Predicted reliability of aerospace electronics: Application of two advanced probabilistic concepts

Two advanced probabilistic design-for-reliability (PDfR) concepts are addressed and discussed in application to the prediction, quantification and assurance of the aerospace electronics reliability: 1) Boltzmann-Arrhenius-Zhurkov (BAZ) model, which is an extension of the currently widely used Arrhenius model and, in combination with the exponential law of reliability, enables one to obtain a simple, easy-to-use and physically meaningful formula for the evaluation of the probability of failure (PoF) of a material or a device after the given time in operation at the given temperature and under the given stress (not necessarily mechanical), and 2) Extreme Value Distribution (EVD) technique that can be used to assess the number of repetitive loadings that result in the material/device degradation and eventually lead to its failure by closing, in a step-wise fashion, the gap between the bearing capacity (stress-free activation energy) of the material or the device and the demand (loading). It is shown that the material degradation (aging, damage accumulation, flaw propagation, etc.) can be viewed, when BAZ model is considered, as a Markovian process, and that the BAZ model can be obtained as the ultimate steady-state solution to the well-known Fokker-Planck equation in the theory of Markovian processes. It is shown also that the BAZ model addresses the worst, but a reasonably conservative, situation. It is suggested therefore that the transient period preceding the condition addressed by the steady-state BAZ model need not be accounted for in engineering evaluations. However, when there is an interest in understanding the transient degradation process, the obtained solution to the Fokker-Planck equation can be used for this purpose. As to the EVD concept, it attributes the degradation process to the accumulation of damages caused by a train of repetitive high-level loadings, while loadings of levels that are considerably lower than their extreme values do not contribute- appreciably to the finite lifetime of a material or a device. In our probabilistic risk management (PRM) based analysis we treat the stress-free activation energy (capacity) as a normally distributed random variable, and choose, for the sake of simplicity, the (single-parametric) Rayleigh law as the basic distribution underlying the EVD. The general concepts addressed and discussed are illustrated by numerical examples. It is concluded that the application of the PDfR approach and particularly the above two advanced models should be considered as a natural, physically meaningful, informative, comprehensive, and insightful technique that reflects well the physics underlying the degradation processes in materials, devices and systems. It is the author´s belief that they will be widely used in engineering practice, when high reliability is imperative, and the ability to quantify it is highly desirable.