Help with DOE

[#1]

Hello,

i'm a novice user of JMP and need some help with DOE. I would like to construct a realtively simple DOE to optimize price of an alloy with combinations of 2 elements. My responses are: mechanical properties = Y1 (fdefined minimum value), price = Y2 (goal to minimize).
I have 2 continous factors X1 and X2 (chemical elements) with different prices and different effects on properties. I wan't to find optimal ratio between these elements. Optimal is that i still achieve minimum requirements for mechanical properties and minimize the cost. 

I have tried to make some response surface designs but a lot of them were not really useful. i already have some data from previous experiments and trials. 

Please give me some advice or at least point me into which direction to go to make a useful design. 

Best regards!

[#2 · Accepted solution]

Hello @JPoklic,

Welcome in the Community ! 

To better understand your use case, here are some questions :

1. Are you interested only in the ratio between X1 and X2 ?
2. Or is also the total quantity (or individual quantities for X1 and X2) worth to consider ?

If you're in situation 1, that means the total quantity is fixed (to a certain value or percentage like 100%), so you only have one independent factor to look at, which is the ratio between X1 and X2. You need to estimate what is the possible experimental range of this ratio to test, based on your domain expertise and preliminary results.

If you're in situation 2, you can consider these factors as you described (quantity for X1 and quantity for X2) or try to use them in a different way, like having a factor for the ratio between X1 and X2 and another factor for the total quantity X1+X2. You can also add constraints between factors if you want to restrict some combinations of levels factors (in the Define Factor Constraints from Custom Design).

In any case, you can use the previous data collected to inform a DoE by using the Augment Designs platform.

If you need more help, don't hesitate to answer with more context and informations, feedback and follow-up questions.

[#3]

Thanks for the answer. For me it's the second option so i will try to work with constraints to set up a logical DoE. 

I will also play around with Augmented design and try to utilise that. 

[#4]

Just to add to Victor's response, here are some additional thoughts:

1. You might want to look at the correlation between the 2 response variables.

2. Have you evaluated the measurement systems?

3. Under what inference are the experiments run (e.g., how consistent is lot-to-lot variation of chemicals?) It seems with only 2 factors, your inference space is quite small.

4. How are you quantifying Y2?  Is this based on a fixed price or is the price fluctuating with the market? If the later, then your model may be less useful (it will depend on market, understanding what effects market is quite challenging and often involves lagged variables).