Confidence interval estimation of Weibull lower percentiles in small samples via Bayesian inference

Weibull distribution has been vastly used for modeling fracture strength of ceramic and composite materials. Confidence interval estimation of Weibull parameters and percentiles in small samples has been an important concern due to high experimental costs. It was shown previously that in classical inference the Maximum Likelihood Estimation Method is the best method among several alternatives for estimating 95% one-sided confidence lower bounds on the 1st and 10th Weibull percentiles, namely A-basis and B-basis material properties. This study proposes the Bayesian Weibull Method as an alternative using the information that ceramic and composite materials have increasing failure rates, which requires the Weibull shape parameter to be at least 1. Through Monte Carlo simulations, it is shown that the performance of the Bayesian Weibull Method is superior in that it achieves the precision levels of the Maximum Likelihood Estimation Method with significantly smaller sample sizes.