Aerospace Electronics Reliability Prediction: Application of Two Advanced Probabilistic Techniques

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Journal of Applied Mathematics and Mechanics

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Two advanced probabilistic design‐for‐reliability (PDfR) techniques are addressed in application to the prediction, quantification and assurance of the reliability of aerospace electronics: 1) Boltzmann‐Arrhenius‐Zhurkov's (BAZ) model, which enables to develop a simple, easy‐to‐use and physically meaningful methodology for the evaluation of the probability of failure (PoF) of an electronic device after the given time in operation at the given temperature and under the given (anticipated) stress (not necessarily mechanical), and 2) Extreme Value Distribution (EVD) technique, which can be used to account for the number of repetitive loadings that eventually lead to the material/device failure by closing, in a step‐wise fashion, the gap between its strength/capacity (characterized and quantified by its stress‐free activation energy) and the applied stress/demand. It is shown that the material degradation (aging, damage accumulation, flaw propagation) can be viewed, when BAZ model is considered, as a Markovian process, and that the BAZ model can be obtained as the steady‐state solution to the Fokker‐Planck equation in the theory of Markovian processes. It is shown also that the BAZ equation addresses the worst and reasonably conservative situation in the lifetime of an electronic system. It is suggested therefore that the transient period preceding the situation addressed by the steady‐state BAZ model need not be accounted for in engineering evaluations. As to the EVD technique, this concept attributes the degradation process to the accumulation of damages caused by a train of repetitive high‐level loadings, while low‐level loadings do not contribute appreciably to the finite lifetime of the material/device. When considering the EVD technique, the stress‐free activation energy is treated as a normally distributed random variable, and Rayleigh law is chosen, for the sake of simplicity, as the basic (generating) distribution underlying the EVD. The general concepts are illustrated by numerical examples. It is concluded that the addressed techniques should be considered as natural, physically meaningful, informative, comprehensive, and insightful approaches, especially in aerospace engineering, when electronic systems performance is critical and therefore ability to quantify this performance is imperative. Because of the very nature of such performance, the quantification of the device lifetime should be carried out on the probabilistic basis. This analysis is an extension and modification of a talk presented at the 2009 IEEE Aerospace Conference in Big Sky, Montana, USA.