OPTIMAL TWO-STAGE BAYESIAN DESIGN FOR PENETRATION LIMIT VELOCITY TESTING

Abstract

Quantile estimation (QE), also called sensitivity testing, is used in many fields of study. Ballistic performance metrics known as limit velocities (V50, V90, etc.) are estimated via QE. A popular QE method for finding said limit velocities is logistic regression. To perform the regression, the experimentalist must determine a set of test impact velocities, known as the experiment’s “design”. Many of the leading design methods used in small arms limit velocity tests are “sequential” in that the mth test velocity is determined by the previous m − 1 test results. Although these designs are typically more optimal from a statistical perspective, they are often impractical. This paper seeks to balance statistical optimality and practical considerations by proposing a two-stage logistic regression design method so that test velocities only need to be set twice during the experiment. While developed for limit velocity testing, this two-stage approach can be used to design any experiment using logistic regression QE.