Design of experiments (DOE) involves changing inputs in an experiment to see how they affect target outputs in a given process. The American Society for Quality notes that “By manipulating multiple inputs at the same time, DOE can identify important interactions that may be missed when experimenting with one factor at a time.” When designing a cannabis extraction process, DOE can help extractors efficiently determine ideal conditions to meet their goals. It is also relevant to Good Manufacturing Practice (GMP) and other quality standards. 
DOE starts by determining the objectives, process factors, and outputs for the experiment. As an example, we covered an experiment in Extraction Magazine where researchers used DOE with the objective to optimize cannabis extraction with supercritical carbon dioxide at the pharmaceutical scale. Input factors included flow rate, pressure, and time; output variables were cannabidiol (CBD) recovery, tetrahydrocannabinol (THC) recovery, and extract weight. They determined that flow rate had the greatest impact; other interesting findings included unique CBD:THC ratios depending on the combination of input factors.
Other examples include finding the best method to quantify cannabinoids in cosmetics and another optimizing experiment involving stir bar sorptive extraction. Multi-factor design means that DOE allows the extractor to see how several factors (not just one variable) relate to and affect outputs. It’s also possible to perform DOE with one factor at a time (less efficient and blind to possible interactions between factors).
The formula 2n describes the required number of experimental runs; n represents the number of input factors. Commonly, two-level factorial design is implemented. In this case, input factors are chosen as either low (-) or high (+). These are determined by the extreme (yet natural) range. In the preceding example of supercritical CO2, the researchers consulted a “review of the literature and the recommendations of the instrument manufacture” for these values.  For example, high (+) flow rate was selected as 150 g/min, and a low (-) flow rate was selected as 40 g/min. They performed 8 runs (23) in their initial DOE.
In an experiment with only two input factors, there would be four runs (22) as follows:
|Input Factor #1||Input Factor #2|
Making sense of the data requires statistical analysis typically performed with specialized software. In our supercritical CO2 example, the researchers used one called Design Expert. The results allow extractors to map relationships between extraction conditions and determine the best process for their goals.
- Fukuda IS, et al. Design of Experiments (DoE) applied to pharmaceutical and analytical Quality by Design (QbD). Braz J Pharm Sci.2018;54. http://dx.doi.org/10.1590/s2175-97902018000001006. [Impact Factor: 0.888; Times Cited: 35 (Semantic Scholar)]
- Rochfort S, et al. Utilisation of design of experiments approach to optimise supercritical fluid extraction of medicinal cannabis. Sci Rep. 2020;10(1):9124. doi:10.1038/s41598-020-66119-1 [Impact factor: 3.998; Times cited: 1 (Semantic Scholar)]