How can I make an empirical model to understand composition-processing-hardness relationships?

[#1]

I've made several disks using calcium carbonate, water, and admixture with different compositions of each of the chemicals. Then I tested the hardness of the disks and hardness of every disk id different due to different chemical composition. Now my idea is making an empirical model using some of the disks I already examined. The hardness will be my response. Now I want to know how can I make an empirical model by JMP-DOE to understand composition-processing-hardness relationships? what are the steps? From where should I start?

I WANT AN INTERACTIVE EXPLANATION

#DOE

#Empirical Model

#JMP

[#2]

Hi,

Have you seen the collection of DOE tutorials in Mastering JMP: https://www.jmp.com/en_us/events/mastering/application-areas/design-of-experiments.html

I would quickly glance through the contents of these and watch one or two that are closest to the problem I'm trying to solve. 

STIPS also has a module on DOE, you may consider checking that out as well: https://www.jmp.com/en_us/online-statistics-course/design-of-experiments.html

[#3 · Accepted solution]

@HadleyMyers offers good advice for your future experiments. It sounds like you have data already. You can use a multiple regression model to account for the relationships with the composition factors. Depending on the data set, you might not be able to estimate all of the possible effects of the composition. A DOE is very useful because it guarantees that you can estimate and learn about everything you want.

Set up a table with a column for each of the composition variables (factors) and the response variable. Select Analyze > Fit Model. Select the response column and click Y. Select the factors and click Add. Click Run.

I do not know if you are familiar with the method of analysis, so let us know if you have questions about the results.

[#4]

yeah, I have data of factors (calcium carbonate, water, admixer) and responses ( hardness). I want to use these data (factors and responses) to produce more data of factors and responses ( which will be made by JMP) so that I can make a mixture profiler by which I can find out the composition of any desired hardness.

Now I'm confused which DOE is appropriate for this. custome design or mixture design?

[#5]

This might be a bit tricky because you did not design the original experiment in JMP. I assume, though, that you have the data in a JMP data table already. I think that best way to  get the right result with a minimum of effort is to use two steps: first create a DOE with the table and then, second, replace the rows with the existing data table.

I suggest using Custom Design. Define the responses, factors and the terms for the model. Specify the same number of runs as the number of rows in your original data table. Click Make Design and then Make Table. You have the right data table. You have the wrong rows. Go to the original data table and copy one column at a time, paste into the corresponding design table. You can close the original data table when you finish. You can use the design table from now on.

You can analyze this data. You can also augment the design to add more runs that will compliment the existing data for various reasons: increase power of tests of parameter estimates, reduce correlation of parameter estimates, estimate new parameters (terms), and so on.

[#6]

Farhana,

Welcome to the community and what a question to start.  This is akin to asking how do we accomplish world peace.  The suggested on-line learning modules can help, but I suggest you take some classes.  There are many approaches and "models" to discover causality.  No one is the right one and quite frankly how you get there is dependent on the situation.  I would start with hypotheses (scientific method).  There may be clues in the data set you have to help you develop hypotheses (Mark suggests regression to get some clues from the existing data set, but even this requires you to understand issues like multicollinearity, RSquares, p-values, RMSE, residuals, etc.) .  Once you have hypotheses, then you can use experimentation to provide insight to those hypotheses.  I would be careful drawing conclusion from the data set you have.  Have you investigated the measurement system?  Have you accounted for measurement errors?  Is the hardness consistent thought the disk?  Have you investigated the consistency of the raw materials?  Did the CaCO3, H2O, et. al. come from one source or batch?  What was the process to combine the chemicals?  Is it consistent?  Hopefully you get the idea.  There are many questions that need to be investigated before having model (an more importantly and understanding) of what factors affect hardness.