Dear Dhanesh G Mohan,

Regarding your question, I recommend you to review topics in this webpage: https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/doe/supporting-topics/response-surface-designs/response-surface-central-composite-and-box-behnken-designs/

Regards,

BBD have less design points when compare to axial points of CCD hence no of experiments are more in CCD compared to BOX BEHNKEN.

CCD also tests at extreme conditions and hence this gives better for quadratic models

CCD will require more experiments (20 experiments for 3 factors) as compared to BBD (15 experiments for 3 factors). BBD is more nearer to the face centered composite design (alpha=1) but with fewer experiments. For CCD However alpha=square root of number of experiments.

In the Box-Behnken method there is no point in the cubic vertex that creates the upper and lower bounds of each variable, that is, all the tested points are within a predetermined range, so that the beginning and end points of the interval are less accurate than They have other points.

When out-of-range tests are not possible due to physical or conceptual limitations, this method is recommended (for example, when the concentration starts at zero with no negative range). The number of factors to consider in this method is 3 to 7 factors.

In the central composit method for each factor there are points outside the minimum and maximum range, so under similar conditions, often the number of tests is greater than Box-Behnken. The number of factors to consider in this method is 2 to 6 factors.

To choose the best design for the experiments, a list of things you should know Central Composite Design and Box-Behnken Design.

Central Composite Design (CCD)

• Developed for estimating a quadratic model
• Created from a two-level factorial design, and augmented with center points and axial points
• Relatively insensitive to missing data
• Features five levels for each factor (Note: The number of levels can be reduced by choosing alpha=1.0, a face-centered CCD which has only three levels for each factor.)
• Provides excellent prediction capability near the center (bullseye) of the design space

Box-Behnken Design (BBD)

• Created for estimating a quadratic model
• Requires only three levels for each factor
• Requires specific positioning of design points
• Provides strong coefficient estimates near the center of the design space, but falls short at the corners of the cube (no design points there)
• BBD vs CCD: If you end up missing any runs, the accuracy of the remaining runs in the BBD becomes critical to the dependability of the model, so go with the more robust CCD if you often lose runs or mismeasure responses.

Sources:

https://www.statease.com/blog/choosing-best-design-process-optimization/

Box-Behnken design often has fewer design points; they can be less expensive to do than central composite designs with the same number of factors. Central composite designs usually have axial points outside the "cube." These points may not be in the region of interest, or may be impossible to conduct because they are beyond safe operating limits. Box-Behnken designs do not have axial points, thus, you can be sure that all design points fall within your safe operating zone. Box-Behnken designs also ensure that all factors are not set at their high levels at the same time. Hence, Box-Behnken design is easy to predict the lower and upper limits at 3 level point.

You can use a central composite design to:

• Efficiently estimate first- and second-order terms.
• Model a response variable with curvature by adding center and axial points to a previously-done factorial design.Central composite designs are especially useful in sequential experiments because you can often build on previous factorial experiments by adding axial and center points.

IN RSM, STEEPNEES SHOWS THE SENSITIVITY OF THE PARAMETER AND FLAT SHOWS THE ROBOUSTNESS OF THE PARAMETER.

My new paper (it is free) is a good practical example:

Article Techno-economical aspects of electrocoagulation optimization...

The main difference between central composite design (CCD) and box behnken design (BBD) is STAR points (axial points). If you have big difference between the value of star point(s) with factorial point(s), it is better to use box behnken design or change the values of parameter(s):

Techno-economical aspects of electrocoagulation optimization in three acid azo dyes’ removal comparison

Compared to Box-Behnken, the center composite design was more accurate yet still effective.

I.D. Boateng, X.-M. Yang, Process optimization of intermediate-wave infrared drying: Screening by Plackett–Burman; comparison of Box-Behnken and central composite design and evaluation: A case study, Ind. Crops Prod. 162 (2021) 113287. https://doi.org/10.1016/j.indcrop.2021.113287