Using Hierarchical Probability Models to Evaluate Robust Parameter Design Methods

A method 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 subsequently used to create a population of responses to which alternative robust parameter design methods are applied. In a case study, product arrays and combined arrays are both applied in simulations of an experimental scenario intended to match a published physical experiment. The model-based case study confirmed the result found in the physical experiment that, in scenarios of this form, product arrays with classical analysis enabled more useful predictions of transmitted variance than did the combined arrays and therefore generally provided more quality improvement. The model-based approach also enabled investigation into the mechanisms by which the advantages are afforded and the assumptions critical to the conclusions.