1. Just please tell me for optimization do we analyze RSM results or do the D-optimal design first?

I think you are confusing the process of optimizing a design/process with an optimal design.

You can perform a standard RSM and use the model resulting from the analysis to optimize your design/process.

An optimal design is a completely different topic. Optimal designs are used to:

- Efficiently fill out an irregular shaped experimental region
- Minimize the number of runs to just what is needed
- Accommodate unusual numbers of blocks or runs per block

2. Second question is in selecting RSM, what is the importance of alpha in selecting design. If I take default values, it creates a DoE matrix using some values out of the cube and bogus. If I take Face centered it gives me reasonable values withing limits.

There are two major types of RSM designs. Central Composite Designs and Box-Benkhen designs. Take a simple design with 3 factors. You can visualize the design space as a cube.

A Box-Benkhen design has experimental runs at the center of each edge of the cube. The main advantage of this design type is to avoid those regions of the experimental space (i.e., the corners) that are either not feasible, or are dangerous.

A Central Composite design has experimental runs at each corner of the cube, at the center of the cube and along an axis running through the center of each face of the cube (and through the center of the cube). The location of these last along those axes is controlled by alpha.

In Minitab, the default alpha (alpha > 1) results in a Central Composite Circumscribed design, which means the corner points and the axial points all fall on the surface of a sphere. This has a lot of advantages, but does have the disadvantage that you encountered. That you have runs that are not feasible. The face centered design (alpha = 1) avoids this problem by moving the axial points onto the faces of the cube. However, this results in greater error in the quadratic coefficients of the model. The custom design allows you to set alpha. Setting alpha < 1 will move the axial points inside the cube. You can also set alpha slightly > 1 to move the axial points slightly outwards, but not as far as the default.

One caution regarding RSM designs in general. The model that you end up with is a quadratic (polynomial) model. This is usually an approximation of a nonlinear model. You can still use it to optimize and even make predictions, but there will be some inherent errors in this approximation. The accuracy of the model will change as you move through the design space. See the attached

image from Wikipedia.