Most of industrial experiments are involved with multi-stage processes.  Our previous research has proven that two experiments of Central Composite Design (CCD) within strip-strip-plot structure for three multi-stage processes are able to extract interaction effects across stages.  Both experimental designs have their properties that meet the requirement of the equivalence of generalize least square (GLS) and ordinary least square (OLS) estimates.  The benefit of the GLS-OLS equivalence is that the parameter estimations do not required estimations of their variance components and thus they can be possibly achieved from any statistical software. This research is addressed to provide GLS-OLS equivalence design construction technique for building balanced second-order strip-strip-plot designs of two or three-multi-stage processes.  Central Composite Design is chosen as the parent of the designs.  The reduction of runs in parent designs resulting to GLS-OLS equivalent D-optimal designs.  D-efficiency is calculated to guarantee the efficiency of a design with estimated variance component ratios equal to one.  By applying this technique, a catalog of design patterns has been generated with maximum three factors of stage-1 and stage-2.

Keywords: D-optimal criteria, GLS-OLS equivalence, second-order model, strip-strip-plot design, multi-stage processes.