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Any suggestion for DoE on chamber matching?

Hi,

 

I have some questions about designing an effective DoE for chamber matching.

Suppose that we have four identical chambers that share global factors "A" & "B", whereas Factor "C(n)" can be applied to each chamber.

In other words, factors "A" & "B" will be applied to all four chambers at a time.

Suppose that all Factors A&B&C have some 2nd order interactions, whilst dominant estimates come from Main effect of each factor to responses.

We have outputs "X(n)" & "Y(n)" for each chambers(=n), but residuals to mean regression line for all four chambers has to go minimum = chamber matching.

Suppose that the regressions for Factors to Responses are generally linear, how can we make this DoE efficient?

 

AnalyticsDOERe: Any suggestion for DoE on chamber matching?

Okay, this sounds quite complicated so let me confirm a few things.

 

• For each run of the experiment you get a value of X and a value of Y for each chamber: X1, Y1, X2, Y2, X3, Y3, X4, Y4.
• And for each run you would plot X vs Y and fit a basic linear model.
• You would then look at the residuals from this model.
• If the residuals = 0, i.e. RMSE = 0, then the chambers are matched.

 

Is that all correct?

Is finding settings that minimise the residuals the objective of this experiment?

 

Also, you say that factor C can be applied separately for each chamber.

So does that mean that you have 4 factors (C1, C2, C3, C4) that can be set entirely independently of each other?

 

Thanks,

Phil

 

Re: Any suggestion for DoE on chamber matching?

Hi @Phil_Kay 

 

Since you have mentioned that you need to think about the way to solve this to build up DoE, will you be able to answer my main thread?

 

Thanks,

Joel

Re: Any suggestion for DoE on chamber matching?

Sorry for not replying sooner.

If all factors can vary independently, would this experiment (data table attached) be possible:

 

where -1 is the lowest setting of the factor, 1 is the highest setting, and 0 is the centre of the range.

This is a definitive screening design.

If you are able to carry out all the runs you could then find which factors are most influential in determining the RMSE of Y vs X.

I would also encourage you to search the internet for "design of experiment" and "chamber matching". There appear to be some published articles about this that you would probably understand better than I can. (I have not worked in the semiconductor industry)

You might also want to think about functional data explorer in JMP Pro because this enables you to model how a functional response varies due to the factors in a designed experiment. You could model how your Y vs X changes with the factors A, B and C1 to C4. This primer might help.

Let me know if this helps,

Phil  

Let me know if this helps.