A sequential design for determining the quantile curve in two-factor sensitivity tests

Many works in the literature have proposed methods for estimating quantiles in sensitivity experiments with a single factor. However, sensitivity experiments with multiple factors are more and more popular in practice. A significant important challenge remains the estimation of quantiles of sensitivity experiments with multiple factors, which are curves or surfaces. While some methods have been proposed to estimate the parameters in such models, the estimation of quantiles has received scant attention. Motivated by this problem and applications for field use, this study proposes a new three-phase optimal method for sensitivity experiments with two factors to estimate the interested quantiles directly. The simulation studies and the illustrative application to a pyrotechnic control subsystem demonstrate that the proposed method has excellent performance.