25 Feb. 14:00 Eric Schoen (KU Leuven, Belgium)
Title: Order-of-addition experiments to elucidate the sequence effects of treatments
Abstract: The sequence in which a set of treatments is applied may have an effect on the properties of the experimental units after applying all the treatments. For example, the order of adding six components of an automobile coating paint can affect the properties of the coating. In this example, a treatment corresponds with adding a particular component and the experimental unit is the paint. In the absence of theoretical guidance, the optimal sequence should be determined experimentally. However, even for moderate numbers of treatments, the total number of possible sequences can be too large to include all of them in an experiment. Instead, a fraction of the total number is tried out and the optimal sequence is inferred from a statistical model of the results. As a matter of fact, the automobile coating paint was investigated by using just 24 out of the possible 720 sequences.
The statistical model involves so-called pairwise order (PWO) factors that take the value +1 if treatment i is carried out before treatment j and -1 if i is carried out after treatment j. There is one PWO factor for each pair of treatments. An experiment to study the sequence effect of m treatments therefore involves m(m-1)/2 such factors
In the talk, I will introduce the PWO factor-based models step by step. Then, I will turn to optimal statistical designs for estimating these models. We collected complete sets of optimal 12-run and 24-run designs under the PWO factor model for up to 7 components. These designs can be subjected to further evaluation criteria featuring estimation efficiency for models that include some two-factor interactions of the PWO factors.
Joint work with R. W. Mee, University of Tennessee, Knoxville TN, USA
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