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 upand-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.
