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06-10-2013
09:49 AM

06-10-2013
09:49 AM

Response Surface Modeling in PTC Mathcad

By Piet Watte

**Using A Box-Behnken experiment**

**About this worksheet:**

- Shows you how to conduct a box-behnken experiment as response surface modeling (RSM)
- Applicable in mechanical engineering
- Performs using box-behnken experiment, response surface modeling (RSM), contrast coefficient matrix, matrices, least squares estimators, t-tests, etc.

This worksheet using PTC Mathcad provides you with an example of a box-behnken experiment with three parameters at three levels. A box-behnken is an example of response surface modeling (RSM) and features the economics of experimentation. With the box-behnken you can estimate the linear, quadratic effects, and first order interactions.

This worksheet shows you how to fit an empirical model with three variables, given by the Meyers and Montgomery paper (in reference). To construct the response surfaces, you can hold one dimension constant and vary the other two. A results matrix returns the:

- coefficients of the model
- t-values
- the power of the t-test
- Significance of the coefficients

For significant testing, you are shown how to use the 'dt' function to perform the t-test. From the results table, coefficients with low power values are the most important and are the variables to be controlled. These types of experiments can be used across the board to aid in the design of experiments. All data, formulas, calculations, solutions, notation, and charts are provided to aid you in calculating your own solutions.

*Download and explore this worksheet yourself! You can download a free lifetime copy of PTC Mathcad Express and get 30 days of full functionality.*

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