A new case file has just fallen across the desk of Private Investigator Particle Pete. Their client has a mystery to unravel. Follow along as PI Pete solves the Mystery of the Design of Experiments!
In the world of manufacturing, whether it be pharmaceuticals, battery production, the automotive industry, etc., strict quality control systems are essential. These systems may include particle characterization: particle size & shape, particle count, density, porosity, pore size distribution, and more. But the question remains: how do we ensure we have the best method for characterization? PI Pete of Particle Technology Labs (PTL) has a special tool up his sleeve called a Design of Experiments that can help answer this question.
The Case
When starting a new case, optimizing a method, confirming a hypothesis, or determining what factors (or variables) are statistically significant, it’s important to identify a few key elements. PI Pete has questions that need answering.
What’s the objective? Being specific about the question we’re trying to answer can help narrow down which factors and responses matter. Are we investigating the effects of a specific variable or optimizing an output?
What are the responses? With a goal in mind, we might be looking for a specific response, i.e., an outcome like particle size, surface area, etc. Are there any specifications associated with this response? How are the responses typically collected or measured?
What are the factors? Knowing what factors or analysis conditions affect a response is important when determining what controlled changes can be made to a method. These factors may include sample mass, obscuration level, or feed rate during analysis.
What are the testing limits? In some cases, the sample is scarce, we’re working under a time limit, or we’re working with a defined budget. This can affect how many factors we can examine, how many factor levels (specific modifications of a single factor) we can apply, and ultimately how many total tests we should carry out (number of aliquots).
The Investigation
So how do we determine what procedures to use for an experiment? A classic approach for method optimization is one factor at a time (OFAT). One factor at a time, as the name suggests, involves changing one factor or variable per test while keeping all others constant. As one might imagine, this may not be the most efficient approach, and it can become very time- and resource-costly. PI Pete, however, has a specialized tool up his sleeve. He might suggest using a Design of Experiments (DOE).
A DOE is an approach for testing the effects of changing multiple factors at a time towards achieving your objective. Particle Technology Labs uses JMP—a statistical software with powerful analytic capabilities—to help us answer multiple statistical questions. One such design that can be made using JMP is called a full factorial design.
A full factorial design calls for all possible combinations of the specified factor levels or treatments. This method allows us to examine possible interactions between factors simultaneously. Testing is randomized to average out possible effects from uncontrolled variables or biases (such as instrument drift, time of day, etc.).
In PI Pete’s new case, a company wants to explore what factors affect the particle size of their suspended API during routine quality control (QC) testing. Factors such as particle concentration, stir speed, and sample mass may be considered when analyzing particle size via laser diffraction. They would like to explore these effects over two levels for each factor, high and low. The number of tests needed can be described by the equation:
Where n is the number of factors to be examined, and k is the number of levels for each factor. PI Pete adds two additional points in the middle range of the factors, called centerpoints, to estimate the error of the model and check for curvature in the model. For our case, the equation can now be written as:
Three factors with two levels and two centerpoints totals ten aliquots for this DOE. The visual below shows the factors, represented by the letters A, B, and C. Test points collected at the high and low ends for each factor are represented by the orange circles, while the centerpoints are represented by the yellow circles.
One can imagine how this DOE would be very helpful, particularly when exploring factor interactions or adding factors to the design.
The Conclusion
For this case, PI Pete recommends using the full factorial DOE to carry out the investigation. He sends his plan off to the lab, and they conduct the needed analyses to find that the particle size of this particular API is most affected by stir speed. This design may not be the best for every case. JMP’s software offers more advanced tools for more complicated cases. PTL and PI Pete are here to help determine what design is best for client-specific needs.
Have a tough case that needs answers? Put PTL on the case. Contact our team today to get started.
By Arielle Lopez, Particle Characterization Chemist III
