Estimation of Confidence Intervals and Lower Bounds for Various Weibull Percentiles

Abstract

The design allowables are derived statistically from measured material properties, and the Weibull distribution is one of the most commonly used distributions for statistical modeling. A- and B-basis design allowables are frequently used; they correspond to the confidence lower bounds for the 1st and 10th percentiles, respectively, with a confidence level of 95%. The maximum likelihood method is generally recommended and commonly used for parameter and confidence lower bound estimation. On the other hand, designers are also interested in confidence lower bounds for other percentiles, and in general, confidence intervals to specify uncertainty in percentile estimates. Monte-Carlo simulation methods have been proposed for this purpose; however, they are not easy to code and take a long time to run to obtain reliable results. As an easy-to-use alternative, this study proposes approximate polynomial functions of sample size for various percentiles and confidence levels. The coefficients of the functions are presented in tabular form for each combination of percentiles and confidence levels. They eliminate the need for simulations and provide precise confidence intervals and lower bounds for a large set of Weibull percentiles.