# design of experiment-related question

Six Sigma – iSixSigma Forums Old Forums General design of experiment-related question

• This topic has 4 replies, 5 voices, and was last updated 15 years ago by Tim.
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• #47030

Savage
Participant

I am trying to design a functional factorial experiment of sorts.I have 3 variables (temperature, composition, and time).Temperature can have 5 values (1000, 1050, 1100, 1150, and 1200)Composition can have 5 values (40, 45, 50, 55, 60)Time can have 4 values (0.5, 1, 2, and 4).A full experimental study would require 5x5x4 = 100 runs.  How can I design an experiment to reduce the number of runs to something more managable?
Thanks!

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#156224

Putnam
Participant

Drop the levels to three for each factor (3X3X3=27) for the first cut.  Verify what factors or interactions are critical (drop the one(s) that aren’t) and design the next experiment around what appear to be the optimum points.  If both experiments are the same size, you’re still just talking 54 runs (plus a few replicates).

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#156225

Robert Butler
Participant

You have choices!
One of the overarching “beliefs” of design philosophy is that if anything is going to happen you are most likely to see it happen under extreme conditions.  From a design standpoint this mean building experiments which focus on extreme parameter combinations – in other words the corners of the design space.  To this end you could do any of the following:
1. Very Fast and Very Cheap – 3 variables in 4 experiments with two replicate points at the center. Total experiments: 6
What this buys you – an investigation of main effects only along with a test for possible curvilinear behavior.
Shortcomings – no investigation of interactions and while you will be able to test for curvature you won’t be able to assign it to any of the variables of interest if it is significant.
2. Full two level factorial design – 8 experiments plus the same to replicates at the center. Total Experiments: 10
What this buys you – complete investigation of all linear effect and two and three way interactions and a check for curvature.
Shortcomings – if curvature is present – no ability to assign it to any particular variable.
3. Augmented full 2 level factorial design – 8 points + 2 center points + 3 additional runs to cover the curvatures. Total Experiments: 13
Shortcomings: The augmented design won’ be 100% orthogonal but the VIF’s and the condition indices are within acceptable limits.
What it buys you – investigation of all mains, all two ways, all curvature. In addition to permitting a check of the effect of any of the prior terms on response mean shift it also allows the use of Box-Meyer to investigate effects of variables on response variability.
There are, of course, many other options but from the standpoint of minimum effort and maximum return the above are some of the best.

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#156228

Manee
Participant

You can use follwing combination and do 25 Experiments
Manee

Temperature
Composition
Time

1000
40
0.5

1000
45
1

1000
50
2

1000
55
4

1000
60
0.5

1050
40
1

1050
45
2

1050
50
4

1050
55
0.5

1050
60
0.5

1100
40
2

1100
45
4

1100
50
0.5

1100
55
0.5

1100
60
1

1150
40
4

1150
45
0.5

1150
50
0.5

1150
55
1

1150
60
2

1200
40
0.5

1200
45
0.5

1200
50
1

1200
55
2

1200
60
4

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#156468

Tim
Member

Set temperature range to Low, Median and High or just Low and High (0, 1) do the same for the other categories.

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