How should a PDS analyst choose the five values in "PDDOEL,par,CCD,PHYS,ALL,val1,val2,val3,val4,val5" when s/he only has the upper and lower boundaries?
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The CCD sampling is a 5-level design having (-alpha, -1, 0, +1, +alpha). The alpha is selected using some statistical criteria such that the variance is constant for all the sampling points from the origin. The constant variance is one of the assumptions required for the response surface modeling. With this in mind, if you provide physical lower and upper boundaries, the physical lower and upper boundaries are mapped into the design levels of - alpha and + alpha respectively. In this case, as you can imagine, regardless of distribution type selected for the input variables, you are exploring the same design space, which means you will have the same response surface. It makes a difference only when you generate probabilistic samples from the response surface, because the samples are generated according to their probability density function, and each distribution type has a different density within the design space. Now, if you define the lower and upper boundaries using probability levels, we will evaluate the physical lower and upper boundaries according to the lower and upper probability levels.With these calculated physical lower and upper boundaries, we then mapped them into design levels of -1 and +1. In this case, the distribution type you define for the input variables will change the explored design space used for response surface fit, because each distribution type has different shape of probability density function (and thus the tails of distribution). You will very likely to have a different look of response surface. It is not surprising if you don`t see any different, because it depends on the physics of the problem; the physics of the problem doesn`t have a dramatic change in these different explored design space. It is recommended to provide lower and upper boundaries, either inprobability levels and physical bounds, and to let us evaluate the intermediate points using the statistical criteria. Unless you know what you want (for advanced users in this area), you can specify your own five values, which we then mapped them directly into the 5 design levels if you provide physical values. We will evaluate the physical values if you provide probability levels before we mapped them into the 5 design levels. |
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