Discussion on application of the Weibull distribution to electrical breakdown of insulating materials

The Weibull distribution is commonly used for statistical processing of breakdown data of electrical insulation. The statistical theory of breakdown that has been proposed since the 1970s has introduced a two-variables Weibull distribution in order to take into account both the stress applied and the failure times. In this paper this distribution is thoroughly discussed and then rejected. Indeed, the random variable is only one; the other is an independent variable that becomes random only through the first, with the same shape parameter. The case of breakdown after electrical or multiple-stress aging (electric strength test on aged specimens) is also examined and the probability distribution function is written even in the general case, where the probability is a function of several variables. Only one of the latter, i.e. the electric strength ES, is the random variable while the others, such as the applied stresses and the time at which the ES measurement is performed, are independent.