Using Hierarchical Probability Models to Evaluate Robust Parameter Design Methods

Abstract

An approach is proposed for evaluating the effectiveness of robust parameter design methods. A hierarchical probability model is presented that enables an investigator to represent assumptions about regularities in system responses such as effect sparsity, hierarchy, and inheritance. The hierarchical probability model is used to create a population of responses to which alternative robust parameter design methods are applied. In a model-based study, product arrays and combined arrays are both applied in simulations of a scenario similar to that in a physical experiment recently published in the literature. The study confirmed the result found in the physical experiment that, in scenarios of this form, product arrays with classical analysis can exploit effects on transmitted variance that interaction analysis and combined arrays often cannot. The model-based approach also enabled investigation into mechanisms by which robust design methods function and into the assumptions critical to their effectiveness.