V-t則モデルとワイブル分布の統計的考察

抄録

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 flxed 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≠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/t₀)^a(v/v₀)^b}, is inappropriate in a sense of indefiniteness of t₀ and v₀.