# ENBIS: European Network for Business and Industrial Statistics

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## ENBIS-18 in Nancy

*2 – 25 September 2018; Ecoles des Mines, Nancy (France)*Abstract submission: 20 December 2017 – 4 June 2018

### Choice of Number of Whole Plots and Number of Runs in the Design of Split-Plot Experiments

*4 September 2018, 14:30 – 14:50*

#### Abstract

- Submitted by
- Jacqueline Asscher
- Authors
- Jacqueline Asscher (Kinneret College)
- Abstract
- A common example of a split-plot experiment is an experiment conducted to improve a process that runs in batches (“whole plots”), where some factors are changed between batches and other factors are changed within batches, resulting in two components of variance. The split-plot structure may be inherent in the process being investigated or in the experimental set up, or may be adopted by choice either to save time or money, or to improve the design.

While split-plot designs are familiar to experts in Design of Experiments (DOE), they are typically not fully understood by practitioners or clients, although they may be very attractive due to the lure of savings and convenience.

A key decision in the design of a split-plot experiment is the choice of how many whole plots and how many runs to include. The issues that arise when this decision is to be made are defined and discussed here.

Before considering the statistical properties of the design, the following questions are addressed: How do we calculate how this choice affects savings in time and/or money? How do we present the calculations? How do we clarify and display the design options to the owner of the experiment?

The variance of the effects depends on the number of whole plots and runs and on the size of the two components of variance, the variation between whole plots and the variation between runs within whole plots. The power of the tests to identify active effects depends on the size of the variance of the effects, the size of the effects, and on our ability to estimate the two components of variance. The latter is also determined by the number of whole plots and runs.

Questions that arise here include: What happens if I assume that the between plot variation is relatively small, or relatively large? What happens if I don’t know? What happens when the estimation of certain effects is of critical importance?

Other considerations in the choice of how many whole plots and how many runs to include are the proportion of factors that can only be changed between whole plots and the choice of model that is to be fitted.

Finally, the relationship between all of the issues involved is discussed.