How to analyze impact of responses (e.g. PSD) on product performance in spray drying process in JMP

[#1]

I am working on a spray drying process and have used CCD design with D₁₀, D₅₀, and D₉₀ as responses. However, its dissolution profile and its flowability are dependent on the size distribution of the powder (D₁₀, D₅₀, and D₉₀). What is the best way to analyze the effect of the responses (particle size) on the product performance (dissolution and flowability) given that the size distribution values are generated experimentally and are usually fixed values unlike other factors which are generated automatically by software?

[#2]

sounds like particle size is a covariate for predicting dissolution rate and flowability.

For each experimental unit are you measuring particle size and dissolution and flowability?

I suppose you could model particle size first, save the prediction formula. Then model dissolution, with all the X's plus the particle size, then save the prediction formula.  The go into Graph>profiler, pick your formula column, and visualize the whole thing all together.   (you might have to check the box to include the intermediates.)

[#3]

Welcome to the community.  I'm not sure what exactly you're asking.  I apologize for my potential misunderstanding. It seems you have run some optimization designs to determine what factors affect particle size?  Now you want an understanding of the effect of particle size on product performance (Y's are dissolution rate and flowability) so particle size is a factor (X)?  If you are trying to understand the causal relationship, you can code levels for particle size and run it as a discrete numeric factor with 3 levels (though you can also start with a 2 level design (bold levels) and iterate.  I'm assuming you have other factors you want to experiment on (e.g., solution chemistry, temperature and noise like batch to batch of particles, ambient conditions)?  You can also measure actual particle size and treat it as a covariate in another experiment.

[#4]

Ultimately, to quantify this relationship, you have to make spray dried material that has enough variation in the particle size distribution that you can see and measure the differences in flowability and ultimately dissolution.  If the experiment you executed achieved that (variation in PSD across the experimental runs), then you can forward process that material, and then used the PSD metrics to build am model to predict flowability and dissolution.  

You may want to look at powder properties beyond D10, D50, D90.  For instance, compressibility, wetability, and flow can be impacted if the powder particle size distribution is not unimodal.    Also, it may be the span (D90-D10) or some other metric that is most predictive of flow and dissolution.