The automatic design of experiments : Some practical algorithms.

The purpose of this study was to develop a methodology, represented as a set of programmable algorithms, for the design of experiments of the types that are generally likely to be useful in the physical sciences. This has beenachieved by adding to the established theory and practice of designing factorial experiments for both qualitative and quantitative variables. Algorithms were developed for designing fractional two-level factorial experiments according to a pre-specified model to be fitted, expressed in terms of required effects to be estimated. These algorithms are extended in two ways.One of these is to allow a fractional two-level factorial design to be augmented with extra points so that quadratic effects can be estimated. The second is to enable fractional asymmetric multi-level factorial experiments to be designed: balanced fractions first by applying the theory of cyclic groups; then further reduction in the size of the design by using the trace and determinant of the information matrix. The application of the algorithms is illustrated with examples drawn from the physical sciences, particularly metallurgy. The algorithms developed in the study have been fully implemented using standard Fortran 4 with a few specified exceptions. These programs are listed in three appendices. The programs have been run on computers in research laboratories in Australia' and the United States as well as in Britain. They will benefit research scientists who are planning experiments and have access to interactive computers.The principles of algorithmic development are explained and the whole text is supported by references and by a glossary of more important terms.