Bayesian Design and Analysis of Small Multifactor Industrial Experiments

Abstract

Unreplicated two level fractional factorial designs are a common type of experimental design used in the early stages of industrial experimentation. They allow considerable information about the e ects of several factors on the response to be obtained with a relatively small number of runs. The aim of this thesis is to improve the guidance available to experimenters in choosing a good design and analysing data. This is particularly important when there is commercial pressure to minimise the size of the experiment. A design is usually chosen based on optimality, either in terms of a variance criterion or estimability criteria such as resolution. This is given the number of factors, number of levels of each factor and number of runs available. A decision theory approach is explored, which allows a more informed choice of design to be made. Prior distributions on the sizes of e ects are taken into consideration, and then a design chosen from a candidate set of designs using a utility function relevant to the objectives of the experiment. Comparisons of the decision theoretic methods with simple rules of thumb are made to determine when the more complex approach is necessary. Fully Bayesian methods are rarely used in multifactor experiments. However there is virtually always some prior knowledge about the sizes of e ects and so using this in a Bayesian data analysis seems natural. Vague and more informative priors are 6 explored. The analysis of this type of experiment can be impacted in a disastrous way in the presence of outliers. An analysis that is robust to outliers is sought by applying di erent model distributions of the data and prior assumptions on the parameters. Results obtained are compared with those from standard analyses to assess the bene ts of the Bayesian analysis.