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Not easy to change factors setting question in DOE

Eric_Wang

I got a split plot design setting question from customer, need your help to make it more clearly.
They need make a design that include two process.

1st process:

•Furnace Temp in degrees centigrade, with levels 360, 370, and 380

•Coating, with levels C1, C2, C3, and C4 depicting four different types of coating

2nd process:

•Furnace Temp in degrees centigrade, with levels 400, 450, and 500

•Coating, with levels C5, C6, C7 depicting three different types of coating

Furnace temp factors in both 2 process are not easy to change factor.

How can we get better DOE for this situation?
Regards both Furnace Temp factor as hard to change factors and proceed split plot design?
Or set 1st Furnace Temp factor as very hard to change factors and 2nd Furnace Temp factor as hard to change factors then proceed split-split plot design?
Or other better suggestion?

Thank you.

Accepted answers

DonMcCormack

@Eric_Wang there are two general ways to set this up. First, for each batch of material (i.e., the experimental units that go into the furnace) you can randomize the 2 temperatures independently. So, apply coatings C1, C2, C3, and C4 randomly to the experimental units (easy to change), group them together for a furnace run at a random temp from within the factor settings, apply the second coating randomly (easy to change - C5, C6, and C7), and run them all at the second random furnace temperature (hard to change). Straight forward split-plot, probably the easier of the two.

The second approach would be to do all the Furnace 1 runs first (each with a batch of experimental units getting the easy to change Coating 1), apply Coating 2, then randomly select the nearly completed experimental units for the Furnace 2 runs. This is a strip-plot. It doesn't matter which of the two furnace runs is set to Very Hard, you need to check the Hard to change factors can vary independently of Very Hard to change factors box and properly randomize the runs receiving the Furnace 1 treatments into the correct Furnace 2 runs. In the attached example, I've made Furnace 2 the Very Hard factor, the Furnace 1 runs with the same Subplots values correspond to a single Furnace 1 run.

As far as I can tell, the split plot will give you slightly more precise estimates. Additionally, having to hold onto the experimental units until all Furnace 1 runs are performed may cause unforeseen problems. In the Semiconductor industry, for example, unwanted growth may occur on a wafer if left sitting too long between processing steps. Ultimately, it gets down to which design is more likely to be run correctly.

Split Plot.jmp

Strip Plot.jmp

DonMcCormack

@Eric_Wang they need a split plot design because the wafers are run as a batch for both process steps. The waiting time is information that is added to the data after the fact. It is not controlled by the experimenter. It is possible that it can be extracted from the data collected by the wafer handling system (e.g., start timestamp for process 2 – end timestamp for process 1).

All comments

Thank you, Don, your explain is very helpful to me.

To make sure that I fully understand the experiment that you suggest
I try to draw the plot for split plot and strip plot, as attached.(the plots are crude and rough, I know)
Can you help me to check is the plot close to the design you describe?
thank you.

BTW, as you mentioned in the last section of previous comment, we have to consider the time between Process 1 and Process 2, in oder not to make the unforeseen problems.
Is it mean we run split plot/ strip plot batch run instead of wafer run(we don't have time to set experiment factor wafer by wafer, that is why we set some factor as hard/very hard to change)?

Split plot.jpg

Strip plot.jpg

DonMcCormack

@Eric_Wang the drawings are perfect, exactly how I would represent split plots and strip plots. There are different ways of thinking about what conditions require a split/strip plot design. We have talked about hard to change factors. Another way, as you have suggested, is to ask, "what gets the experimental treatment?". In your example, an individual wafer gets the coating treatment while a batch of wafers gets the oven temperature treatment. In the first case the experimental unit is wafer and in the second the experimental unit is the batch of wafers. Whenever you have two or more different sizes of experimental units, you need a split plot (or one of its variations).

Eric_Wang

Thank you, @DonMcCormack .

It looks like if we consider wafer by wafer to set we can use split plot, and if we consider batch of wafers for very hard to change, strip plot is suitable, however we need some Qtime(waiting time) bewteen 2 process. After discussing with my customer, they face a problem is the process 1 and process 2 are continous, that is the wafer doesn't be pull out furnace until entire process finished, the Qtime is short(or no Qtime). As you mentioned in previous comment about unwanted growth on a wafer. Do you have any suggestion to design experiment for the continuous process?