Inference for Unreplicated Factorial and Fractional Factorial Designs.

The ability to determine which factors significantly affect a product or process can help to improve its quality. Usually there are many factors to be considered initially, but a limited amount of time and money, so it is important to screen the numerous factors with a limited number of experimental trials. In this situation, unreplicated factorial and fractional factorial designs are often used, but because these experiments are unreplicated they do not possess a formal estimate of the experimental error variance. Several methods have been proposed by Daniel, Box and Meyer, Benski, Lenth, and Schneider, Kasperski, and Weissfeld to determine the significant effects in these experiments. This research focuses on an in-depth comparison of the aforementioned methods under a variety of practical situations commonly found in industrial experiments. Each method will be critically evaluated, with the culmination of the work being a recommendation for the use of the various methods