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The
relationship between the V-t characteristic and the 2 parameter Weibull
distribution for the dielectric breakdown voltage has long been discussed
by engineers and statistical scientists. In this paper, it is revealed
from a probabilistic view-point that the slope n in the power-law
model, the Weibull shape parameter a in lifetime distribution, and
the Weibull shape parameter b in dielectric breakdown voltage distribution
have a possible relation, n=b/a, if time is Weibull's random variable
with fixed voltage stress in lifetime distribution and voltage stress
is also Weibull's random variable with fixed time in the breakdown
distribution. However, it has found that this relation does not hold
in some experimental tests. The results of statistical analysis for
polyethylene insulated cables show such a case; n ne b/a is demonstrated
under dry condition of the cables, while n=b/a holds under wet condition.
The paper also claims that the adoption of well-known formula, F(t,v)=1-exp{-(t/t_0)^a)(v/v_0)^b}
, is inappropriate in a sense of indefiniteness of t_0 and v_0.
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