Foundation of mathematical deterioration models for the thermal stress

We construct mathematical models to represent the relationship between the thermal stress and the deterioration rate for electrical insulation. The Arrhenius-log-normal model has been used generally for such a deterioration model due to the thermal stress. The Arrhenius law is based on the chemical reaction theory between the absolute temperature and the activity of materials. On the other hand, as for the log-normal distribution, we have been only followed the traditional statistical treatment such that the deterioration could be represented by the normal distribution when logarithmic time is used. The Arrhenius-log-normal model is a combination of these two models. However, in the International Electrotechnical Commission 60216-1, deterioration due to the thermal stress is represented by the mechanical strength, and the time showing 50% mechanical strength to the initial strength is defined as the failure time. We assume here the generalized Pareto distribution model, the generalized logistic distribution model, or the normal distribution model for such a model. Thus, in this paper, we construct new mathematical models combined by the Arrhenius law with the generalized Pareto distribution model, the generalized logistic distribution model, or the normal distribution model.