How to design a DoE to compare appliances with different batch size

[#1]

Hello!

I want to compare if two machines have the same pressure output. However, one machine, namely A, outputs batches of size 15 and machine B output batches of size 90.

Ideally, my model would be

y_ijk = mu + m_i + m_i/b_ij + e_ijk

where y is the pressure at machine i, batch j and replicate k, m is the machine, b is the batch and e is the random error.

How would I create this design in JMP, making sure I have the correct number of observations in each block (batch)?

[#2]

@PValueEnemy  Some of your model notation is not clear to me. In particular, what exactly does “m_i/b_ij” represent?

[#3]

m_i/b_ij is the effect of the batch j nested in the machine i. Hope it is clearer now

[#4 · Accepted solution]

Hi @PValueEnemy,

Have you tried looking at the "MSA Design" platform (in "DoE" -> "Special Purpose" -> "MSA Design") ?

Regarding your topic and the nesting between batch and machine, I think the platform may be able to handle your constraint.
Here is an example with factor batch nested within factor machines, and other possible factors :

Here is the JSL code :

DOE(
	MSA Design,
	{Add Response( None, "Y", ., ., . ), Add Factor(
		Categorical,
		{"L1", "L2"},
		"Machine",
		MSA( 3, 1 )
	), Add Factor(
		Categorical,
		{"L1", "L2", "L3", "L4", "L5", "L6", "L7", "L8", "L9", "L10", "L11", "L12",
		"L13", "L14", "L15"},
		"Batch",
		MSA( 2, 1 )
	), Add Factor( Categorical, {"L1", "L2", "L3"}, "Operator", MSA( 4, 1 ) ),
	Set Random Seed( 72339109 ), Replicates( 2, 1 ),
	Nesting Structure( {"Machine", {"Batch"}} || "Operator" ), Make Design,
	Simulate Responses( 0 )}
);

You can start your design with this platform, and if needed manually add batch replicates or rows on your datatable to account for the difference between batch sizes for the two machines.

I hope this idea may help you,

[#5]

I'm not sure that experimentation is your best method for this study.  Lots of questions:

What is a batch?  What is the appliance?  Why would pressure output depend on batch size? Is there a "known" relationship between batch size and pressure? Must you use all batches? How much of a change in pressure output is of interest?  Is the pressure output from either machine consistent? (If not, no comparison should be made)?  Has the measurement system been studied?  I believe you might be better off doing a sampling study where you take multiple measures of pressure over time (the length of the study and the frequency of the measures should be a function of SME hypotheses as to why the pressure would vary in time).  Batches are nested within machine and will be confounded with measurement error.