How does Hyperstudy calculate interaction Effects in a Resolution IV Screening DOE?

L_Wessels

Hello,

I have Question regarding the Calculation of Interaction Effects in Hyperstudy 2024.1.
I ran a fractional Factorial Screening DOE with Resolution IV, with 10 Parameters and 24 total runs.

As far as i know "Resolution IV" means, that the Main Effects are not confounded with Two Factor Interaction, so they can be distinguished from each other. Two Factor Interactions are confounded with each other. For example: the calculated Effect for AB might be the same as BC. If you want to find out the exact Effects for AB or BC, you might need to do more runs focused on these parameters.

But if i check the Interaction results from the DOE i made, then does every Interaction have a different Effect Value. No Effect occurs two times, so there is no confounding.

I am a bit confused by this. How is Hyperstudy able two calculate exact Effects for each Interaction, without doing more runs?

Thank you in Advance
Ludger

Garima_Singh

Hi @L_Wessels,

Fractional Factorial designs are used to reduce the number of runs required to extract pertinent information about the main effects & two-factor interactions.

This reduction in computational effort comes at the cost of an inability to completely resolve all of the main effects & interactions.

• Higher order interactions are often confounded with each other and, in some cases, can be confounded with the two-factor interactions.
• For example, for factors A, B, and C, each at two levels, only four runs would be required to resolve the main effects.
• However, all of the two-factor interactions would be confounded with the main effects (A:BC, B:AC, C:AB).

The amount of confounding in a Fractional Factorial design is classified by its resolution.

Resolution IV : The effects are resolved with respect to each other & the two-factor interactions, but the two-factor interactions are confounded with respect to each other.

Hope the information clarifies the doubts.

Many thanks.

Kind Regards

Garima Singh

L_Wessels

Hello Garima,

Thank you for your answer, but i know already that much.

You say

"Resolution IV : The effects are resolved with respect to each other & the two-factor interactions, but the two-factor interactions are confounded with respect to each other."

But this is exactly my question, why does hyperstudy still caculate differenct effects for each Interaction, when some of them must be confounded in some way?

For example in my case Hyperstudy calculated for the Interaction A B an Effect of 518,02. If the interactions are confounded, there should be atleast one other Interaction with the same Effect, but there isnt. I checked this for every Interaction Effect and no Effect was the same.

So there is no confounding. Then there must be some kind of different algorithm in the background to calculate different effects for each Interaction, without the need to make more Runs.

Do you understand my question better now?

Thank you in Advance
Ludger

Garima_Singh

Hi @L_Wessels,

Thank you for providing a clarification.

As per HyperStudy development team, to maintain generality in cases of non-screening DOEs, HyperStudy uses a regression calculation for the effects.

The calculation for the interactions is described in the below help section:

https://help.altair.com/hwdesktop/hst/topics/design_exploration/post_process_interactions_r.htm

Hope the additional information serves useful.

Kind Regards

Garima Singh

L_Wessels

Hello Garima,

i found the answer to my problem.
HyperStudy does sometimes use Placket Burman DOEs for fractional fractorial Designs, the same happened in my case, thats nothing new to me.

The special thing with Placket Burman Designs is the Fact, that Interactions are not confounded the same way as regular fractional factorial Designs, in which the some of the of two factor interactions Effects are the same. In placket Burman Designs Interactions are confounded in an other way, but they still are confounded.

It would be easier to understand the dynamics from each factor and the interactions if there would be a way to take a look in the confound/alias structure, i still didnt find a function to look into this.

Still, my Question is answered.

Best regards
Ludger