door to obtaining probabilistic design that satisfies also the FAA code based rules for deterministic design. We also find that probabilistic design is insensitive to errors committed while assessing the stress probability distribution of the deterministic design, which is the starting point of the probabilistic design. This suggests that using the deterministic design as the basis for the probabilistic design insulates the latter from the extreme sensitivity to statistical data that have been observed in the past. Finally, we find that for independent components subject to the same failure mode, the probabilities of failure at the probabilistic optimum are approximately proportional to the weight. So a component which is ten times lighter than another should be designed to be about 10 times safer.