Design and analysis of response surface designs with restricted randomization

Many industrial experiments are conducted under various conditions which do not facilitate complete randomization of all the experimental factors. In response surface methodology whenever there are restrictions on randomization the experimental procedure usually follows the split plot design approach. Split plot designs are used when there are factors which are difficult or costly to change or adjust during an experiment. Split plot designs are currently generating renewed interest because of their usefulness and practical application in industrial settings.;Despite the work accomplished through various research efforts, there is still a need to understand the optimality properties of these designs for second-order response surface models. This dissertation provides the development of an analytical approach for the computation of various optimality properties for the assessment of second-order split plot designs. The approach involves a thorough investigation of the impact of restricted randomization on the information matrix, which characterizes much of the relationship between the design points and the proposed response surface model for split plot designs.;Several important insights are presented for the construction of second-order split plot designs. In addition, the analytical equations reported compute exact design optimality values and are more efficient than currently available methods. A particular feature of these analytical equations is that they are functions of the design parameters, radius and variance ratio. Further, a significant result is the ability to efficiently compute the exact value of the integrated prediction variance for both split plot designs and completely randomized designs. The functionality of the computational procedures presented provides easy evaluation of the impact of changes in the design structure and variance ratio on the optimality properties of second-order split plot designs.