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One of the most common techniques for analyzing the results of a DOE study in Minitab is to review the factor plots. These will provide insight into the optimal settings for control factors. The interactive plots will also highlight the settings associated with local maximum or minimum performance levels.

Quick reference

DOE Factorial Plots

Minitab will also create factorial plots that can be used for predicting performance and to identify optimal settings for various conditions. 

When to use

The factorial plots found in Minitab are normally used with refining and optimizing studies are with full factorial DOE analyses.

Instructions

As stated before, to use these features of Minitab, first create the study in Minitab as discussed in an earlier lesson.  Then record your test run data in the Response variable column of Minitab.  You are now ready to start the analysis.  The DOE factorial plots and related analyses are all found by using the STAT menu, selecting DOE, then selecting factorial.  After that, there are various menu items that provide different types of analyses. 

Factorial Plots

This analysis will generate two sets of graphs.  One set is titled the Main Effects plots and it has a graph for each factor.  A steep line on the graph indicates a major effect due to that factor.  A shallow slope or horizontal line indicates virtually no effect.  When the plot is horizontal, I will select a factor value that is best for the overall business.  When the plot is steep, I will select the point that corresponds with optimal output response performance.  

A second set of plots is the Interaction plots.  This plots the effect of the interaction between two of the factors.  Often the slope for both factors is going the same direction and they are nearly parallel.  However, sometimes one is sloping up and the other is sloping down or they intersect.  If these lines intersect, there is a strong probability that the response variable will be a minimum or maximum when the factors are at those values.  You can use this point on an optimizing study to find the absolute best performance.

Predict

The predict option allows you to predict the response variable based upon setting the control factors.  This prediction is based upon the DOE model, so it is only valid when selecting control factors settings that are between the low and high values used in the DOE experimental runs. This tool within Minitab can be useful for establishing the final few settings to be used in an optimizing study.

Response Optimizer

The final analytical technique I would like to discuss is the Response Optimizer. You reach this by selecting STAT, then DOE, then Factorial, and go to the bottom of the menu to select Response Optimizer.  This tool is very useful when there are multiple output or response variables.  For each response, you can select whether you want to minimize it, maximize it, or hit a specific target value.  You can also add constraints on the input factors.  The Response Optimizer plots show the optimal condition with a red line and the values in red at the top of each factor plot.  The very powerful feature with this tool is that you can select any of the red lines with your cursor, move that line to any spot within the factor range, and the plots will automatically change to show the new optimum value.  This is tremendously helpful when doing “what if …” analysis or preparing a final optimizing study. 

Hints & tips

  • Minitab has many more analytical plots and tools.  I have only showed you the ones that I have found most useful.  Feel free to play with the application and look for other analyses.
  • You may want to use different analyses for different phases of a Fractional Factorial DOE.  For instance the significance plots are very useful in a screening study and the factorial plots are very useful in a refining study and the predict or response optimizer can help you set the values for a final optimizing study.
  • If using Predict, do not enter values for control factors that are outside the upper and lower limits that were tested.  If you want to test beyond those limits, use the path of steepest ascent or descent to shift the study to that region.
  • Make sure you have correctly entered the data results and recorded the values with the correct test configuration in the worksheet.
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  • 00:05 Hi, I'm Ray Sheen, we've looked at significance and
  • 00:08 the design space equation.
  • 00:10 Now let's see what Minitab can do with factorial plots.
  • 00:14 What do we mean by factorial plots?
  • 00:16 These are graphs that show how a control factor impacts the response factor
  • 00:21 from its low value to its high value.
  • 00:23 With this plot, we can tune the design to get the ideal performance from the system.
  • 00:28 You know the saying a picture is worth 1,000 words?
  • 00:31 Well, let's look at a picture of the factors.
  • 00:34 Again, select Stat then DOE and Factorial.
  • 00:38 Now go a little further down the menu and select Factorial plots.
  • 00:42 This will bring up a panel where you need to select your response variable and
  • 00:46 then select your control factors or input variables.
  • 00:50 When you select OK, you will get the factorial plots.
  • 00:54 The main effects plot will indicate the optimum design point for
  • 00:58 the factor if treated as an independent factor.
  • 01:01 So if you wanted your output to be high, you would pick the left setting and
  • 01:05 the first factor material and the high setting for
  • 01:08 the second factor injection pressure.
  • 01:11 Looking at these plots,
  • 01:12 the other two factors don't make much difference in the output.
  • 01:15 So I would probably set them at the level that was the lowest cost or
  • 01:19 easiest to work with.
  • 01:21 The plots with two lines or interaction plots.
  • 01:24 These become interesting when the two lines cross.
  • 01:27 The point of intersection is often a minimum or maximum in the response value.
  • 01:32 In this case, we only have one plot with an intersection, the material and
  • 01:36 injection pressure.
  • 01:38 This is the second one down in the left column.
  • 01:41 It looks like the intersection is about three-fourths of the way
  • 01:44 through the span of the factor.
  • 01:46 Now in this case, the material is a qualitative measure, not quantitative.
  • 01:51 So I would select the left side value of the material since it is the high side.
  • 01:54 And my final optimizing study, we just vary the injection pressure between this
  • 01:59 intersection point and the far right value.
  • 02:02 Incidentally, if lines are converging but not yet
  • 02:05 crossed, you may want to consider using the path of steepest ascent or descend, so
  • 02:10 as to study in the region where they will cross.
  • 02:14 You can use Minitab to help you predict the value for
  • 02:16 the response variable based upon different control factor inputs.
  • 02:21 But be very careful, don't use the control factor levels that are outside your upper
  • 02:26 and lower control limits of the factors in the study.
  • 02:28 The DOE should not be used to extrapolate outside the design space study.
  • 02:34 That it doesn't mean you can't collect additional data outside that design space
  • 02:37 of the current study.
  • 02:39 Just follow the path of steepest ascent or
  • 02:41 descent to move towards an optimal design point.
  • 02:45 To do a prediction of the response variable, go to Stat,
  • 02:48 then DOE, select Factorial and then select Predict.
  • 02:53 You will get a panel with a table where you can enter your control factors, and
  • 02:58 when you click OK, it will calculate a response variable.
  • 03:03 The last graph to discuss is my favorite, the response optimizer.
  • 03:07 This tool in Minitab can quickly help you find the optimal setting
  • 03:11 given different initial conditions.
  • 03:13 Remember, Minitab has created the design space equation.
  • 03:16 So you can set some factors in the equation and Minitab will tell you
  • 03:19 the best point to set the others to get the best overall performance.
  • 03:24 So like Stat, DOE, Factorial and then go to the bottom of the menu for
  • 03:29 response optimizer.
  • 03:31 When you do that, the panel will come up asking you to select a goal for your
  • 03:35 response variable of maximum, minimum or to headed target value right on the nose.
  • 03:42 After that, I recommend you select the Options button.
  • 03:45 This will let you apply constraints on some of the factors.
  • 03:48 So when the boss starts asking you the what if questions,
  • 03:51 you can say hold a second, and I'll show you.
  • 03:55 Put in their constraints, it could be a target value or a min max range.
  • 03:59 Then click OK on this panel, and the previous one and
  • 04:02 you will have a graphs that show you the best case settings with that constraint.
  • 04:07 Optimizer shows the best factor values with a vertical red line associated with
  • 04:12 each factor.
  • 04:13 And the values are in red at the top of the graph.
  • 04:16 You can grab one of those lines with your cursor and move it to another point.
  • 04:21 When you do that, all the rest will recalculate for the new optimum value.
  • 04:26 And this tool is very helpful when there are multiple response variables.
  • 04:31 In this case, we have three response variables.
  • 04:34 So I can shift the values around and
  • 04:36 find an optimum point based upon different response variable goals.
  • 04:41 I hope you can see how powerful this tool will be when you have a complex situation.
  • 04:46 So the bottom line is, Minitab can do all sorts of things, so
  • 04:51 it'll help you to analyze your DOE data.

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