FAQ
Working a substitute material into a mixture design for optimal formulations
Original question from an R&D Manager:
“I am currently looking at the best way to optimize the content of three distinct enzymes to maximize (or minimize) glucose production. We generally use Stat-Ease software’s mixture designs for this type of work. However, I am confronted with the need to discern the impact of substituting Enzyme 3 with its counterpart, Enzyme 3A. Although these two enzymes share a high degree of similarity, commercially, Enzyme 3A is deemed more suitable for the intended application. The primary concern revolves around determining the consequential effects of this enzyme substitution without resorting to the execution of two separate experiments.
"For clarity Enzyme 3 and 3A cannot be used together. I am looking for a design approach to account for this substitution within the confines of a single optimization design if possible. Any ideas?”
Answer:
I suggest you set this up as an optimal combined design with 3 mixture components (E1, E2, E3) and 1 categoric factor specifying which type of E3 to use (old versus new). For example, I created a randomized 18-run I-optimal design for a quadratic mixture model crossed with a main effects (categoric) model using point exchange. It includes 4 lack-of-fit and 4 replicate points—plus one extra center point to provide one for each of the E3 options (old versus new). See the layouts and standard error surfaces below:
