"The envisaged achievement of this project is to perform groundbreaking work in the optimal design of experiments for estimating variance components in random effects models and for the joint estimation of fixed effects and variance components in mixed effects models, in general, and split-plot, strip-plot and split-split-plot models, in particular. The design of experiments for an efficient estimation of variance components is one of the remaining challenges in the field of optimal experimental design, so that the successful completion of this project would thus be a major breakthrough in statistical design of experiments. In Work Package 1, the focus is on the derivation of analytical expressions for the information matrices for random effects models and linear mixed models. This work will be based on the state-of-the-art restricted maximum likelihood estimation of the variance components. This is unlike the limited amount of published work in this research area, which is based on maximum likelihood or ANOVA-based estimation of the variance components. The theoretical results from Work Package 1 will then be used to tackle two challenging unanswered research questions in industrial statistics. First, in Work Package 2, we will deal with the optimal design of split-plot, strip-plot and split-split-plot experiments for estimating fixed effects as well as variance components. These designs are highly popular experimental plans for research about innovation in industry because they are cost-efficient, but the estimation of the variance components has been entirely ignored in all of the published work on their construction. Second, in Work Package 3, we will deal with the optimal setup of measurement capability studies, also known as gauge repeatability and reproducibility studies (also referred to as R&R studies). This subject is also an unexplored research area."