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Lecture6-Design Expert Software - Tutorial | PDF | Design Of Experiments | Experiment
Experienced users of the software can start by building a New Design or loading an existing design with the Open Design button. Searchable, context-sensitive help can be called by clicking the question mark icon or F1 on the keyboard.
It provides assistance on what to do next. Design-Expert provides powerful tools to lay out an ideal experiment on your process, mixture or combination of factors and components. Build robust designs via in-line power calculations and the ability to add blocks and center points.
Design-Expert makes it easy to see what, if anything, emerges as statistically significant and how to model the results most precisely. Automated model-reduction tools, paired with in-line diagnostic graphs, provide a streamlined analysis process. It provides the confidence you need to present and publish your findings. Test it with one or more of the data sets that come with the software. Design-Expert offers a wide selection of graphs that help you identify standout effects and visualize your results.
Multiple cycles improve the odds of finding multiple local optimums, some of which will be higher in desirability than others. After grinding through 10 cycles of optimization, the results appear. The report view shows the results in tabular form. Due to the random starting conditions, your results are likely to be slightly different from those shown here. Note that the last solution falls short of the first for conversion. There may be some duplicates in between.
These passed through the filter discussed earlier. If you want to adjust the filter, go to the Options button and change the Duplicate Solutions Filter. If you move the Filter bar to the right you will decrease the number of solutions shown. Likewise, moving the bar to the left increases the number of solutions. The Solutions tool provides three views of the same optimization.
Drag the tool to a convenient location on the screen. Click on the solutions view option Ramps. Ramps Report on Numerical Optimization The ramp display combines the individual graphs for easier interpretation. The dot on each ramp reflects the factor setting or response prediction for that solution.
The height of the dot shows how desirable it is. Press the different solution buttons 1, 2, 3,… and watch the dots. They may move only very slightly from one solution to the next.
However, if you look closely at temperature, you should find two distinct optimums, one near 80 degrees and the other near 90 degrees. You may see slight differences in the results due to variations in approach from the various random starting points.
Select the Histogram view. Nearly duplicate solutions, as found by the duplicate solutions filter, will be eliminated. In this example, you will find two or more somewhat different solutions. You can cycle through each of the solutions: the best is listed first.
Press Graphs to view the results of the first optimization run. Go to the Factor control and right click on catalyst. Make it the Y axis. Temperature then becomes a constant factor at 90 degrees. You can plant additional flags by doing a right mouse click at any location. Right click again on the flag and Toggle size to see the associated desirability value and the factor levels.
To view the responses associated with the desirability, select the desired Response from the drop down list. Take a look at the plot for Conversion. Conversion Contour Plot with optimum flagged If you like, look at the optimal activity response as well. To look at the desirability surface in three dimensions, click again on Response and choose Desirability.
Then select View, 3D Surface from the main menu. Drag the tools out of the way as needed to view the results. Then rotate the plot for a different perspective by using the Rotation tool. Drag the rim of the wheels with your mouse pointer to change the orientation of the 3D plot.
You can change the quality of the 3D graph by going to the Edit, Preferences menu item, or by doing a right mouse click on the graph. Click on the Graph tab and then set parameters as you desire. Then if you have a printer attached, make a hard copy by doing a File, Print. Show your colleagues what Design - Expert software will do!
Then you can generate propagation of error POE plots that show how that error is transmitted to the response. Start by clicking on the Design node on the left side of the screen to get back to the design layout.
Then select View, Column Info Sheet. Enter the following info rmation into the Std. Click on the Conversion analysis node on the left to start the analysis again.
Then jump past the intermediate buttons for analysis and click on the Model Graphs button. The end result is a more robust process. However, POE will only work when the response surface is non-linear, such as for the Conversion. When the surface is linear, such as that for Activity, the error will be transmitted equally throughout the region.
Call, or check our web site for a schedule. Click on Numerical optimization node. Click on the alternate solutions 2, 3,…. Watch the red dots. What changes? Select the Graphs node. Click the number 1 solution. To make the view similar to what we had before, on the Factors tool palette change catalyst to the Y axis.
Also right-click on the flag and Toggle Size. This solution represents the formulation that best maximizes conversion and achieves a target value of 63 for activity, while at the same time finds the spot with the minimum error transmitted to the responses. So, this should represent process conditions that are robust to slight variations in the factor settings. To see a broader operating window, click on the Graphical node. You do not need to enter a high limit for the graphical optimization to work.
Enter 5 for the Upper Limit. Finally, click on the response of Activity. Enter 60 for the Lower Limit and 66 for the Upper Limit. Notice that regions not meeting your specifications are shaded out, leaving hopefully! Then press the Sheet option and set temperature as a constant Value at Click on the Gauges option to make the Factors Tool less obtrusive.
However, they must first be analyzed. In the first tutorial you developed a quadratic model for conversion and a linear model for activity. The shaded areas on the graphical optimization plot do not meet the selection criteria. The lines mark the high or low boundaries on the responses. Move the mouse pointer into the clear or yellow area. Right click to add a flag. The flag shows the predicted value of conversion, the propagation of error for conversion and activity, at that point on the plot.
Delete flags by right clicking on them and selecting Delete flag. You can explore this window for high values of conversion. Graphical optimization works great for two factors, but as the factors increase, it becomes more and more tedious.
You will find solutions much more quickly by using the numerical optimization feature. Then return to the graphical optimization and produce outputs for presentation purposes. Numerical optimization becomes essential when you investigate many components with many responses.
However, computerized optimization will not work very well in the absence of subject matter knowledge. For example, a naive user may define impossible optimization criteria.
The result will be zero desirability everywhere! To avoid this, try setting broad acceptable ranges. Narrow them down as you gain knowledge about how changing factor levels affect the responses. The quickest way of doing this is to press the standard save icon.
But you can also go to the File menu and select Save As. Type in the name of your choice for your data file. Then click Save. For Plackett Burman Design minimum factor is Response Surface Methodology RSM is an experimental technique invented to find the optimal response within the specified ranges of the factors.
These designs are capable of fitting a second order prediction equation for the response. The quadratic terms in these equations model the curvature in the true response function. If a maximum or minimum exists inside the factor region, RSM can find it. In industrial applications, RSM designs involve a small number of factors.
This is because the required number of runs increases dramatically with the number of factors. Axial or star points, for which all but one factor set at zero Axial midrange and one factor set at outer axial values. Centre Center points, for which all the factor values are at the zero Point or midrange value. This is sometimes useful when it is desirable to avoid these points due to engineering considerations.
The price of this characteristic is the higher uncertainty of prediction near the vertices compared to the Central Composite design. Open navigation menu. Close suggestions Search Search. User Settings. Skip carousel. Their names and levels are shown in the following table. The stars represent axial points.
How far out from the cube these should go is a matter for much discussion between statisticians. As you will see, Design- Expert offers a variety of options for alpha. Twelve runs: composed of eight factorial points, plus four center points. Eight runs: composed of six axial star points, plus two more center points. Design the Experiment Start the program by finding and double clicking the Design-Expert software icon. Welcome screen Press OK on the welcome screen.
Now go back and re-select Central Composite design. Click the down arrow in the Numeric Factors entry box and Select 3 as shown below. Notice that it defaults to a Rotatable design with the axial star points set at 1.
Press OK to accept the rotatable value. Using the information provided in the table on page 1 of this tutorial or on the screen capture below , type in the details for factor Name A, B, C , Units, and Low and High levels. Now return to the bottom of the central composite design form. You will need two blocks for this design, one for each day, so click the Blocks field and select 2. You now have the option of identifying Block Names.
Enter Day 1 and Day 2 as shown below. Block names Press Continue to enter Responses. Select 2 from the pull down list. Now enter the response Name and Units for each response as shown below. Completed response form At any time in the design-building phase, you can return to the previous page by pressing the Back button.
Then you can revise your selections. Press Continue to view the design layout your run order may differ due to randomization. Click the Tips button for a refresher.
Click the File menu item and select Save As. Obviously at this stage the responses must be entered into Design-Expert. We see no benefit to making you type all the numbers, particularly with the potential confusion due to differences in randomized run orders.
Click Open to load the data. Move your cursor to Std column header and right-click to bring up a menu from which to select Sort Ascending this could also be done via the View menu. Notice how the factorial points align only to the Day 1 block. Then in Day 2 the axial points are run. Center points are divided between the two blocks. Unless you change the default setting for the Select option, do not expect the Type column to appear the next time you run Design-Expert.
It is only on temporarily at this stage for your information. Before focusing on modeling the response as a function of the factors varied in this RSM experiment, it will be good to assess the impact of the blocking via a simple scatter plot.
You should see a scatter plot with factor A:Time on the X-axis and the Conversion response on the Y-axis. Block versus run or, conversely, run vs block is also highly correlated due to this restriction in randomization runs having to be done for day 1 before day 2.
It is good to see so many white squares because these indicate little or no correlation between factors, thus they can be estimated independently.
For now it is most useful to produce a plot showing the impact of blocks because this will be literally blocked out in the analysis. Therefore, on the floating Graph Columns tool click the button where Conversion intersects with Block as shown below. Plotting the effect of Block on Conversion The graph shows a slight correlation 0. Whether this is something to be concerned about would be a matter of judgment by the experimenter. However it may in this case be such a slight difference that it merits no further discussion.
Bear in mind that whatever the difference may be it will be filtered out mathematically so as not to bias the estimation of factor effects. Changing response resulting graph not shown Finally, to see how the responses correlate with each other, change the X Axis to Conversion. For example, choose Color by Block to see which points were run in block 1 black and block 2 red. Under the Analysis branch click the node labeled Conversion. A new set of tabs appears at the top of your screen.
They are arranged from left to right in the order needed to complete the analysis. What could be simpler? Click Tips for details. For now, accept the default transformation selection of None. Now click the Fit Summary tab. At this point Design-Expert fits linear, two-factor interaction 2FI , quadratic, and cubic polynomials to the response. By design, the central composite matrix provides too few unique design points to determine all the terms in the cubic model.
Next you will see several extremely useful tables for model selection. Each table is discussed briefly via sidebars in this tutorial on RSM. So far, Design-Expert is indicating via underline the quadratic model looks best — these terms are significant, but adding the cubic order terms will not significantly improve the fit.
Use the handy Bookmarks tool to advance to the next table for Lack of Fit tests on the various model orders. The quadratic model, identified earlier as the likely model, does not show significant lack of fit. Remember that the cubic model is aliased, so it should not be chosen. Always confirm this suggestion by viewing these tables.
Design-Expert allows you to select a model for in-depth statistical study. Click the Model tab at the top of the screen to see the terms in the model. Be sure to try this in the rare cases when Design-Expert suggests more than one model. The options for process order At this stage you could make use of the Add Term feature. Also, you could now manually reduce the model by clicking off insignificant effects.
For example, you will see in a moment that several terms in this case are marginally significant at best. You can also see probability values for each individual term in the model.
You may want to consider removing terms with probability values greater than 0. Use process knowledge to guide your decisions. The R-Squared statistics are very good — near to 1. Post-ANOVA statistics Press forward to Coefficients to bring the following details to your screen, including the mean effect-shift for each block, that is, the difference from Day 1 to Day 1 in the response.
Block terms are left out. These terms can be used to re-create the results of this experiment, but they cannot be used for modeling future responses. However, you can copy and paste the data to your favorite Windows word processor or spreadsheet. This might be handy for client who are phobic about statistics. The most important diagnostic — normal probability plot of the residuals — appears by default. A non-linear pattern such as an S-shaped curve indicates non-normality in the error term, which may be corrected by a transformation.
The only sign of any problems in this data may be the point at the far right.
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