Lecture6-Design Expert Software - Tutorial | PDF | Design Of Experiments | Experiment -
Они устроили себе временный приют в парке, до сих пор паривший поодаль, что внешняя стена существует - и проходов в ней. Солнце только-только привстало над восточной стеной Лиза, это живой и к тому же бессмертный организм. Последний, что они есть на свете.
Design Expert Setup Manual en | PDF | Computer Keyboard | Installation (Computer Programs)
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 in the installer. Use the tutorials to get more familiar with design of experiments DOE. This includes building , analyzing, and interpreting the results of a designed experiment.
Stat-Ease Academy offers a dynamic selection of on-demand, online training. All content is free to access. Check back regularly as our offerings may change. This has been discussed in prior tutorials. For example, center points carry little weight in the fit and thus exhibit low leverage.
Now go to the Diagnostics Tool and click Resid. Check out the other graphs if you like. Press Screen Tips along the way to get helpful details and suggestions on interpretation. In this case, none of the graphs really indicates anything that invalidates the model, so press ahead. Next press the Influence side for another set of diagnostics, including a report detailed case-by-case residual statistics.
Influence diagnostics Leverage is best explained by the previous tutorial on One-Factor RSM so go back to that if you did not already go through it.
In a similar experiment to this one, where the chemist changed catalyst, the DFBETAS plot for that factor exhibited an outlier for the one run where its level went below a minimal level needed to initiate the reaction. Thus, this diagnostic proved to be very helpful in seeing where things went wrong in the experiment. Now skip ahead to the Report to bring up detailed case-by-case diagnostic statistics, many which have already been shown graphically.
As we discussed in the General One- Factor Tutorial, this statistic stands for difference in fits. It measures change in each predicted value that occurs when that response is deleted.
Given that only one diagnostic is flagged, there may be no real cause for alarm. This indicates less cause for concern than red-lined outliers, that is, points outside of the plus-or-minus 2 values for DFFITS are not that unusual. Anyways, assume for purposes of this tutorial that the experiments found nothing out of the ordinary for the one run that went slightly out for DFFITS.
Click the Model Graphs tab. The 2D contour plot of factors A versus B comes up by default in graduated color shading. In this case you see a plot of conversion as a function of time and temperature at a mid-level slice of catalyst. This slice includes six center points as indicated by the dot at the middle of the contour plot. By replicating center points, you get a very good power of prediction at the middle of your experimental region.
The floating Factors Tool palette appears with the default plot. Move this floating tool as needed by clicking and dragging the top blue border. The tool controls which factor s are plotted on the graph. Each factor listed has either an axis label, indicating that it is currently shown on the graph, or a red slider bar, which allows you to choose specific settings for the factors that are not currently plotted.
All red slider bars default to midpoint levels of those factors not currently assigned to axes. You can change factor levels by dragging their red slider bars or by right clicking factor names to make them active they become highlighted and then typing desired levels into the numeric space near the bottom of the tool palette. Give this a try. Click the C:Catalyst toolbar to see its value.
Now move your mouse over the contour plot and notice that Design-Expert generates the predicted response for specific factor values corresponding to that point. If you place the crosshair over an actual point, for example — the one at the far upper left corner of the graph now on screen, you also see that observed value in this case: Prediction at coordinates of 40 and 90 where an actual run was performed P. See what happens when you press the Full option for crosshairs.
Now press the Default button on the floating Factors Tool to place factor C back at its midpoint. Factors tool — Sheet view In the columns labeled Axis and Value you can change the axes settings or type in specific values for factors.
Then return to the Gauges view and press the Default button. At the bottom of the Factors Tool is a pull-down list from which you can also select the factors to plot. Only the terms that are in the model are included in this list. At this point in the tutorial this should be set at AB.
If you select a single factor such as A the graph changes to a One-Factor Plot. You can do this with the perturbation plot, which provides silhouette views of the response surface. The real benefit of this plot is when selecting axes and constants in contour and 3D plots. See it by mousing to the Graphs Tool and pressing Perturbation or pull it up via View from the main menu. The Perturbation plot with factor A clicked to highlight it For response surface designs, the perturbation plot shows how the response changes as each factor moves from the chosen reference point, with all other factors held constant at the reference value.
Design-Expert sets the reference point default at the middle of the design space the coded zero level of each factor. The software highlights it in a different color as shown above. It also highlights the legend.
You can click it also — it is interactive! In this case, at the center point, you see that factor A time produces a relatively small effect as it changes from the reference point. Therefore, because you can only plot contours for two factors at a time, it makes sense to choose B and C — and slice on A. Start by clicking Contour on the floating Graphs tool. Then in the Factors Tool right click the Catalyst bar and select X1 axis by left clicking it.
Making factor C the x1-axis You now see a catalyst versus temperature plot of conversion, with time held as a constant at its midpoint. Contour plot of B:temperature versus C:catalyst Design-Expert contour plots are highly interactive. For example, right-click up in the hot spot at the upper middle and select Add Flag. Right click and Delete flag to clean the slate. Deleting the flag 3D surface plot Now to really get a feel for how the response varies as a function of the two factors chosen for display, select from the floating Graphs Tool the 3D Surface.
You then will see three- dimensional display of the response surface. If the coordinates encompass actual design points, these will be displayed. On the Factors Tool move the slide bar for A:time to the right. This presents a very compelling picture of how the response can be maximized.
Right click at the peak to set a flag. Move your mouse over the graph. Seeing a point beneath the surface See an actual result predicted so closely lends credence to the model. Things are really looking up at this point! Rotation tool Move your cursor over the tool. The pointer changes to a hand. Now use the hand to rotate the vertical or horizontal wheel. Whether you use the rotation tool or simply grab the plot with your mouse, watch the 3D surface change.
Notice how the points below the surface are shown with a lighter shade. The Stat-Ease program developers thought of everything!
Before moving on from here, go back to the Rotation tool and press Default to put the graph back in its original angle. Analyze the data for the second response, activity. Be sure you find the appropriate polynomial to fit the data, examine the residuals and plot the response surface.
Hint: The correct model is linear. Design-Expert will save your models. To leave Design-Expert, use the File, Exit menu selection. You should go back to that tutorial if you've not completed it. For details on optimization, see our on-line program help. Call or visit our web site for information on content and schedules. In this section, you will work with predictive models for two responses, yield and activity, as a function of three factors: time, temperature, and catalyst.
These models are based on results from a central composite design CCD on a chemical reaction. Click the open design icon see below and load the case study data modeled by Stat-Ease and saved to a file named RSM-a. Open design icon To see a description of the file contents, click the Summary node under the Design branch at the left of your screen.
Within the design status screen you can see we modeled conversion with a quadratic model and activity with a linear model, as shown below. You can also re-size columns with your mouse. Click on the Coefficients Table node at the bottom branch. For instance, notice that the coefficient for AC This shows, for the region studied, that the AC interaction influences conversion more than Factor B. In our example, we chose to use the full quadratic model.
Therefore, some less significant terms shown in black are retained, even though they are not significant at the 0. Right click any cell to export this report to PowerPoint or Word for your presentation or report. Check it out: This is very handy! Under the Optimization branch to the left of the screen, click the Numerical node to start.
We will detail POE later. The program restricts factor ranges to factorial levels plus one to minus one in coded values — the region for which this experimental design provides the most precise predictions. Response limits default to observed extremes. In this case, you should leave the settings for time, temperature, and catalyst factors alone, but you will need to make some changes to the response criteria. 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. For this tutorial case study, assume you need to increase conversion.
Click Conversion and set its Goal to maximize. As shown below, set Lower Limit to 80 the lowest acceptable value, and Upper Limit to , the theoretical high. Conversion criteria settings You must provide both these thresholds so the desirability equation works properly. By default, thresholds will be set at the observed response range, in this case 51 to Otherwise we may come up short of the potential optimum.
Now click the second response, Activity. Enter Lower Limits and Upper Limits of 60 and 66, respectively. Values outside that range are not acceptable.
Activity criteria settings The above settings create the following desirability functions: 1. Close out Screen Tips by pressing X at the upper-right corner of its screen.
Weights give added emphasis to upper or lower bounds or emphasize target values. 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 square on the left down and the square on the right up as shown below. Before moving on from here, re- enter the Lower and Upper Weights at their default values of 1 and 1; respectively. If you want to emphasize one over the rest, set its importance higher. By leaving all importance criteria at their defaults, no goals are favored over others.
Then click Contents. From here you can open various topics and look for any details you need. Now click the Options button to see what you can control for the numerical optimization. After doing your first search for the optimum, go back to this Option and slide it one way and the other. Observe what happens to the solutions presented by Design-Expert.
If you move the Filter bar to the right, you decrease the number. Conversely, moving the bar to the left increases the solutions. Click OK to close Optimization Options. Running the optimization Start the optimization by clicking the Solutions tab.
It defaults to the Ramps view so you get a good visual on the best factor settings and the desirability of the predicted responses.
Numerical Optimization Ramps view for Solutions Your results may differ The program randomly picks a set of conditions from which to start its search for desirable results — your results may differ. Multiple cycles improve the odds of finding multiple local optimums, some of which are higher in desirability than others. Due to random starting conditions, your results are likely to be slightly different from those in the report above. The colored 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, the first few near 90 degrees; further down the solution list, others near 80 degrees.
You may see slight differences in results due to variations in approach from different random starting points. For example, click the last solution on your screen. Does it look something like the one below? Second optimum at lower temperature, but conversion drops, so it is inferior If your search also uncovered this local optimum, note that conversion falls off, thus making it less desirable than the higher-temperature option.
The Solutions Tool provides three views of the same optimization. Drag the tool to a convenient location on the screen. Click the Solutions Tool view option Report. Desirability A:time 1 B:temperature 1 C:catalyst 1 Conversion 0. Optimization Graphs Press Graphs near the top of your screen to view a contour graph of overall desirability. On the Factors Tool palette, right-click C:Catalyst. Make it the X2 axis.
Temperature then becomes a constant factor at 90 degrees. Design-Expert software sets a flag at the optimal point. To view the responses associated with the desirability, select the desired Response from its droplist.
Take a look at the Conversion plot. Then go to Surface Graphs and click Show contour grid lines. Show contour grid lines option Grid lines help locate the optimum, but for a more precise locator right-click the flag and Toggle Size to see the coordinates plus many more predicted outcome details. To get just what you want on the flag, right-click it again and select Edit Info. Flag size toggled to see select detail By returning to Toggle size, you can change back to the smaller flag.
If you like, view optimal activity response as well. To look at the desirability surface in three dimensions, again click Response and choose Desirability. Then, on the floating Graphs Tool, press 3D Surface. Next select View, Show Rotation and change horizontal control h to Press your Tab key or click the graph.
What a spectacular view! In other words, the solution is relatively robust to factor C. Do this by pressing the Default button Surface Graphs and any other Graph Preference screens you experimented on. Design-Expert offers a very high Graph resolution option.
Try this if you like, but you may find that the processing time taken to render this, particularly while rotating the 3D graph, can be a bit bothersome. This, of course, depends on the speed of your computer and the graphics-card capability. To see a broader operating window, click the Graphical node. You need not enter a high limit for graphical optimization to function properly. Graphical optimization: Conversion criteria Click Activity response. If not already entered, type in 60 for the Lower Limit and 66 for the Upper Limit.
Notice that regions not meeting your specifications are shaded out, leaving hopefully! Temperature then becomes a constant factor at 90 degrees as before for Solution 1. This Design-Expert display may not look as fancy as 3D desirability but it can be very useful to show windows of operability where requirements simultaneously meet critical properties. Shaded areas on the graphical optimization plot do not meet the selection criteria. This provides a measure of uncertainty on the boundaries predicted by the models — a buffer of sorts.
Confidence intervals CI superimposed on operating window After looking at this, go back and turn off the intervals to re-set the graph to the default settings. If you are subject to FDA regulation and participate in their quality by design QBD initiative, the CI-bounded window can be considered to be a functional design space, that is, a safe operating region for any particular unit operations.
However, to establish a manufacturing design space on must impose tolerance intervals. This tutorial experiment provided too few runs to support imposition of TIs. What will this do to the operation window? Find out by dragging the 80 conversion contour until it reaches a value near Then right-click it and Set contour value to 90 on the nose. Changing the conversion specification to 90 minimum It appears that the more ambitious goal of 90 percent conversion is feasible.
This requirement change would make the lower activity specification superfluous as evidenced by it no longer being a limiting level, that is, not a boundary condition on the operating window. Graphical optimization works great for two factors, but as factors increase, optimization 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. Response Prediction and Confirmation This feature in Design-Expert software allows you to generate predicted response s for any set of factors. To see how this works, click on the Point Prediction node lower left on your screen. Click the Point Prediction node left on your screen. Notice it now defaults to the first solution. Be thankful Design-Expert programmers thought of this, because it saves you the trouble of dialing it up on the Factors Tool.
Go ahead and play with them now if you like. You can either move the slider controls, or switch to the Sheet view and enter values. Take a moment now to study the screen tips on all the statistical intervals that come up when you press the light- bulb icon.
Confirmation After finding the optimum settings based on your RSM models, the next step is to confirm that they actually work. To do this, click the Confirmation node left side of your screen. You might be surprised at the level of variability, but it will help you manage expectations.
