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 tem- perature and the activity of materials. On
the other hand, as for the log-normal distri- bution, we have
been only followed the traditional statistical treatment such
that the de- terioration 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 con- struct new mathematical models combined
by the Arrhenius law with the generalized Pareto distribution
model, the generalized logistic distribution model, or the normal
distribution model.
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thermal deterioration, Arrhenius law, generalized
Pareto distribu- tion, generalized logistic distribution,
log-normal distribution, ordinary differential equation,
growth curve, maximum likelihood estimation method, method
of least squares.
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