Hi everyone, I attempted to apply Response Surface Methodology (RSM) using a Central Composite Design (CCD) to optimize a 3-factor system for a specific component yield. The factors were:
- Time: 5–15 min
- Pressure: 100–200 MPa
- Enzyme concentration: 0.5–2.5%
I used both R Studio and Minitab to generate the experimental design. However, in both cases, the software produced one or two negative values for time and enzyme concentration, and in one instance, the pressure exceeded the specified maximum of 200 MPa.
Is this behavior typical when generating CCD designs? How can I fix the problem?
Dear Abu Saeid,
Yes, it is typical for Central Composite Design (CCD) in Response Surface Methodology (RSM) to generate experimental points that fall outside the specified factor ranges, including negative values or values exceeding your maximum limits. This occurs due to the inclusion of axial (or star) points in CCD, which are placed beyond the factorial region to help estimate curvature in the model. For three factors, the axial distance (α) is usually set around 1.682 to maintain rotatability, which can result in values below your minimums (e.g., time < 5 min or enzyme concentration < 0.5%) or above your maximums (e.g., pressure > 200 MPa). If these extremes are not experimentally feasible, you can address the issue by switching to a face-centred CCD, where α = 1, ensuring all points lie within the original factor bounds. Alternatively, you can use a Box–Behnken Design (BBD), which also avoids extreme combinations and stays within practical operating ranges. If you are using R or Minitab, both allow you to specify a face-centred design to avoid invalid values while still supporting accurate model fitting within your desired range.
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