Received: 27 November 2018 Revised: 8 April 2019 Accepted: 28 May 2019 DOI: 10.1002/qre.2524 SPECIAL ISSUE ARTICLE Robustness of response surface designs to missing data Hleil Alrweili Stelios Georgiou Stella Stylianou School of Science, RMIT University, Melbourne, Victoria, Australia Correspondence Stelios Georgiou, School of Science, RMIT University, Melbourne, Victoria, Australia. Email: stelios.georgiou@rmit.edu.au Abstract In this paper, minimax loss response surface designs are constructed. These designs are more robust to one missing design point than the original designs. The proposed designs are compared with the designs in the literature, and they are better in terms of loss and number of runs. Moreover, the new suggestion for the value of  generates designs not only with less losses but also with higher D-efficiency. KEYWORDS central composite designs, D-efficiency, minimax loss criterion, missing data 1 INTRODUCTION Missing observations, even in well-planned experiments, can rarely be avoided. Researchers have discovered ways of handling problems associated with missing observations. These include methods either replace the missing values or to apply robust techniques to their analysis. The term “robust” that was first used by Box 1 is often encountered when studying the effects of missing observations. According to Wendelberger, 2 robustness is crucial in the real world of experimentation; thus, the need for experimental designs that are robust in the presence of missing observations arise. Many researchers have discussed the robustness of statistical designs against missing observations. Hedayat and John 3 and Ghosh 4 considered robust balanced incomplete block (BIB) designs. Herzberg and Andrews 5,6 studied the problem of missing observations in a design from a different angle. They considered the probability of losing an observation at a design point. In a later study, Andrews and Herzberg 7 suggested maximizing the expected value of the determinant of the information matrix to compensate for possible missing observations. Ahmad et al 8 considered multilevel augmented second-order response surface designs and their robustness to missing observations. In investigating the information contained in an observation, Ghosh 9 stated that in most designs, some design points were more informative than others and that the effects of one or more design points, when missed, attracted a higher loss in efficiency. Other economical designs requiring fewer design points were constructed and studied for their robustness to missing observations by Ahmad and Akhtar. 10 Angelopoulos et al 11 constructed new central composite designs (CCDs) that are more economical than the classical CCDs that were introduced by Box and Wilson 12 since the newer designs were built with fewer runs. Using their designs, they found that the minimum number of runs for a four-factor design was 18. Another economical design was constructed by Georgiou et al. 13 They constructed a class of composite designs with a higher D-value (see the study of Lucas 14 ) than Angelopoulos's designs but with the same number of runs. Various robust-to-missing-observations criteria have been proposed in the literature. Akhtar and Prescot 15 developed the minimax loss criterion and applied it to the evaluation and generation of CCDs. They found that, when they applied minimax loss criterion on the classical CCDs with four factors, the number of runs was 26. Since then, this criterion has been adopted by many researchers including Ahmad and Gilmour, 16 who used it to study the robustness of subset designs. In addition, the hat matrix, also known as the projection matrix, performs a major role in quantifying the effect of removing one or more observations from a design. 17 Box and Draper 18 pointed out the connection between the diagonal This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2019 The Authors Quality and Reliability Engineering International Published by John Wiley & Sons Ltd. Qual Reliab Engng Int. 2019;1–9. wileyonlinelibrary.com/journal/qre 1