| This thesis addresses the problem of analyzing fractional factorial and other orthogonal experimental arrangements that are carried out without replication, so that the usual estimate of standard error computed from replications cannot be used. Although the usefulness of unreplicated factorial experiments in industry was recognized soon after R. A. Fisher developed the basic ideas of statistical design of experiments, the influence of the Japanese ideas of quality improvement over the last few years has increased considerably the utilization of these experiments, and their analysis has become a major concern. Considering that these experiments are frequently analyzed by non-statisticians, it is desirable to provide easy to use and understand techniques to assess the significance of the estimates of the different effects involved in a particular experiment. After a literature review, four methods for the analysis of unreplicated factorials are chosen, implemented, made comparable on an error rates basis, and applied to a substantial number of real experiments taken from the statistical literature and other sources. In the process of making the methods comparable for the most common sizes of the experiments, one of the methods, which is found to be miscalibrated, is corrected. On the basis of the result of the comparison of those methods, a modification of a procedure of statistical testing with half-normal plots is presented. The method proposed, besides having the advantages of the half-normal plot, seems to be more powerful than other comparable methods, for experiments of small and moderate sizes. Finally some ideas to make a Bayesian procedure proposed by Box and Meyer more general and robust are explored for situations suggested by 30 examples of small experiments. |
