Bayesian inference of lower percentiles within strength modeling

Abstract

The interest in the study and modeling of the strength within material science has continuously been of interest within engineering and the built environment, with the Weibull distribution frequently being the model of choice in this area. Oftentimes there is a high cost involved with obtaining enough samples to perform suitable inference, and a Bayesian approach has exhibited suitable inference based on smaller samples for parameter- and confidence interval estimation. This study considers alternative Weibull candidates from a general Weibull family for the data likelihood candidates, and noninformative prior choices for parameters of these considered members are derived for their corresponding parameters. In addition to this, some previously unconsidered priors are introduced for consideration with the standard Weibull model. An introductory simulation study is presented and the effect of the alternative prior choices for the standard two-parameter Weibull model is investigated. Real data analysis rounds off the contributions of this study.