Fractional Factorial DOE Methodology

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About this lesson

This lesson describes the nine steps to be followed when using one of the fractional factorial DOE methods. The emphasis is one how the steps differ from the full factorial DOE methodology.

Quick reference

Fractional Factorial DOE Methodology

The Fractional Factorial DOE methodology is similar to the Full Factorial DOE methodology.  However, the Fractional Factorial DOE methodology divides the study into three phases: Screening, Refining, and Optimizing.

When to use

When business conditions indicate a Fractional Factorial DOE is appropriate, the Fractional Factorial DOE methodology should be followed.  This methodology provides a high-level description of each step in the study.

Instructions

The Fractional Factorial DOE methodology is similar to Full Factorial DOE, except that the study is divided into phases.  The results of each phase are used to plan the next phase. 

The first phase, screening, normally tests only a small fraction of the configuration and its focus is to identify significant control factors.  The second phase, refining, tests the significant factors – often as multi-level factors.  The focus of this phase is to understand how these factors affect performance.  The final phase, optimizing, is a validation of the optimal settings that are selected based upon the analysis of the preceding two phases.

When describing a fractional factorial DOE, there is a standard nomenclature that indicates the DOE design.  This nomenclature is a value for the number of levels with a subscript for the resolution of the DOE matrix.  That value is then raised to the power of the number of factors – minus the degree of fractioning.   For instance, 2V5-1 means the DOE will have five two-level factors.  The level of fractioning is one level – so it is a one-half fraction.  And that means that the resolution will be V – meaning that main effects and two level interactions can be identified.  There is more about resolution in the next lesson.   

The typical steps for a Fractional Factorial DOE are:

  1. Establish the DOE study objective and determine the maximum number of runs.
  2. Select the factors.
  3. Determine the values for the factor levels in the screening phase.
  4. Build screening samples for testing and establish the procedure for conducting screening runs and collecting data.
  5. Complete the screening phase tests.
  6. Analyze the screening phase results and plan the refining phase.
  7. Build refining samples and establish the refining phase procedure.
  8. Complete the refining phase test runs and analyze the results to determine the need for an optimizing phase.
  9. Build optimized sample and conduct a full round of tests.

By conducting the study in three small phases, the effort is normally easier to plan, schedule, coordinate and manage. 

Hints & tips

  • Make sure you plan for all three phases including preparing three test samples and scheduling three test windows.
  • The execution of the steps are similar to Full Factorial.  Samples are prepared the same way, tests are conducted the same way, and some of the analysis will be the same.
  • When only doing a fraction of the possible configurations, it is critical that the correct fraction configurations are selected.  The selection process will be covered in another lesson, however, monitor sample preparation closely to ensure the configurations are correct.
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  • 00:04 Hello, I'm Ray Shane.
  • 00:05 Well, now let's discuss the steps to do a fractional factorial DOE.
  • 00:09 We'll start with some comments about the methodology.
  • 00:14 The good news is that many of the steps and
  • 00:16 actions are the same as those that you would do with a full factorial DOE.
  • 00:21 You will conduct a number of tests or runs using varying combinations of the control
  • 00:25 factor settings, and then statistically analyze the result, that sounds familiar.
  • 00:30 The nomenclature for the fractional factorial DOE is based upon
  • 00:35 the nomenclature of the full factorial DOE.
  • 00:38 The main term is the factor level, and
  • 00:40 it is raised to the power of the number of factors.
  • 00:43 However, there are two additional terms.
  • 00:46 One is a subscript Roman numeral,
  • 00:49 which is the resolution of the fractional factorial matrix.
  • 00:53 We'll talk about that resolution more in the next lesson.
  • 00:57 And the exponent includes an expression that is minus the level of fractioning.
  • 01:03 So a half fraction is minus 1, a one-fourth fraction is minus 2, and
  • 01:08 a one-eighth fraction is minus 3.
  • 01:10 While it is a more complex nomenclature, the number of experiment runs is often
  • 01:15 significantly less than the full factorial designs.
  • 01:19 In fact, we usually do this study in three phases.
  • 01:22 Where we use the information gathered at each phase to tailor the design of
  • 01:26 the runs that are done in the next phase.
  • 01:29 One of the benefits is that it highlights the most significant factors in the early
  • 01:32 phase, which lets us do a more in-depth study of those factors in the later phase.
  • 01:38 And the good news is that even though there are multiple phases,
  • 01:41 it still will normally require fewer runs than a full factorial
  • 01:45 study of the same number of factors.
  • 01:47 In fact, often, a lot fewer runs, and of course, that saves time and money.
  • 01:53 Let's go through the steps in a typical fractional factorial DOE.
  • 01:57 Some of these steps are the same as with the full factorial DOE, so
  • 02:00 I will cover them very quickly.
  • 02:02 I will take more time with the new steps, which I'll show in red.
  • 02:06 First, set your objective and determine how much time and
  • 02:08 money you have to work with.
  • 02:10 This is the same as with a full factorial DOE.
  • 02:13 Then select the factors that you would like to study.
  • 02:15 Again, this is done the same way as you would with a full factorial DOE,
  • 02:19 except of course, you can often start with many more factors.
  • 02:23 Next, for the first significant difference, determine the values for
  • 02:26 the factors in the first phase of the study for the screening phase.
  • 02:30 I normally do these as two-level factors, and I try to use the full span for
  • 02:35 the quantitative factors.
  • 02:37 Of course, with the qualitative factors, this is easy, it's the two states.
  • 02:41 Then build the samples and create your procedure for the screening phase.
  • 02:44 We've talked about this before.
  • 02:46 Now complete the screening phase tests.
  • 02:49 Since this will be just a fraction of the tests that you do for a full factorial
  • 02:53 study, it's critical that you get the correct settings for the control factors.
  • 02:57 We'll only be testing a subset of the combinations.
  • 03:01 Now analyze the results to determine which factors are significant and which are not.
  • 03:06 For the qualitative factors decide, which setting is best.
  • 03:09 For the quantitative factors,
  • 03:10 determine which are significant based upon the values of the coefficients.
  • 03:14 The significant ones will be tested in the next phase.
  • 03:17 The insignificant ones do not normally require further testing.
  • 03:21 Pick the value that is either best performance or lowest cost,
  • 03:25 whatever is the business objective.
  • 03:27 So based upon the results, plan the next phase,
  • 03:30 usually with only a few of the control factors being varied.
  • 03:33 Just like before, build the test samples and, if required,
  • 03:37 make changes to the procedure.
  • 03:38 Conduct the refining phase tests and analyze the data.
  • 03:42 Based on the results, you can pick optimum performance levels for each factor.
  • 03:47 If the focus was characterization of a new product, process, or system, you may
  • 03:51 use your results to set optimal targets and tolerances for the control factors.
  • 03:56 If the optimal settings were not in your subset of test runs, I recommend doing
  • 04:00 a final optimizing or confirming study using those optimal settings.
  • 04:05 And that is the last step, prepare the number of samples that you need to test,
  • 04:10 and then do the runs and evaluate the data to ensure it is what you expected.
  • 04:15 Let's summarize some guidelines for these phases.
  • 04:18 First, it's often easier to run several small studies than one giant one.
  • 04:23 You're less likely to need to do blocking.
  • 04:25 And there's less need for center points,
  • 04:27 because the likelihood of drifting test systems is reduced.
  • 04:31 But make sure you allow enough time in your project schedule to go through two or
  • 04:36 three rounds of testing.
  • 04:38 That means allowing time for test sample preparation, and
  • 04:41 for conducting the tests in multiple phases.
  • 04:45 Also, it's easier to manage and coordinate small studies.
  • 04:48 There's less coordination needed when there are only 16 tests instead of 64.
  • 04:53 You can normally keep the same team and operators in place, so
  • 04:57 communication is easier.
  • 04:59 Also, completing each phase feels like you've made progress,
  • 05:03 whereas working through 64 or 128 runs seems interminable.
  • 05:07 One other major benefit is that each phase informs the team as to what needs to be
  • 05:12 done in the next phase.
  • 05:13 Again, the team is making progress as they focus on an optimal solution.
  • 05:18 As mentioned, a fractional factorial DOE normally has three phases.
  • 05:22 The first phase, which only uses a small fraction,
  • 05:25 will be a screening phase to decide which is important.
  • 05:28 The second phase will usually be the largest phase in
  • 05:31 terms of the number of runs.
  • 05:33 And its purpose is to refine the relationship and
  • 05:36 our understanding of the most significant factors.
  • 05:40 The final phase, the optimization phase, is used to confirm or
  • 05:44 fine-tune the final solution.
  • 05:47 As you saw, if you can do a full factorial DOE,
  • 05:50 you can do a fractional factorial DOE.
  • 05:53 It's a similar process, only done across several phases.

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