Bootstrap Confidence Regions for Optimal Operating Conditions in Response Surface Methodology

TL;DR

This paper introduces a bootstrap-based method to construct confidence regions for optimal operating conditions in response surface methodology, avoiding assumptions of normality and unknown parameters, with demonstrated effectiveness through simulations.

Contribution

It presents a novel bootstrap likelihood-based approach for confidence regions in response surface optimization that does not rely on classical assumptions or stationary point analysis.

Findings

The bootstrap confidence regions have accurate coverage probabilities.

The method is applicable to concave-down and saddle surface cases.

Simulation results validate the approach's effectiveness.

Abstract

This article concerns the application of bootstrap methodology to construct a likelihood-based confidence region for operating conditions associated with the maximum of a response surface constrained to a specified region. Unlike classical methods based on the stationary point, proper interpretation of this confidence region does not depend on unknown model parameters. In addition, the methodology does not require the assumption of normally distributed errors. The approach is demonstrated for concave-down and saddle system cases in two dimensions. Simulation studies were performed to assess the coverage probability of these regions.