A practical diagnostic framework for modified response-surface designs in robust parameter design

Quality engineers often choose experimental designs for robust parameter design before the final response model is fully known. Designs with fewer runs are attractive, but scaled criteria can obscure the practical tradeoff between run savings and achieved prediction precision when candidate designs differ in size. This paper develops a practical diagnostic framework for modified response-surface designs under omitted-effect uncertainty. Candidate designs are first screened for estimability of a common fitted working model, and only full-column-rank designs are carried forward to the diagnostic comparison. Admissible designs are then compared using unscaled nominal prediction error variance and noise-transmission slope variance at their actual run sizes. Model misspecification is represented by a norm-bounded set of omitted-effect coefficients, leading to worst-case prediction contamination and an unscaled contamination-adjusted prediction error. Simplified fraction-of-design-space displays summarize nominal and contamination-adjusted performance, while a supporting bound assesses distortion of the induced response-variance function. Numerical comparisons show that substantial run savings can coexist with nearly unchanged nominal prediction error variance, whereas slope variance and contamination-adjusted prediction error can reveal pronounced vulnerability for some economical designs. The results demonstrate that practical design choice should jointly consider estimability, actual-run-size precision, experimental economy, and protection against plausible model misspecification.