Situational concerns regarding manipulated factors and noise in industrial experiments with restrictions on randomization

Split-plot experiments were introduced in an agricultural setting. Their use in industry is discussed. Six types of situation are proposed. These situations underline the need for industrial experimenters to understand the concepts of split-plot experiments.

The randomization in split-plot experiments is restricted by the protocol for changing the level of certain (whole-plot) factor during the experiment. In order to understand the consequences of the restriction on randomization, multiple error terms should be considered. Rules are recommended that can be used to analyze a split-plot experiment. Too often experimenters focus on the factors they manipulated during the experiment, and ignore information about factors that were not included. Error terms can be revealing as to the sources of variation in the industrial processes being considered.

Traditionally, a one-tailed F-test has been used to estimate whether the whole-plot error term is larger than the split-plot error term. The split-plot error term would be smaller than the whole-plot error term when there is a source of variation acting between the (whole-)plots, that is not captured within the plots. In this dissertation it is recommended that the analyst perform a two- tailed test. The computed split-plot error term can be larger than the whole-plot error term when there is a consistent, stratified source of variation captured within the (whole-)plots. A chapter discusses analysis of covariance that can be used to compensate for the stratified source of variation.

The F-test comparing the error terms is typically not statistically powerful. One chapter of the dissertation discusses designing an experiment so that the analysis is less dependent on the F-test.