On the confidence limits for Weibull reliability and quantiles: The case of maximum likelihood estimation from small size censored samples

Abstract

For the two-parameter Weibull distribution, this paper reviews the existing methods of obtaining the interval estimate for reliability R(t), and gives tables of exact lower confidence limits for R(t) in the case of maximum likelihood estimation. These tables extend the previous ones, since they cover samples of size n = 3(1)20, censored after the first m observations, m = 3(1)n, and confidence levels γ = 0·90, 0·95 and 0·98 . A numerical example illustrates how the same tables can be used to obtain lower confidence limits for population quantiles. Bias and variance of the maximum likelihood estimator R̂(t), for some n and m, are also given.