Determination of the Joint Confidence Region of Optimal Operating Conditions in Robust Design by Bootstrap Technique

TL;DR

This paper introduces bootstrap-based methods to determine joint confidence regions for optimal operating conditions in robust design, enhancing the understanding of the accuracy of these estimates.

Contribution

It develops new bootstrap procedures for joint confidence regions in robust design, addressing the gap in interval estimation for optimal conditions.

Findings

Bootstrap methods effectively estimate joint confidence regions.

Two procedures using Bonferroni and normal approximation are proposed.

Numerical example demonstrates the methods' applicability.

Abstract

Robust design has been widely recognized as a leading method in reducing variability and improving quality. Most of the engineering statistics literature mainly focuses on finding "point estimates" of the optimum operating conditions for robust design. Various procedures for calculating point estimates of the optimum operating conditions are considered. Although this point estimation procedure is important for continuous quality improvement, the immediate question is "how accurate are these optimum operating conditions?" The answer for this is to consider interval estimation for a single variable or joint confidence regions for multiple variables. In this paper, with the help of the bootstrap technique, we develop procedures for obtaining joint "confidence regions" for the optimum operating conditions. Two different procedures using Bonferroni and multivariate normal approximation are introduced. The proposed methods are illustrated and substantiated using a numerical example.