Any prior information an experimenter has should be incorporated into the design of further experiments. Assume such information is expressed as probabilities that each parameter of the full factorial model is nonzero. This report develops optimal design procedures by posing the experimental design problem as a finite decision problem. Bays and mini-max design strategies are then derived and their application illustrated. The major computational step is the evaluation of all possible matchings of physical variables to the abstract variables of all potential designs. The technique of telescoping sequences of blocks permits the consideration of experiments to be performed in stages.

This book contains the most comprehensive coverage available anywhere for two-level factorial designs. The re-analysis of 50 published examples serves as a how-to guide for analysis of the many types of full factorial and fractional factorial designs. By focusing on two-level designs, this book is accessible to a wide audience of practitioners who use planned experiments.

This research develops a multistage decision process designed to obtain the maximum amount of information from the evaluation of a fractorial design while minimizing the amount of resources used in obtaining the information. The use of screening experiments in building the factorial design is investigated in order to maximize the amount of information gained. The use of sequential analysis procedures to terminate experimentation at the earliest possible time is investigated in order to minimize the amount of resources used. The research is limited to 2 to the n power factorial designs involving univariate response models assumed to come from a normal population; however, the procedure can be easily extended to any factorial design. The approach is demonstrated for an operational test involving a 2 to the 6th power factorial design and the results are compared to classical procedures. The sensitivity of the required input parameters is investigated and related applications are discussed. The proposed approach is found to be a viable method of designing, conducting, and evaluating an operational test involving a factorial experiment. (Author).