Robust Parameter Design: A Penalized Likelihood Approach

• Activity Number: 321
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Kwame Kankam* and James L. Rosenberger
• Companies: Penn State and Penn State
• Keywords: Adaptive Lasso ; Dual Response ; Parameter estimation uncertainty

Abstract

In the dual response Robust Parameter Design (RPD), estimated response surfaces for the mean and the variance are obtained and based on the goal of the experiment an appropriate objective function determined. This is then optimized with respect to the control factors with the goal of finding the best settings at which the process should be carried out.

We apply a penalized likelihood technique, the Adaptive Penalized Likelihood Effects Selection (APLES), to simultaneously estimate the mean and variance response surfaces. Our approach maximizes the log likelihood subject to (adaptive) constraints on the L1 norms of the mean and variance parameters. We demonstrate the performance of the proposed approach for the heteroscedastic RPD model both under Certainty Equivalence (CE) and under parameter estimation uncertainty. The performance is measured in terms of the integrated mean square error of the estimated response surfaces as well as the distance between predicted optima and the true optima.