Two-level orthogonal experimental designs in the presence of zero, one or two blocking factors
12 September 2016
UAntwerpen, Stadscampus, Building Meerminne - M.101 - Sint-Jacobstraat 2 - 2000 Antwerp (route: UAntwerpen, Stadscampus
Prof Peter Goos
Prof Eric Schoen
PhD defence Nha Vo-Thanh - Faculty of Applied Economics
Industrial products and processes are increasingly complex. As a result, it is a major challenge to optimize these products and processes. One of the key tools in the engineering toolbox to deal with such a challenge is designed experiments. A designed experiment is an approach in which systematic changes are made to the product or process under investigation to observe their influences on one or more performance measures. In factorial experiments, the systematic changes are made to multiple characteristics of the product or process. These characteristics can be viewed as dimensions and are generally called factors. Using multiple linear regression techniques, the most influential factors can be identified after the factorial experiment has been conducted. Generally, the primary goals of the researcher are to identify any factor that has a large effect individually and to detect whether a factor’s effects depend on the settings of other factors.
Planning factorial experiments is also challenging, especially when many factors need to be studied. This is because the budget available for experiments is generally limited. The quality of the experiment largely depends on the choice of the systematic changes made during the experiment. This PhD thesis is about how to choose the changes to be made during the experiment optimally. Throughout the thesis, we assume that the researcher’s primary interest is in individual effects of the factors and that the researcher prefers precise estimates of these effects. For this reason, we restrict ourselves to experimental designs that belong to the class of two-level orthogonal arrays.
In the first part of the thesis, the focus is on experiments that can be performed under homogeneous circumstances. More specifically, the focus is on finding experiments involving 24 and 28 test combinations.
In the second part of the thesis, the focus shifts to experiments in which the tests need to be performed in groups, because not all of them can be done under the same circumstances. For example, it might not be possible to perform all the experiments on a single day, so that two or more days are needed to complete all the tests. In that case, the groups correspond with the different days. In the thesis, two different approaches are presented to arrange the tests in groups. One approach is based on a complete enumeration of orthogonal arrays, while the other approach is based on integer linear programming.
While there is one reason for grouping the experimental tests in the second part of the thesis, the third part deals with experiments that require two kinds of grouping at the same time. Again, two approaches are presented. The first approach is again based on a complete enumeration, while the second approach relies on quadratic programming and integer linear programming techniques.
In the experimental design jargon, the first, second and third part of the thesis are concerned with completely randomized experiments, blocked experiments and row-column experiments, respectively. The completely randomized experiments involve zero blocking factors, while the blocked experiments involve a single blocking factor and the row-column experiments involve two blocking factors.