Statistics Toolbox

Design of Experiments Demo

The rsmdemo utility is an interactive graphic environment that demonstrates the design of experiments and surface fitting through the simulation of a chemical reaction. The goal of the demo is to find the levels of the reactants needed to maximize the reaction rate.

Suitable designs for this experiment include the central composite designs and Box-Behnken designs, described in the previous two sections, and the D-optimal designs, described in D-Optimal Designs. This demo uses D-optimal designs.

There are two parts to the demo:

• Comparing Results from Trial-and-Error Data and a Designed Experiment
• Comparing Results Using a Polynomial Model and a Nonlinear Model

Comparing Results from Trial-and-Error Data and a Designed Experiment

This part of the experiment compares the results obtained using data gathered through trial and error and using data from a designed experiment.

1. To begin, run the rsmdemo function.

• rsmdemo
  

2. Click Run in the Reaction Simulator window to generate a test reaction for the trial and error phase of the demo.

   

1. To perform the experiment, you can click Run as many as 13 times. For each run, based on the results of previous runs, you can move the sliders in the Reaction Simulator window to change the levels of the reactants to increase or decrease the reaction rate.

   Each time you click the Run button, the levels for the reactants and results of the run are displayed in the Trial and Error Data window. You can use the Export button to write the values of the reactants and the reaction rate for each run to the base workspace.

   

Note    The results are determined using an underlying model that takes into account the noise in the process, so even if you keep all of the levels the same, the results will vary from run to run. In this case however, the Analyze function will not be able to generate a fit for the results.

3. When you have completed the runs, use the Plot menu on the Trial and Error Data window to plot the relationships between the reactants and the reaction rate. For this set of 13 runs,

   

1. You can use the Export button to write the values of the reactants and the reaction rate for each run to the base workspace.

   rsmdemo produces the following plot if you select Isopentane vs. Rate.

   

4. Click the Analyze button to call the rstool function, which you can then use to try to optimize the results. See Exploring Graphs of Multidimensional Polynomials for more information about using the rstool demo.
5. Now, perform another set of 13 runs, this time from a designed experiment. In the Experimental Design Data window, click the Do Experiment button. rsmdemo calls the cordexch function to generate a D-optimal design, and then, for each run, computes the reaction rate.

   

6. Now use the Plot menu on the Experimental Design Data window to plot the relationships between the levels of the reactants and the reaction rate. This figure shows the plot for Isopentane vs. Rate.

   

7. You can also click the Response Surface button to call rstool to find the optimal levels of the reactants.
8. Compare the analysis results for the two sets of data. It is likely (though not certain) that you'll find some or all of these differences:
• You can fit a full quadratic model with the data from the designed experiment, but the trial and error data may be insufficient for fitting a quadratic model or interactions model.
• Using the data from the designed experiment, you are more likely to be able to find levels for the reactants that result in the maximum reaction rate. Even if you find the best settings using the trial and error data, the confidence bounds are likely to be wider than those from the designed experiment.

Comparing Results Using a Polynomial Model and a Nonlinear Model

This part of the experiment analyzes the experimental design data with a polynomial (response surface) model and a nonlinear model, and compare the results. The true model for the process, which is used to generate the data, is actually a nonlinear model. However, within the range of the data, a quadratic model approximates the true model quite well.

1. Using the results generated in the designed experiment part of Comparing Results from Trial-and-Error Data and a Designed Experiment, click the Response Surface button on the Experimental Design Data window. rsmdemo calls rstool, which fits a full quadratic model to the data. Drag the reference lines to change the levels of the reactants, and find the optimal reaction rate. Observe the width of the confidence intervals.

   

2. Now click the Nonlinear Model button on the Experimental Design Data window. rsmdemo calls nlintool, which fits a Hougen-Watson model to the data. As with the quadratic model, you can drag the reference lines to change the reactant levels. Observe the reaction rate and the confidence intervals.

   

3. Compare the analysis results for the two models. Even though the true model is nonlinear, you may find that the polynomial model provides a good fit. Because polynomial models are much easier to fit and work with than nonlinear models, a polynomial model is often preferable even when modeling a nonlinear process. Keep in mind, however, that such models are unlikely to be reliable for extrapolating outside the range of the data.

Box-Behnken Designs

D-Optimal Designs