Foundation of mathematical deterioration models for the thermal stress

Abstract

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.

Optimum and semi-optimum life test plans of electrical insulation for thermal stress

“…value in the conventional test. The table also indicates that the efficiencies in the cases of (n H , n M , n L ) = (5, 10, 15), (15,10,5) are not so different from the efficiency in the case of (n H , n M , n L ) = (10, 10, 10). In Table 3, the values of ratio s.d.…”

“…These are, 1) the normal distribution model, 2) generalized logistic distribution model, and 3) the generalized Pareto distribution model as shown in [10]. We usually observe the degradation phenomenon by the logarithmic time scale, we may transform y such that y = log t where t is time to failure.…”

“…However, there are not so many references describing the probability distribution model for the thermal deterioration due to the thermal stress. Recently, Hirose and Sakumura proposed the mathematical deterioration models due to the thermal stress, where three probability distribution models are combined with the Arrhenius law [10]. In the mathematical models, we assume that the Arrhenius law holds between the thermal stress and the lifetime, and that the logarithmic lifetime follows some probability distributions at a constant stress.…”

Optimum Life Test Plan under the Thermal Stress Deterioration Using the Mechanical Strength

“…In the IEC (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. Recently, Hirose and Sakumura [8] proposed the mathematical deterioration models due to the thermal stress, where three probability distribution models are combined with the Arrhenius law. In addition, the optimum life test plan is also proposed [7] in the case of 0/1 discrete life representation.…”

“…TEST CONDITION AND TEST RESULT (POTTING COMPOUND) These estimates are different from[8] because of the different sample data.…”