Use of probabilistic-mathematical-analogies in aerospace-safety problems

Predictive modeling using probabilistic-mathematical-analogies (PMAs) is never a must, but, in addition to other possible experimental and modeling effort, often enables shedding supplementary useful light on some critical aerospace-safety tasks and problems (ASP) by providing valuable quantitative information about the most likely outcome of an aerospace mission or an off-normal situation. In this write-up some well-known, "classical”, analogies employed in the past in various areas of applied science and engineering by outstanding researchers, as well as some currently used ones suggested in the aerospace-safety field by the author, are indicated with an emphasis on the application of the probabilistic analytical (“mathematical”) modeling. The approach is based on the use of the probabilistic-design-for-reliability (PDfR) concept. The concept was initially introduced to address the reliability physics of aerospace electronic and photonic products, and then applied to various human-in-the-loop (HITL) situations, when the reliability of the instrumentation, both its hard- and software, and the performance of the humans involved, if any, contribute jointly to the outcome of an aerospace mission or an extraordinary situation. Several medical (surgical), clinical, automatic driving and even astrobiology problems using the PMA-based approach are also indicated. It is concluded that while some kind of predictive modeling should always be considered and conducted for aerospace safety problems of importance prior to and, if possible, also during accelerated reliability (”life”) testing of critical electronic and photonic products, predictive modeling and particularly the one employing PMA based approach should always complement computer simulations. Analytical (“mathematical”) modeling and computer simulations are based on different assumptions and employ different calculation techniques, and if the obtained results using these two major modeling tools are in agreement, then there is a good reason to believe that the calculated data are accurate and trustworthy. Future work should consider other possible applications of the PMA approach including the development of methodologies for establishing ultimate acceptable risk levels for critical undertakings, even beyond the aerospace-safety field, taking into consideration both the probabilities of possible (never zero) field failures and the most likely consequences of such failures.