Fractional Factorial Design of Experiments

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About this lesson

A fractional factorial DOE conducts only a fraction of the experiments done with the full factorial DOE. It then statistically analyzes the results to fine tune the design and normally does a second optimizing study. Even though there are typically several sets of experiments, the total is still less than the number conducted with a full factorial study and much less than OFAAT.

Quick reference

Fractional Factorial Design of Experiments

Fractional Factorial DOE is a statistical test methodology that uses a selected set of test samples with a precise configuration of factor settings to determine the impact of the factors on the system response throughout the design space represented by the factors.

When to use

Fractional Factorial DOE is normally used when determining the simultaneous impact of many factors on system response.  It does require the ability to control the test sample configuration with respect to the factors being analyzed. 

Instructions

The Fractional Factorial DOE is similar in many respects to the Full Factorial DOE.  A set of factors is selected and a high and low level is established for each factor.  However, now the differences start.  Rather than testing all combinations of highs and lows, the Fractional Factorial DOE only tests a fraction of those combinations.  Which configurations will be carefully selected so that the results can still be statistically analyzed. 

Often this methodology will have several phases of testing.  The first is the fraction of tests just mentioned.  After this test, if there are factors that are significant and whose effect is likely to be non-linear, they are further analyzed with a second set of tests that are only using those factors.  If necessary, a final confirming test is done using the optimal settings.

This approach will provide an analysis and equation that define the full design space based upon the factors represented.  However, this analysis may not be able to fully analyze all interaction effects.  Even with the two phases, this approach normally will not conduct nearly as many tests as the Full Factorial DOE.

Hints & tips

  • The factor levels must be controllable in order to establish the correct test sample configuration of high and low values.
  • All the tests must be completed in order to do the statistical analysis.  This is not like the OFAAT method where performance continues to improve as more tests are done.
  • The two-level factors will assume the factor effects on system response are linear.  If the effects are non-linear, multi-level factors must be used.
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  • 00:04 Hi, I'm Ray Sheen.
  • 00:06 Well, now, it's time to introduce the fractional factorial DOE methodology.
  • 00:12 It's probably not a surprise to find that Fractional Factorial Design
  • 00:17 of Experiments will used only a fraction of the Full Factorial DOE test.
  • 00:22 Like both Full Factorial DOE and
  • 00:25 OFAAT, we need to select a potential set of factors that could influence the problem.
  • 00:30 And once again, we will set the high and low levels for each factor usually based
  • 00:35 upon the specification limits, tolerances, or normal variations in that factor.
  • 00:40 And now things are different.
  • 00:42 Instead of creating all the possible combinations of high and
  • 00:46 low factor test specimens, we will use only a carefully selected fraction of
  • 00:50 those test specimens whose results can still be analyzed statistically.
  • 00:55 But while we can analyse those results statistically,
  • 00:58 there's not as much accuracy with them.
  • 01:00 So normally, we do a second study that only looks at a few factors and
  • 01:05 really focuses in on those.
  • 01:07 The factors that are used are determined based upon the results of the first study.
  • 01:12 The second round of test is statistically analysed and
  • 01:15 the optimal performance settings are determined.
  • 01:17 And finally, like with the full factorial DOE, we normally do a final
  • 01:22 confirmation test to ensure that the results are what we expected.
  • 01:26 So one more time, let's take a look at the benefits and
  • 01:30 keys to success, first the benefits.
  • 01:32 As with the full factorial DOE, we get a full understanding of the design space for
  • 01:37 the system being analyzed.
  • 01:39 And a benefit over the OFAAT approach is that we can analyze some of
  • 01:43 the interaction effects.
  • 01:45 A further benefit is that we can do this analysis with fewer tests than the full
  • 01:50 factorial DOE, and often a lot fewer tests, which will save time and money.
  • 01:55 And as long as we are careful about the selection of the factor configuration,
  • 02:00 we can still do a statistical analysis of the results which will give us a lot
  • 02:04 more confidence than the possibility of a random success or
  • 02:07 failure that sometimes occurs with trial and error or OFAAT.
  • 02:11 Now for the keys to success.
  • 02:13 As we said with the full factorial DOE, you need to trust the process,
  • 02:17 do all the experiments, and then run the statistical analysis.
  • 02:21 Don't jump to a conclusion.
  • 02:23 And as with the full factorial DOE, you need to able to control the factor
  • 02:28 settings to precisely hit the high and low setting values.
  • 02:32 Of course, there are a few problems, traps, and pitfalls to discuss.
  • 02:36 The first is that the analysis assumes linear effects whenever 2-level
  • 02:40 factors are being analyzed.
  • 02:42 And the first phase of tests is almost always 2-level factors,
  • 02:46 although it is much more common to use 3-level factors in the second phase.
  • 02:51 The test sample preparation can be difficult to control the low and
  • 02:55 high factor settings and in this case,
  • 02:57 they must be very precisely controlled and tracked.
  • 03:01 When I said that you could probably be able to analyze some interaction effects,
  • 03:06 the key would be the word some.
  • 03:08 The fractional factorial limits, the number and
  • 03:11 complexity of the interaction effects.
  • 03:13 We'll spend an entire lesson on that topic later in the course.
  • 03:17 Finally, it is a statistical analysis, and
  • 03:20 you need to have some proper statistical tools to do the analysis.
  • 03:24 Many statistical software applications now have DOE templates embedded in them.
  • 03:29 We will be using the Minitab application in this course which has the statistic
  • 03:33 setup for the analysis.
  • 03:35 However, we will also discuss how to do at least some of the analysis using Excel,
  • 03:40 or even paper and pencil and calculator.
  • 03:43 Fractional factorial DOE is the most commonly used DOE approach, in fact,
  • 03:47 there are many different flavors of fractional factorial DOEs and
  • 03:52 we'll discuss some of them in this course.
  • 03:55 The important point to remember is that it is a statistical analysis of a limited
  • 04:00 number of test samples that gives a robust understanding of the design space.

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