Full Factorial Design of Experiments

Quick reference

• 00:04 Hi, I'm Ray Sheen.
• 00:05 Well now I would like to discuss the experimental
• 00:09 methodology known as full factorial design of experiments.
• 00:14 Let me describe what I mean by a full factorial DOE.
• 00:18 Somewhere to the OFAAT method, we start by selecting a list of factors that will be
• 00:23 studied by the set of experiments.
• 00:25 But now for a difference.
• 00:27 Instead of determining a series of factor levels, only two or
• 00:30 three levels are selected.
• 00:32 Normally a high and low, and sometimes a high, low and mid point.
• 00:37 And now experiments will be conducted with different combinations of all
• 00:41 the highs and lows.
• 00:42 There may also be some center points where the experiment is
• 00:45 done with all the factors set at the center point.
• 00:48 This is usually done for
• 00:49 calibration to make sure that there has been no change in the test process.
• 00:54 Also in some cases, a replicate or
• 00:56 a second test with the same combinations of highs and lows will be conducted.
• 01:00 This is done to increase the number of data points which will improve
• 01:04 the accuracy of the statistical analysis that goes along with this method.
• 01:09 Which brings me to the next step.
• 01:10 The results are statistically analyzed to determine the optimal setting for
• 01:14 each factor.
• 01:15 Because there have been a number of tests with each factor at its high or
• 01:20 low level, minor variations between experiments will be leveled out, and
• 01:24 the statistical analysis will provide a design space equation that can be used to
• 01:29 predict system performance in any set of factor conditions.
• 01:33 Now with respect to experimental study, if the optimal performance is a set
• 01:38 of factor settings that has not yet been tested, a confirmatory test is
• 01:42 done to make sure that the settings do provide satisfactory performance.
• 01:47 Once again, let's consider the benefits and keys to success.
• 01:51 First the benefits, that design space equation I mentioned will give you a full
• 01:56 understanding of the design space.
• 01:58 Not just the points that were specifically tested.
• 02:01 This will also pick up any interaction effects between factors and
• 02:05 those effects will also be part of your design space equation.
• 02:09 Normally, the approach will require fewer tests than the OFAAT method.
• 02:13 And this method lends itself to statistical analysis.
• 02:17 Let me take a minute to explain why this is important.
• 02:20 Whenever you are doing physical experiments,
• 02:22 there will be factors that affect results that are not part of the experiment.
• 02:27 A little uncertainty.
• 02:28 For instance, when doing the OFAAT methodology, you may not have selected
• 02:32 the factor setting that gives the optimal performance every time.
• 02:36 But you selected the one that gave you an optimal performance that time.
• 02:41 But that was only one data point.
• 02:44 When you have multiple data points that can be described statistically,
• 02:48 you can determine both the optimal point and you can also get a sense of
• 02:52 the typical uncertainty or variability that exists in the system performance.
• 02:57 Let's look at the keys to success now.
• 03:00 First, you need to be able to control the factors so that you can reliably set
• 03:05 them at the designated high and low levels required for each test.
• 03:09 Another thing is that you need to trust the process and the statistics.
• 03:13 Unlike OFAAT, you are changing many factors simultaneously on each test.
• 03:19 But you are doing that in a prescribed manner that will let you run
• 03:22 the statistical analysis.
• 03:23 Finally, you need to make sure that you have the resources to do all the tests in
• 03:28 the DOE.
• 03:29 In order for the statistical analysis to be valid,
• 03:32 all the data points must be used.
• 03:34 This is not like OFAAT,
• 03:35 where you can stop as soon as you have an acceptable performance level.
• 03:38 You must do all the tests.
• 03:41 And like with the other methodologies, there are problems, traps, and pitfalls.
• 03:45 One is that if only high and low levels are used,
• 03:48 the analysis will assume a linear relationship.
• 03:51 If you know the relationship between the factors, and
• 03:54 the results is nonlinear, you need to do the DOE with more levels for your factors.
• 03:59 But a caution is that when adding these additional levels, or even center points
• 04:03 for that matter, you're increasing the number of tests that you need to run, and
• 04:07 that takes more time and money.
• 04:09 The test sample configuration in terms of factor level highs and
• 04:14 lows must precisely follow the deal we plan.
• 04:17 So that means that you need to build or
• 04:19 create the exact configuration specified for the statistics to be valid.
• 04:24 Finally, the number of tests starts to get very large when you have many factors, and
• 04:28 even larger if they are three level factors.
• 04:31 The number of tests is essentially 2 to the N for two level factors, and 3 to the N for
• 04:36 three level factors, and that is where N is the number of factors.
• 04:41 When most people think of design of experiments,
• 04:44 they're thinking of full factorial DOE.
• 04:47 It is the basic methodology, and the other variations we will
• 04:51 discuss will always start first from the full factorial DOE.
• 04:55 The statistical analysis of the test data gives us a design space equation
• 05:01 that fully describes how the factors impact system performance.

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