## Abstract

Increasingly, industrial experiments use multistratum designs, such as split-plot and strip-plot designs. Often, these experiments span more than one processing stage. The challenge is to identify an appropriate multistratum design, along with an appropriate statistical model. In this article, we introduce Hasse diagrams in the response surface context as a tool to visualize the unit structure of the experimental design, the randomization and sampling approaches used, the stratum in which each experimental factor is applied, and the degrees of freedom available in each stratum to estimate main effects, interactions, and variance components. We illustrate their use on several responses measured in a large study of the adhesion properties of coatings to polypropylene.We discuss quantitative, binary, and ordered categorical responses, for designs ranging from a simple split-plot to a strip-plot that involves repeated measurements of the response. The datasets discussed in this article are available online as supplementary materials, along with sample SAS programs.

Original language | English |
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Pages (from-to) | 340-354 |

Number of pages | 15 |

Journal | TECHNOMETRICS |

Volume | 54 |

Issue number | 4 |

DOIs | |

Publication status | Published - Nov 2012 |

## Keywords

- Binary data
- Cumulative logit regression
- Generalized linear mixed model
- Hasse diagram
- Lifetime data
- Ordered categorical data
- Poisson regression
- Separation problem