Confidence limits for Weibull parameters estimated using linear least squares analysis

Abstract

© 2017 Elsevier Ltd Confidence limits (at selected levels of 68.27%, 90%, 95% and 99%) for unbiased estimation of Weibull parameters obtained using linear least squares (LLS) analysis were investigated in this paper. A Monte Carlo procedure was used to obtain probability distributions for unbiased estimates of Weibull modulus, m, and Weibull scale parameter, S o , as a function of total specimen number, N (10 = N = 200), and m (1 = m = 25). Inspection of the probability distributions indicated that confidence limits for m depended only on N whereas those for S o depended on both N and m. Whilst the determination of confidence limits for m proved to be relatively straightforward, the respective values for S o were obtained by fitting an empirical equation to the S o probability distributions approximated by a Gaussian curve. Example values of m and S o confidence limits for selected N have been presented in this work.