3-way ANOVA statistical methods random and mixed-effect models: Their application in gage repeatability and reproducibility studies

This thesis presents some of the theory that enables the application of a three-way ANOVA model to measurement system analysis. It describes all the possible scenarios using random and mixed models when three factors are considered and derives formulae to assist the analyst in determining significance of components of variance associated with those three factors and their interactions. It proposes a method to go from a full model to a reduced version that only contains the significant sources of variation that are of interest to the analyst. Formulae for point estimates of variance components as well as for confidence intervals associated to the significant components included in the reduced model are also offered. This thesis also proposes some ratios that may be helpful for the analyst in determining the overall adequacy of the measurement system and exhorts further knowledge in even more complex statistical models in their application to measurement systems.