Estimation for the parameters in the step-up voltage test under the weibull power law model

• Published in: IEEE transactions on dielectrics and electrical insulation 2009-12, Vol.16 (6), p.1755-1760
• Main Authors: Hirose, H., Tsuru, K., Tsuboi, T., Okabe, S.
• Format: Article
• Language: English
• Subjects: Breakdown voltage; cumulative exposure model; Dielectrics and electrical insulation; Electric potential; Estimates; Estimating; Failure times; independence model; Insulation; Insulation testing; Least squares approximation; Mathematical models; Maximum likelihood estimation; method of least squares; Parameter estimation; Power law; Probability distribution; Shape; Step-up voltage test; Stress; Studies; Voltage; Weibull distribution; Weibull power law
• ISSN: 1070-9878; 1558-4135
• DOI: 10.1109/TDEI.2009.5361599

In assessing the insulation withstand level of the electric power apparatus, the step-up test method is used. However, there are still many unknown matters regarding the treatment of the results. In this paper, we assume that the underlying probability distribution of failure time with a constant voltage level follows a Weibull distribution and that there is an inverse power law relationship between the mean lifetime and the imposed voltage, that is, the Weibull power law holds. Under such a condition, we investigate whether we can estimate the unknown parameters using the results obtained by the step-up test. In dealing with the step-up test data, we assume two models: the cumulative exposure model (CEM) and the independence model (IM). In parameter estimation, we use two methods: the maximum likelihood estimation (MLE) method and the method of least squares (LS). The estimates obtained by using the MLE have markedly smaller estimating errors than those by using the LS in both the models of the CEM and IM. While the MLE has a property of the consistency, the LS does not have it. In applying the CEM we can obtain the power law constant and the Weibull shape parameter simultaneously; however, in applying the IM, we cannot do that.