Effects of error in factor levels on orthogonal composite designs for second-order models

Abstract

In this work, four orthogonal composite designs (orthogonal-array composite designs (OACDs), orthogonal-array composite minimax-loss (OACM) designs, orthogonal uniform composite designs (OUCDs) and orthogonal uniform composite minimax-loss (OUCM) designs) for second-order models were evaluated in the presence of errors for 3 ≤ k ≤ 7 factors with 1 ≤ n_c ≤ 3 center points. The design efficiency (in terms of D- and G-efficiency values) and fraction of design space (FDS) plots were used to evaluate the performance of these designs in the presence of errors. The results showed that in terms of D-efficiency values, OACDs and OUCDs performed poorly for k = 6 and 7 factors in the presence of errors while OACM designs were the best-performing designs. The OUCM designs outperformed all the other designs for G-efficiency values with OACM designs as the next best performing designs. The FDS plots showed that OACM and OUCM designs maintained high G-efficiency values in the presence of errors.

Keywords:

• Second-order model
• orthogonal composite designs
• optimality criteria
• prediction variance
• error in factor level

Disclosure statement

No potential conflict of interest was reported by the author(s).