Robustness Measures and Numerical Approximation of the Cumulative Density Function of Response Surfaces

Abstract

Robust design optimization is used to examine the effect of variations in the design variables, for example production tolerances, on the response variables. This article presents a new approach for uncertainty propagation, supplemented by a comparative study of various methods. These are design of experiments in combination with quantile and kernel density estimation to approximate the cumulative density function of the response. The accuracy and efficiency of the novel methods in comparison to the standard method of determining, which is the empirical distribution function is investigated by means of mathematical analyses and a numerical study proving the suitability of the proposed proceeding. The article also discusses different robustness measures and their suitability in engineering. A new one based on quantiles is introduced.

Keywords:

• Cumulative density function
• Quantile estimation
• Response surface
• Robust parameter optimization
• Robustness

Mathematics Subject Classification:

• 93B35