Subset selection procedures for populations following weibull distributions

Abstract

In reliability studies, practitioners often need to compare several populations and identify the one with the most favorable lifetime behavior. When sample sizes are limited, populations are similar, or observations are censored, selecting a single best population can be unstable. This dissertation studies subset selection procedures for reliability populations in which the best population is defined as the one with the largest threshold parameter. Since the threshold parameter represents a lower endpoint or minimum lifetime under the assumed model, it provides a meaningful criterion in applications where early failures are especially costly.The dissertation develops and compares both frequentist and Bayesian subset selection procedures. In the frequentist setting, exponential populations with threshold parameters and a common known scale parameter are considered. Selection rules based on sample minima and sample means are developed and calibrated to satisfy a prescribed probability of correct selection. Their performance is evaluated using operating characteristics such as the probability of correct selection, the probability of incorrect selection, and the expected subset size. Exact operating characteristics are also derived for the two-population case, including comparisons of minimum-based, CLT-based mean, and gamma-based mean rules. The Bayesian component extends the threshold-based subset selection framework to three-parameter Weibull populations. Posterior simulation is used to estimate the probability that each population has the largest threshold parameter, and the Bayesian selected subset is constructed to achieve a target posterior probability of containing the best population. The method is illustrated using a fully generated five-population Weibull study and a semi-simulated censored study based on Alloy T7987 fatigue-life data. Overall, this dissertation provides a unified framework for threshold-based subset selection in reliability settings. The frequentist procedures emphasize calibrated probability guarantees and operating-characteristic performance, while the Bayesian procedure provides a posterior probability interpretation that naturally incorporates parameter uncertainty and censoring.