3) [15 pts.] An aluminum master alloy manufacturer produces grain refiners in in

Question

3) [15 pts.] An aluminum master alloy manufacturer produces grain refiners in ingot form. The company produces the product in four furnaces. Each furnace is known to have its own unique operating characteristics, so any experiment run in the foundry that involves more than one furnace will consider furnaces as a nuisance variable. The process engineer suspects that stirring rate impacts the grain size of the product. Each furnace can be run at four different stirring rates. a) Identify the experiment structure that fits the best to this situation. b) Write the effects model for the structure you selected in part a c) Compute the degrees of freedom for each term in this model.

Explanation / Answer

a) Since we want to check stirring rate impact on grain size. we have four furnace and each furnace can be run at four different stirring. and if we use more than four furnace we will consider furnace as a nuisance variable hence we will use randomize block design. where we have four stirring as treatment and four furnace as blocking factor. our design will look like.

M= Stirring Method , F= Furnace

each furnace will recive each stirring method and as a result we will measure size of grains for each furnace and stirring combination.

b)

The model for a randomized block design with one nuisance variable is

where

c)

I hope this will help you.

Cheers!!

Furnace / Stirring method M1 M2 M3 M4 F1 F2 F3 F4

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