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Response surface designs are generally used in process/product optimization studies. Sequential third-order response surface designs are advantageous when the experimenter encounters the significance of  lack of fit  of a fitted second-order model while establishing the relationship between the input and response variables. In some experimental situations, responses pertaining to certain design points may be destroyed or unobtainable or inaccessible. The unavailability of the observations pertaining to certain experimental run(s) affects the design property and affects the analysis of variance. In this paper, we have examined the robustness of sequential third-order rotatable design and investigated the loss of information when one or two observations pertaining to experimental run(s) is (are) missing, which are at different radii from the design centre. It has been found that the maximum loss of information occurs when the observation at the design points which are at higher radii from the design centre is lost and the design has the minimum efficiency.

Robustness of sequential third-order response surface design to missing observations