  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.
