This is the first installment in the Industrial Statistics Virtual Collaboratory, from Peter Parker at NASA. Feel free to comment directly on this post, though commenting is presently limited to ASA members. If interested in collaborating with Dr. Parker, you may also contact him directly at peter.a.parker@nasa.gov.
The next post on this forum will happen the week of July 17.
If you would like to contribute an entry to the ISVC (see
the initial post for details), please contact Byran Smucker (smuckerb@miamioh.edu).
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Near Replication in Response Surface Designs
In classical design of experiments and response surface methods (RSM), we cherish our model independent, pure error estimates based on replication. However, in my experience, we often have the ability to measure the actual set point values to a higher precision than we can set them. For the regression model building, these slight departures from nominal set point values do not pose any problems. However, for replicates that are defined by identical factor level settings, we can no longer perform a simple estimate of pure error. In this case, we have near replicates, but not exact replicates.
Various approaches have been considered. An intuitive, simple approach analyzes the deviation in the factor settings and makes a determination based on the response surface model whether there is a significant amount of variation in the explanatory variables transmitted to the pure error estimates. Another approach is proposed by Montgomery, Martin, and Peck (1980) to compute an estimate of pure error from points that are near neighbors. Alternatively, rather than using a global RSM model, a local model in the vicinity of the replicates may be useful to numerically adjust the response to a nominal factor level setting, essentially creating pseudo–replicates.
In practice, I have not found any of these approaches to be wholly satisfactory and decisions on their application remains a bit ad hoc. I would welcome the opportunity to brainstorm approaches, compare and evaluate them, and write a review paper providing practitioner guidance on this topic.
Reference:
Montgomery, Martin, and Peck (1980), "Interior Analysis of the Observations in Multiple Linear Regression," Journal of Quality Technology, 12(3), pg. 165-173.
Peter A. Parker, Ph.D., P.E.
Senior Statistician
Team Lead, Advanced Measurement Systems
NASA Langley Research Center
peter.a.parker@nasa.gov
Office: 757-864-4709