Determination of the joint confidence region of the optimal operating conditions in robust design by the bootstrap technique

Robust design is widely recognised as a leading method for reducing variability and improving quality. Most of the engineering statistics literature focuses on finding point estimates of the optimum operating conditions for robust design. Various procedures have been considered for calculating point estimates of the optimum operating conditions. Although the point estimation procedure is important for continuous quality improvement, the immediate question is ‘‘how accurate are these optimum operating conditions?” The answer is to consider interval estimation for a single variable or joint confidence regions for multiple variables. In this paper, using 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.