Confidence limits for Weibull parameters estimated using linear least squares analysis

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, So, 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 So depended on both N and m. Whilst the determination of confidence limits for m proved to be relatively straightforward, the respective values for So were obtained by fitting an empirical equation to the So probability distributions approximated by a Gaussian curve. Example values of m and So confidence limits for selected N have been presented in this work.