Advanced DoE plans (part 1)
There are many different experimental design plans too choose from: full factorial, fractional, central composite design (CCD), Box-Behnken, latin hypercube, Plackett-Burman, and more.
In this blog post we are going to take a closer look at fractional design for initial screening, full factorial design to get a better understanding of interactions, and CCD for optimization and non-linear dependencies.
If you think of your experimental design space as a cube (3-factors), a 2 level full factorial design would position your individual experiments on the edges of the cube. A fractional design contains only a fraction of the experiments that a full factorial design would. Central composite designs (CCDs) include additional tests at the center and the faces of the design cube, enabling the fitting of more complex models with fewer experimental runs than for example a 3-level full factorial design.
(1) Fractional design for screening
Full factorial design plans are not always the best choice because they tend to be impractical when dealing with a high number of factors. This is where fractional designs step in.
Fractional designs, as their name suggests, use only a fraction of the experiments required in a full factorial design. They are particularly useful in the early stages of research and development, where the objective is to identify key factors fast. Fractional designs allow for a preliminary understanding of the main effects and lower-order interactions, which are anyway the most significant in practice.
It's true that fractional designs provide less information compared to full factorial designs, particularly regarding higher-order interaction terms. However, in many cases, especially at the beginning of a research project, this extra detail about higher-order interactions is often unnecessary. The primary goal at this stage is usually to screen for the most significant factors, not to map out every possible interaction.
Therefore, fractional factorial design can be considered a compass in the initial phase of every research project. They allow you to identify the key factors that warrant further investigation without exhausting resources on unimportant ones.
Moreover, an added advantage of fractional factorial designs is their scalability. If your initial results suggest that more detailed information is required, they can be easily extended to a full factorial designs.
(2) Full factorial design to identify interactions
After having identified the key factors that have the most significant impact on the response through fractional design, a full factorial design can be used to explore these factors in depth.
Full factorial designs are a cornerstone in experimental design due to their comprehensive nature. They offer detailed insights into the main effects and interactions of selected factors. In a full factorial design, every combination of factor levels is tested. This provides a detailed map of the studied system.
Subsets of fractional designs can be analyzed as full factorial design if one or more factors turn out to be insignificant. This means that if, during the analysis of a fractional design, it becomes clear that certain factors have negligible effects, these factors can be dropped, and the remaining design can be treated as a full factorial design for the significant factors. This adaptability is another reason why starting with a fractional design plan is often more efficient than beginning with a full factorial design.
(3) Central composite design (CCD) for optimization
A central composite design is the third stage of your experimental journey. Full factorial and fractional designs are typically implemented as 2-level designs. These designs are effective for initial screening and understanding the linear relationships between factors and responses. However, they restrict the analysis to linear models, which may not capture the complete picture, especially in complex systems where effects can be non-linear.
Linear models, while simple and useful in many cases, may sometimes be insufficient for capturing the true nature of the process being studied. This is where CCD comes into play. CCD extends the design space by adding additional points to the existing design. This expansion allows for the exploration of curvature. While 3-level factorial designs are an alternative to explore non-linear relationships, they require a high number of experiments.
Another great application of CCDs is in the identification of robust process parameters. Those are less sensitive to variations and thus ensure consistent performance.
