An aluminum master alloy manufacturer produces grain refiners in an ingot form. The company produces the product in four furnaces. Each furnace is known to have its own unique operating characteristics, so any experiment runs in the foundry that involves more than one furnace will consider furnaces as a nuisance variable. The process engineers suspect that the stirring rate affects the grain size of the product. Each furnace can be run at four different stirring rates. A randomized block design is run for a particular refiner, and the resulting grain size data are as follows. Stirring rate Furnace grain size 5 1 8 10 1 14 15 1 14 20 1 17 5 2 4 10 2 5 15 2 6 20 2 9 5 3 5 10 3 6 15 3 9 20 3 3 5 4 6 10 4 9 15 4 2 20 4 6 1) Does the stirring rate affects grain size? 2) Analyze the residuals from the experiment. Are all assumptions satisfied?
An aluminum master alloy manufacturer produces grain refiners in an ingot form. The company produces the product in four furnaces. Each furnace is known to have its own unique operating characteristics, so any experiment runs in the foundry that involves more than one furnace will consider furnaces as a nuisance variable. The process engineers suspect that the stirring rate affects the grain size of the product. Each furnace can be run at four different stirring rates. A randomized block design is run for a particular refiner, and the resulting grain size data are as follows.
| Stirring rate | Furnace | grain size |
| 5 | 1 | 8 |
| 10 | 1 | 14 |
| 15 | 1 | 14 |
| 20 | 1 | 17 |
| 5 | 2 | 4 |
| 10 | 2 | 5 |
| 15 | 2 | 6 |
| 20 | 2 | 9 |
| 5 | 3 | 5 |
| 10 | 3 | 6 |
| 15 | 3 | 9 |
| 20 | 3 | 3 |
| 5 | 4 | 6 |
| 10 | 4 | 9 |
| 15 | 4 | 2 |
| 20 | 4 | 6 |
1) Does the stirring rate affects grain size?
2) Analyze the residuals from the experiment. Are all assumptions satisfied?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
