Trans. IEE of Japan, Vol.118-A, No.10,
pp.1087-1093 (1996.10)
Abstract
A new analysis of the up-and-down method is considered
when sampled data give us not only the 2-valued information of breakdown
and non-breakdown but also the values of breakdown voltages or flashover
voltages. The conventional up-and-down method requires more than
40 trials and suitably tuned up-and-down distance to the standard
deviation of an underlying normal distribution in advance; there
may be chances that the estimates of the parameters of a normal
distribution cannot be obtained numerically; the estimates of the
standard deviation is highly biased when sample size is small.
The proposed analysis method gives us four major advantages; (1)
only 10 trials are required if we need the same confidence interval
of the estimate of the standard deviation by using the new analysis
method as the confidence interval by using the conventional 40 trials
up-and-down sequence; (2) a careful tuning of the up-and-down distance
is not needed; (3) the estimates of the parameters can be obtained
whenever the sample size is larger than 10; (4) the biases of the
estimates of the standard deviation and the low-percentile breakdown
voltage are smaller than those obtained from the conventional up-and-down
method.