Statistical methods for the diagnosis of small-size training set models : application to the lifespan modelling of insulation materials

This paper presents and compares statistical methods for evaluating the performance of parametric model estimation for insulation lifespan in the case of small size training sets. Parametric models are derived from accelerated aging tests on twisted pairs covered with an insulating varnish under different stress constraints (voltage, frequency and temperature). The estimation of the parametric model coefficients requires some hypothesis on the lifespan statistical distribution. However, since the number of measurements for each configuration is constrained by the experimental cost, the results given by classical goodness-to-fit tests and graphical tools may be questionable. This paper thus proposes to use the bootstrap technique for a more thorough statistical analysis. Indeed, bootstrap has been specifically designed to infer the statistical properties of an estimator when only few observations are available. In our case of study, the bootstrap technique confirms the results obtained using graphical tools and goodness-to-fit tests and thus the adequacy of the underlying statistical hypothesis required for model parameter estimation