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Design expert 11 pdf free. Design-Expert 9 User's Guide Mixture Tutorial  1 Mixture Design Tutorial (Part 1/2 – The Basics

 

You now need to enter responses into the Design-Expert software. For tutorial purposes, we see no benefit to making you type all the numbers. Select File, Open Design. Click the file named Mix. Press OK. You now should be displaying the response data shown below. Note the design layout returns to the default selection, which we have not changed.

In some cases this improves the statistical properties of the analysis. For example, when responses vary over several orders of magnitude, the log scale usually works best. Also, leave the coding for analysis as pseudo because this re-scales the actual component levels to 0 — 1. In the meantime, bring up Help, Contents. Select Component Scaling in Mixture Designs.

After studying all the information you find here, close Help by pressing X. Next click the Fit Summary tab. Here Design-Expert fits linear, quadratic, special cubic, and full cubic polynomials to the response. Drag it to the right. To begin your analysis, look for any warnings about aliasing.

In this case, the full cubic model and beyond could not be estimated by the chosen design — an augmented simplex design. Remember, you chose only to fit a quadratic model, so this should be no surprise. Now on the floating Bookmarks press forward to the Sum of Squares breakdown. This is the default model if none of the factors causes a significant effect on the response.

The output then shows the significance of each set of additional terms. Due to the constraint that the three components must sum to a fixed total, you will see only two degrees of freedom associated with the linear mixture model.

In this case, these terms are aliased. Always confirm this suggestion by reviewing all tables under Fit Summary. On the floating Bookmarks tool click Lack of Fit to move on to the next table. This table compares residual error with pure error from replication. If residual error significantly exceeds pure error, then deviations remain in the residuals that can be removed using a more appropriate model.

Residual error from the linear model shows significant lack of fit this is bad , while quadratic, special cubic, and full cubic do not show significant lack of fit this is good. Lack of fit table At this point the quadratic model statistically looks very good indeed. These tables, or any selected subset, can be cut and pasted into a word processor, spreadsheet, or any other Window application.

You may select models other than this defaulting quadratic model from the pull down list. Be sure to do this in the rare cases when Design-Expert suggests more than one model.

On the current screen you are allowed to manually reduce the model by clicking off terms that are not statistically significant. For example, in this case, you will see in a moment that the AB term is not statistically significant. You will see a recommendation pop up on what works best as a general rule. If you really want to be competent on this, attend our Mixture Design for Optimal Formulations workshop.

Close Tips by clicking X. That is good as you will infer from the annotation provided by Design-Expert. The probability values show the significance of each term. Because the mixture model does not contain an intercept term, the main effect coefficients linear terms incorporate the overall average response and are tested together.

Use Bookmarks to jump to the next report — R-Squared statistics. Note the more than adequate precision Adeq Precision value of Next, view the coefficients and associated confidence intervals for the quadratic model. The annotations provide ideas on how they differ.

Diagnose the Statistical Properties of the Model The most important diagnostic, the normal probability plot of the residuals, comes up by default. Normal Probability Plot of Residuals The data points should be approximately linear. A non-linear pattern such as an S-shaped curve indicates non-normality in the error term, which may be corrected by a transformation. There are no signs of any problems in our data.

Be aware that residuals are externally studentized unless you elect otherwise not advised. Studentization counteracts varying leverages due to design point locations. For example, center points carry little weight in the fit and thus exhibit low leverage.

Externalizing the residuals isolates each one in comparison to the others so discrepant results stand out more. Now click the Influence option. To bring up bring up case-by-case details on many of the statistics shown graphically for diagnostic purposes: Press Report. It measures change in each predicted value that occurs when that response is deleted. Given that only this one diagnostic is flagged, it probably is not a cause for alarm.

Explanations for most of these graphs are addressed in earlier tutorials. Get more details via Screen Tips and Help. Click the Model Graphs tab. The 2D contour plot comes up by default in graduated color shading. In this case you see a plot of viscosity as a function of the three mixture components. Move this floating tool as needed by clicking on the top blue border and dragging it. The tool controls which factor s are plotted on the graph. The Gauges view is the default. Each component listed has either an axis label, indicating that it is currently appearing on the graph, or a red slider bar, which allows you to choose specific settings for those not currently plotted.

This case study involves only three components, all of which fit on one mixture plot — a ternary diagram. Therefore, you do not see any red slider bars. If you did, they would default to the midpoint levels of the components not currently assigned to axes. You could then change a level by dragging the red slider bars left or right. Place your mouse cursor over the contour graph. Then notice in the lower-left corner of the screen that Design-Expert displays the predicted response and coordinates.

Coordinates display at lower-left corner of screen To enable a handier tool for reading coordinates off contour plots, go to View, Show Crosshairs Window. Showing crosshairs window Now move your mouse over the contour plot and notice that Design-Expert generates the predicted response for specific values of the factors that correspond to that point.

Full Crosshairs display Close the crosshairs window by clicking X. With your left mouse button held down, drag over the lower right corner of the contour graph.

Corner identified for zoom Now the area you chose is magnified. You can do this with the trace plot, which provides silhouette views of the response surface. The real benefit from this plot is for selecting axes and constants in contour and 3D plots. From the floating Graphs Tool select Trace. Trace plots show the effects of changing each component along an imaginary line from the reference blend defaulted to the overall centroid to the vertex.

For example, click on the curve for A and it changes color. Check this out by going to the Trace Graph tool and pressing Cox. In the Cox direction, as the amount of any component increases, the amounts of all other components decrease, but their ratio to one another remains constant.

Chemists may like this because it preserves the reaction stoichiometry. However, when plotted in this direction, traces for highly constrained mixture components such as a catalyst for a chemical reaction become truncated.

For this reason Piepel is the preferred plot in Design-Expert. Trace plots depend greatly on where you place the starting point by default the centroid. See for yourself by moving slide bars on the Factors Tool. When you are done, press the Default. Consider that the traces are one- dimensional only, and thus cannot provide a very useful view of a response surface. A 3D response plot provides a better picture of the surface, and ultimately provides the basis for numerical optimization. If you experiment on more than three mixture components, use the trace plot to find those components that most affect the response.

Choose these influential components for the axes on the contour plots. Set as constants those components that create relatively small effects. Your 2D contour and 3D plots will then be sliced in ways that are most visually interesting. For example, if you design for four components, the experimental space is a tetrahedron.

Generating a 3D View of the Response Surface Now to really get a feel for how response varies as a function of the two factors chosen for display, select View, 3D Surface. A three-dimensional display of the response surface appears.

If coordinates encompass actual design points, these emerge. Then click and hold the left mouse-button and drag. Try it! Control for rotating 3D plot Move your cursor over the tool.

The pointer changes to a hand. Now use the hand to rotate the vertical or horizontal wheel. Watch the 3D surface change. Give this a try, too. Then press Default and X off the view of Rotation tool.

Design-Expert offers many options for 3D graphs via its Graph Preferences, which come up with a right-click over the plot. Response Prediction Response prediction in Design-Expert software falls under the Post Analysis branch, which will be explored more fully in the next tutorial in this series.

It allows you to generate predicted response s for any set of factors. To see how this works, click the Point Prediction node. The Factors Tool opens along with the point prediction window. Move the floating tool as needed by clicking and dragging the top border.

You can also drag the handy red sliders on the component gauges to view other blends. Note that in a mixture you can only vary two of the three components independently. Can you find a combination that produces viscosity of 43? Hint: push Urea up a bit. Design-Expert makes adjustments as you go — perhaps in ways you do not anticipate. Analyze the data for the second response, turbidity Y 2.

Be sure you find the appropriate polynomial to fit the data, examine the residuals, and plot the response surface. Hint: The correct model is special cubic.

Before you quit, do a File, Save to preserve your analysis. Design-Expert saves your models. To leave Design-Expert, use the File, Exit menu selection.

This tutorial gives you a good start using Design-Expert software for mixtures. We suggest you now go on to the Mixture Optimization Tutorial. You also may want to work the tutorials about using response surface methods RSM for process variables. To learn more about mixture design, attend Mixture Design for Optimal Formulations, a two-day workshop presented by Stat-Ease. Call or visit our web site at www. Call for information on content and schedules, or better yet, visit our web site at www.

Start the program by finding and double clicking the Design-Expert software icon. To ensure being on the same page for this tutorial, go to File and Open Design file Mix-a. The file you just loaded includes analyzed models as well as raw data for each response. Recall that the formulators chose a three-component simplex lattice design to study their detergent formulation.

The components are water, alcohol, and urea. The experimenters held all other ingredients constant. They measured two responses: viscosity and turbidity.

You will now optimize this mixture using their analyzed models. Drag the left border and open the window to see the report better.

You can also re-size columns with your mouse. Now look at the bottom lines on responses R1 viscosity and R2 turbidity. That is good to know. For complete details on the models fitted, click the Coefficients Table node at the bottom left of the Design-Expert screen the last branch. We lead you through the last above case: a multiple-response optimization.

Under the Optimization branch of the program, click the Numerical node to start the process. We will get to POE later. The limits for the responses default to the observed extremes.

Desirabilities range from zero to one for any given response. The program combines individual desirabilities into a single number and then searches for the greatest overall desirability.

A value of one represents the ideal case. A zero indicates that one or more responses fall outside desirable limits. In this case, components are allowed to range within their pre-established constraints, but be aware they can be set to desired goals. For example, because water is cheap, you could set its goal to maximize.

Options for goals on components Notice that components can be set equal to specified levels. Enter Limits as Lower of 39 and Upper of Press Tab to set your entries. Values outside that range have no zero desirability.

Now click the second response — Turbidity. Select its Goal to minimize, with Limits set at Lower of and Upper of You must provide both these thresholds to get the desirability equation to work properly. By default they are set at the observed response range, in this case to On the other hand, when turbidity exceeds , it looks as bad as it gets. Aiming for minimum on second response of turbidity These settings create the following desirability functions: 1.

Close out Tips by pressing X at the upper-right corner of its screen. Weights give added emphasis to upper or lower bounds, or emphasize a target value. With a weight of 1, di varies from 0 to 1 in linear fashion. Weights greater than 1 maximum weight is 10 give more emphasis to goals. Weights less than 1 minimum weight is 0. Try pulling the handle on the ramp down as shown below.

Weights change by grabbing handle with mouse Notice that Weight now reads Before moving on, re-enter Upper Weights to its default value of 1 and press the Tab key. This straightens the desirability ramp. If you want to emphasize one variable over the rest, set its importance higher. By leaving all importance criteria at their defaults, none of the goals is favored over any other. It is intended to insulate experimenters that are new to Design-Expert from the myriad of design choices, and act as an informative guide.

This feature can also benefit the experienced DOE practitioner. 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. Click on a number in a cell of the report and right-click in the cell to request help to learn more about its contents. Screen tips provide instructions for what to do or what to look for on the current screen. Stat-Ease Tutorials are available online and included on installation CDs.