Analysis considerations in industrial split-plot experiments with non-normal responses

Non-normal responses are common in many industrial experiments. When there are factors whose levels are difficult and/or costly to control, an experiment is typically run within a split-plot context. Industrial split-plot experiments have received a great deal of attention in the literature in the normal response, linear model setting. Generalized linear models have been proposed for the analysis of completely randomized designs when the response is non-normal. When one uses a completely randomized design, there is an implication that responses are independent. For split-plot experimentation there is an assumption that responses within a given whole plot are correlated. To account for this correlation, generalized linear mixed models (GLMM) can be used for analysis. Generalized linear mixed models fall into two categories: population-averaged models and batch-specific models. We give an expository treatment of GLMM and discuss the differences in interpretations of the population-averaged and batch-specific models using an example from film manufacturing.