Αποδοτικοί σχεδιασμοί κρησαρίσματος τριών επιπέδων για τη μελέτη ποσοτικών παραγόντων

Abstract

In many experimental situations in Statistics the object of study is to investigate whether one or more factors affect a quantity of interest. This experimental process has a significant role in Statistics. In this Thesis, we will deal with some experimental designs that they help us to answer the question “which factor effects are important in the experiment”. The simplest factorial design is the 2k factorial design, which involves factors with two levels each. One of the advantages for such designs is that, in relation to factors that have more levels, fewer replicates are needed. However, as the factors increase, the experimental replicates that we need to carry out grow exponentially. For this reason, we use fractional factorial designs, which reduce the experimental replicates, as we deal with a smaller number of factors. One issue that arises with 2k factorial design is that there is a possibility of some curvature in the response surface. This clearly cannot be controlled by two levels in each factor. One solution on this is to add center points into our design. Another solution is the use of factors with 3 levels. In this case we can consider the presence of curvature, but the problem is that we cannot use a lot of factors because we need too many replicates. As in the 2k factorial designs, in 3k factorial designs we may have fractional designs. An economical solution, both in terms of time and cost, is the use of Definitive Screening Designs (DSD), which is the main topic of this dissertation. In such designs, we typically need fewer runs than in the cases mentioned above. The two designs proposed are those of Jones & Nachtsheim and Xiao et al. The final issue is the measurement of the efficiency for the designs proposed by Jones & Nachtsheim.