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Orthogonal‐array composite designs (OACDs) and orthogonal‐uniform composite designs (OUCDs) are orthogonal composite designs that combine two‐level full or fractional factorial and three‐level orthogonal‐array/uniform designs for estimation of the linear, bilinear, and quadratic effects in a second‐order response surface model. In this study, the effects of missing one observation in the various design portions (factorial (f) axial (a) and center (c)), on the precision of parameter estimates, prediction variance and design efficiency of OACDs and OUCDs for 5 ≤ k ≤ 9 factors at different values of α (the distance of a non‐zero co‐ordinate in an additional design point from the center) are evaluated. The results showed that missing a factorial and an axial point have adverse effect on the precision of parameter estimates of OACDs and OUCDs, while missing a center point has little effect. Missing an axial point caused the highest effect on the prediction variance and design efficiencies. The FDS plots showed OACDs to be better designs for k ≤ 7 and OUCDs for k = 8 and 9 factors. [ABSTRACT FROM AUTHOR]