To Find Out Second Order Model from First Order Factorial Design (DOE)

Hello DOE Friends.

Now on I try to find out the second order from factorial design. How the situation to confirm that the first order design can proceed to second order?

What things I need to consider?


Best regards,
Ridzwan Rahim
UiTM

If you are using Minitab, and you ran a standard 2^k-p fractional factorial design with center points, you can select Modify Design and Add Axial Points to change the design into a sequential Response Surface Design. You are limited to a Circumscribed or Face Centered design, but this is rarely an issue unless the new settings are not feasible.

Miner, thank you very much.

Yes I used MINITAB, and ran standard order 2^k-p fractional factorial with 3 center point. I have 4 factor and 3 center point.

The issue here, what are the rules and regulation that my first order can proceed to second order model miner?

Is that, I need to consider the main effect or interaction or curvature for getting significant before go to second order analysis?

Sorry Miner, I'm now in completing master. I don't have any statistical background. I think, this forum help me very much..

Thanks for your reply.

Best regards,
Ridzwan Rahim

I think I understand where you heading with this.

Let's assume that you want to optimize your process, and this requires moving your study beyond your existing design space. This is called sequential experimentation and involves three scenarios.

1. Scenario 1: There is no curvature and no interactions. Action: Find the path of steepest ascent or steepest descent (depending on the direction you need to move the response). Run a series of experiments along this path until you locate the region of interest then design and run another 2^k-p experiment in this region.

• Scenario 2: There is no curvature, but there are interactions. Action: Find the corner point with the largest (or smallest) value. Use this as the center point of a new 2^k-p experiment.

• Scenario 3: There is curvature. Action: Add axial points to the existing design to create a response surface design to determine the second order model. Use surface plots to determine path of exploration.

This is the basic approach. Obviously I am leaving a lot out because you can fill a textbook on this topic.

Miner, you mean when no curvature. The P-value for curvature is significant?

After I fit first order model, the P-value for curvature is 0.947.. Can I proceed to second order? Furthermore, can you give the name of text book that discuss about this methods..

Please every body... Help me.. :-(

Patience. Remember the time difference between Malaysia and the USA and Europe.

A high p-value means that there is no curvature and no need to proceed to a second order model. A low p-value (e.g., < alpha) means that there is curvature and you should progress to a response surface design in order to estimate the second order model.

Try Response Surface Methodology by Myers and Montgomery.

I'm sorry Miner. Alright, Thanks for your advices..

Miner, if I was developed second order equation model. The equation has a boundry condition or not. For example, My factors in this research are:

Torch Angle (70 degree, 110 degree)
Width Plate (50 mm, 150 mm)
Clamping Pose (0 mm, 100 mm)
Time Gaps (0 second, 60 second)

Is that my second order equation model just can be used within the parameter above, or can be beyond the parameters above?

RIDZWAN

I am unsure why you want to study the 2nd order model when curvature is not significant (p=.947).

Regarding the mechanics of what you are asking, the lower bounds of 0 on two of your factors preclude using a circumscribed central composite design. You have several options. You can augment your existing design by adding axial points that create a face centered central composite design, or you can create entirely new designs around the same center points. These designs include the inscribed central composite design or the Box-Behken design. All three of these options would stay within your existing design space.

Having said that, why do you expect to find significant second order terms when your curvature was not significant?