Abstract
This paper calculates the minimum-variance unbiased one-order-statistic estimator of the parameter of a one-parameter exponential population. The estimator is given for N = 2(1)20 along with its efficiency with respect to an unbiased M-order-statistic estimator for a sample of N items which truncated after M items have failed. Furthermore, it is shown that by using the estimator for exponential populations one can obtain a consistent estimator for the scale parameter of Weibull populations with any known shape parameter and with the location parameter zero. A section on the use of the tabled data and a numerical example are included.