This report presents a design analysis workflow for graphite core components and assemblies, based on the design rules of ASME Boiler Pressure and Vessel Code, Section III, Division 5, Article HHA-3000. The workflow contains three stages: developing the design of the graphite core component, modeling the component with the finite element software MOOSE, and assessing if the component passes/fails the criteria of the HHA-3000 design rules. Since the design rules use probabilistic metrics specifically established to evaluate brittle materials, we developed a python library that performs all the statistical calculations necessary for the evaluations of the HHA-3000 criteria.