How many center points to add in a design?

[#1]

I understand we add center points to designs to test for curvature in design. Does adding more than 1 center point to design helps with better estimation?

[#2]

Center points are beneficial if one is restricting their core DOE tactics to some sort of two level, perhaps RSM design. Recent research suggests that if power and estimability of effects is a primary goal of the investigator then one should consider an optimal design of experiments approach. A great reference for optimal DOE strategies, tactics, and case studies is "Optimal Experimental Design - A Case Study Approach" by Goos and Jones. In JMP you can formulate all manner of specific designs and then use the Compare Designs platform to evaluate the performance of each design BEFORE actual experimentation for power, prediction variance, correlation of coefficients, and many additional experimental design performance criteria.

[#3]

Thank you Bartell for your response. I understand what you are saying but I want to know is there any advantage of adding more than 1 center point or what is the advantage of adding more than 1 center point if we can test for curvature with 1 center point?

[#4]

The lack of fit test requires more than 1 center point to estimate the pure error for the usual design with two levels.

You could exclude the lone center point from the regression analysis and visually assess if it agrees or disagrees with the first order model in the Actual by Predicted plot, but this assessment might not provide a clear answer. The lone center point observation could be an outlier or an 'inlier.' Your response could be relatively noisy, too.

[#5 · Accepted solution]

Adding one more run always helps estimation. Adding more than one center point guarantees that you can estimate the pure error and perform a lack of fit test with this estimate. (There are other benefits of the information provided by the center points.) If you are asking about estimating any non-linear effects, then no additional center points alone will support it. You must add terms to the model (e.g., powers of factor levels) to insure that the design will contain treatments that support estimating such effects. The number of runs will affect the power of the lack of fit test but generally the cost of the additional center points determines the number.

You appear to not know if there are non-linear effects in the response. That is OK. It just says something about prior knowledge that is available to the design of the next experiment. You might also not know much about potential interaction effects. If you have a large number of factors (e.g., more than 5) and you are concerned about the number of runs, then you might consider a definitive screening design. These design are economical and supposing that the screening principals hold, you are likely to be able estimate all the effects, linear and non-linear. If these principals do not hold, of course, you might not have sufficient or correct runs to sort out all the effects.

[#6]

Thnak you Mark for the explanation. This helps.