We assess a method of quantification of margins and uncertainties (QMU) in applications where the main source of uncertainty is an imperfect knowledge or characterization of the material behaviors. The aim of QMU is to determine adequate design margins given quantified uncertainties and a desired level of confidence in the design. We quantify uncertainties through rigorous probability bounds by exercising an existing deterministic code in order to compute the largest deviation in the system behaviors. The resulting framework, based on the optimization package DAKOTA, is non-intrusive and can be wrapped around existing solvers. The use of rigorous probability bounds ensures that the resulting designs are conservative to within a desired level of confidence. We assess the QMU framework by means of an application concerned with sub-ballistic and ballistic impact of AZ31B Mg alloy plates. The performance of the plates is characterized by the maximum backface deflection of the plate and the residual velocity of the projectile in the sub-ballistic and ballistic cases, respectively. As a simple scenario, we specifically assume that, under the conditions of interest, the plate is well-characterized by the Johnson-Cook plastic and fracture models, but the parameters of the two models are uncertain. In calculations, we employ the commercial finite-element package LS-DYNA. The assessment demonstrates the feasibility of the approach and how it results in rigorous uncertainty quantification and high-confidence safe designs that are well-within the practical range of engineering application.