Algorithmic generation of empirical life-stress models with statistical methods

Life-stress models are used to express the relationship between the applied stress and the resulting lifetime of a product. There are several life-stress models which are widely known and have been widely applied for decades. The most prominent examples are arguably the Arrhenius relationship, the Eyring model, and the Inverse Power Law. While these conventional life-stress models have proven their validity in countless examples, they are at risk of being applied without verification for cases where other models are more suitable. An application case for which conventional life-stress models are potentially not suitable is the presence of several stress variables, as they cannot be integrated in a standard model without further steps. Another example are applications with unknown physics of failure, where it is unclear whether the presumptions made in the derivation of a conventional life-stress model are valid or not. For such cases, the algorithmic development of empirical life-stress models is considered in this paper. The suggested algorithm derives such models by combining different transformations of stress factors, which effectively creates a set of life-stress candidate models from scratch. These candidate models are then fitted to empirical data and iteratively assessed and modified using statistical methods. The resulting empirical models are compared to the conventional models in terms of their accuracy and plausibility. The suggested methodology is applied to experimental data from capacitors, which have been exposed to thermal and electrical stress factors. The results verify the effectiveness of the suggested algorithm in finding well-fitting empirical models.

Keywords: Life-stress models, acceleration model, accelerated testing, statistical evaluation, capacitor lifetime.