




Estimation for the Parameters in the Stepup
Voltage Test under the Weibull Power Law Model








H. Hirose, K. Tsuru, T. Tsuboi, and S. Okabe








IEEE Trans., Dielectrics
and Electrical Insulation, Vol.16, No.6,pp.17551760 (2009.12)






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 stepup test. In dealing with
the stepup 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.





Stepup voltage test, cumulative exposure
model, independence model, maximum likelihood estimation,
method of least squares, Weibull power law.









Times Cited in Web of Science: 3
Times Cited in Google Scholar: 5
Cited in Books:
WoS: IEEE TRANSACTIONS ON RELIABILITY
巻: 61 号: 3 ページ: 625633 DOI: 10.1109/TR.2012.2207575 発行: SEP
2012; Journal of Computational and Applied Mathematics
volume 235, issue 17, year 2011, pp. 5259  527; IEEE TRANSACTIONS ON RELIABILITY
巻: 61 号: 3 ページ: 625633 DOI: 10.1109/TR.2012.2207575 発行: SEP 2012
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