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In order to get the estimate and its reliablity of lifetime tinder the stress of service voltage, the validity and the suitability about various mathematical models which are used for long-term V-t characteristics were considered. The following models were proposed. ( I ) T. W. Dakin : semi-log plot model (physical explanation) . ( 2 ) W. B. Nelson: the one-dimensional (time t) Weibull distribution model where the inverse power law (as the empirical law) is embedded in the scale parameter of the Weibuil distribution function. ( 3 ) J. M. Oudin : The two-dimensional but one variable (time t) and conditional (under stress E) Weibull distribution model. ( 4 ) E Occhini : the two-dimensional two variable
(time t, stress E) Weibull distribution model from ivhich he attempted to deduce the inverse pol~er law. ( 5 ) L. Simoni : the model to estimate the n･valtie of inverse power law from short time test. From the intensive consideration, the following facts are revealed. ( i ) The author thinks it is the wrong interpreta-tion that the inverse power law is deduced from the two-dimensional Weibull distribution function with variables time t and stress E. It is better to think that the empirical inverse power law is embedded in the Weibull distribution function. ( ii ) Especially, the two variable function F(t,E) proposed by Occhini does not satisfy the condition of multi-variate probability distribution function. Therefore, it is impossible to estimate the Weibull parameters of F( t,E ), as f( t,E ), the density func-tion of F(t,E), can have a negative value. (iii) The auther thinks the model proposed by Nelson and Oudin must be the simplest and the most fundamental one to estimate the lifetime and its reliability statistically.