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This lesson describes the eight steps to be followed when conducting a full factorial DOE.

Quick reference

Full Factorial DOE Methodology

The full factorial DOE methodology is the most complete of the DOE approaches.  All others are derived from this methodology.  There is a standard process that should be followed to ensure the statistical results are meaningful.

When to use

The primary use for the full factorial DOE is to understand the design space of a new technology.  This technique determines the sensitivity of the main factors and the interaction effects between the factors.  This approach can also be used in problem solving when the underlying root cause of the problem is unclear.  In that case, the full factorial DOE provides insight and guidance concerning how the factors can impact performance – including the problem performance being investigated.

Instructions

When describing a full factorial DOE, there is a standard nomenclature that indicates the DOE design.  This nomenclature is a value for the number of levels, raised to the power of the number of factors.  For instance, 25 means the DOE will have five two-level factors.  This highlights one of the most important decisions that must be made on full factorial DOE analyses which is the number of factors and their level.  The more factors and levels and more accurate the results, but also the more work required.  Because of the level of work, full factorial DOE is often used when there are between two and five factors.  A fractional factorial is used when the number of factors is greater.  Also, two-level factors will be create linear models, while multi-level factors can create quadratic models.

 

The steps for the full factorial DOE should be followed in sequential order, except for the two cases where the steps are conducted in parallel.  By completing them in the correct order, the DOE study team can ensure the validity of the results.

  1. Construct the DOE study. This is based upon the study objective that was provided by the stakeholders.  This step can be conducted in parallel with step 2.
  2. Select the factors.  These factors will form the parameters of the design space equation and are often selected based upon what is controllable by the operators.  This step can be done in parallel with step 1.
  3. Determine the values for the factor levels.  Once the study design is set and the factors selected, the appropriate levels for each factor are set.  These levels must be controllable so the test operator can ensure the correct test run is being completed.
  4. Build all samples for testing. If the test is a process or system test, the samples may be generic samples.  If the test is a product test, the samples are generally the combinations of factor settings within the test article configuration.  This step can be conducted in parallel with step 5.
  5. Establish the procedure for conducting runs and collecting data.  This procedure must be rigorously followed by the test operators so that valid data is collected and available for analysis.  This step can be done in parallel with step 4.
  6. Conduct the runs in the random order, recording the results.  This is the step in which the experimental runs are completed and the data recorded.  Normally the data is collected in a spreadsheet or statistical software.  It is critical that the data point is associated with the test or test sample configuration.
  7. Analyze the results using statistical software and analysis.  The specific of this step will be discussed in later lessons.
  8. Conduct a set of confirmatory runs with optimal settings.  Based upon the results, optimal design settings are selected and test sample(s) completed with that configuration to confirm that the analysis is valid.

Hints & tips

  • Follow the steps in sequence except for the two occasions of parallel steps ( 1 / 2 and 4 / 5 ).
  • Fractional factorial DOE studies will follow similar steps, the differences will be identified in later lessons.
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  • 00:04 Hello, I'm Ray Sheen.
  • 00:06 In this lesson, I'll introduce the full factorial DOE methodology and
  • 00:10 talk about the steps of this technique.
  • 00:12 We call this the full factorial DOE because we will use all
  • 00:17 combinations of the factor settings based upon the study design.
  • 00:22 This can be quite a few experimental runs, so this is usually the largest and
  • 00:27 most expensive of the DOE study approaches.
  • 00:30 While it is the largest and most expensive approach,
  • 00:32 they will often also be the most complete view of the design space.
  • 00:36 That means it describes the main effect on performance
  • 00:39 of each factor of the product processor system.
  • 00:42 In addition, it will identify interaction effects between those factors.
  • 00:46 Some factors magnify others and some depress or minimize others.
  • 00:51 This methodology will illustrate those effects.
  • 00:54 It does this by creating a design space equation.
  • 00:58 This equation will predict the product and process or
  • 01:00 system performance based upon whatever values are inserted for the factors.
  • 01:05 This will allow the design team to optimize the product processor system
  • 01:09 performance by solving the design space equation for
  • 01:12 a given set of starting conditions or other constraints.
  • 01:16 Full factorial DOE is often used with new technology
  • 01:20 in order to understand the full design space.
  • 01:23 It is sometimes used in conjunction with fractional factorial after the fractional
  • 01:28 analysis has reduced the number of factors to a very small quantity.
  • 01:32 It is used in problem solving when the problem is complex
  • 01:36 with several interrelated factors.
  • 01:39 If the problem is due to a singular root cause,
  • 01:41 a DOE is not needed since the cause is known.
  • 01:44 However if there is no obvious correlation with just one factor, the DOE is done to
  • 01:49 understand the sensitivity of each factor and the factor interactions.
  • 01:54 Before we review the steps let's take a minute to understand a few key concepts.
  • 01:59 There's a special nomenclature that is used when identifying a full factorial
  • 02:03 DOE.
  • 02:04 This nomenclature describes the input factors,
  • 02:07 is essentially the factor level raised to the power of the number of factors.
  • 02:12 So for instance, if the design has 5 2-level factors,
  • 02:16 it's shown as 2 to the 5th full factorial design.
  • 02:20 If only 4 2-level factors, it would be 2 to the 4th.
  • 02:24 And if instead of 2-level factors it had used 3-level factors,
  • 02:28 the nomenclature would have been 3 to the 5th.
  • 02:31 As we've mentioned before,
  • 02:32 factor selection will be a key to the validity of the results of the DOE.
  • 02:37 You can use both qualitative and quantitative factors, but
  • 02:41 keep in mind, if using two level factors the results are linear.
  • 02:45 To get quadratic or higher order results, you will need to use multilevel factors.
  • 02:50 As the number of factors goes up the size of the full factorial DOE matrix goes up.
  • 02:55 For that reason, most full factorial DOEs have between 2 and 5 factors.
  • 03:02 In fact, you will see that once we consider the fractional factorial design,
  • 03:07 often a full factorial DOE is done after an initial screening study has
  • 03:11 determined the vital few factors.
  • 03:13 In a much larger fractional factorial DOE.
  • 03:17 The full factorial can determine the optimal performance setting for
  • 03:21 those vital few factors.
  • 03:24 I would like to take you through the steps of a study.
  • 03:26 We've already mentioned that the DOE study is a process not an event.
  • 03:31 There are steps that must be followed.
  • 03:32 I will go through all the steps for a full factorial DOE study now.
  • 03:36 When we do the fractional factorial study I'll just talk about
  • 03:39 the steps that are different at that time.
  • 03:41 Step 1 is to construct the study.
  • 03:44 This will be based upon the study objective.
  • 03:46 Often the objective is determined by the stakeholders and
  • 03:49 you are given the objective for which you must then design or perform the study.
  • 03:54 If you are not given an objective, then you must actually start at a step one half
  • 03:58 and create an objective in order to do Step 1.
  • 04:02 We'll discuss how to design the study in a later lesson.
  • 04:05 Step 2 is factor selection.
  • 04:08 Actually, Steps 1 and 2 are often done iteratively and in either order.
  • 04:12 The study design will specify the number of factors and
  • 04:15 if you have a set of factors that you're particularly interested in,
  • 04:18 you'll create a study design that can accommodate that many factors.
  • 04:22 The bottom line is that Steps 1 and 2 are related and are often done simultaneously.
  • 04:28 We'll have some rules for factor selection in an upcoming lesson.
  • 04:32 Step 3 is to establish the factor levels for the control factors.
  • 04:36 The DOE methodology requires that you create precise configurations
  • 04:41 of the test articles.
  • 04:42 That means that each of the control factors must be controllable so
  • 04:47 that you can set their values.
  • 04:48 The study design will determine how many settings you need but
  • 04:52 at a minimum you must have two levels.
  • 04:55 Steps 4 and 5 can be done in parallel.
  • 04:58 Let's talk about Step 4 first.
  • 05:00 In this step all the test articles are created.
  • 05:03 If the test is a destructive test that can be many articles, one for
  • 05:07 each configuration.
  • 05:08 If the test is not a destructive test and the factor settings are adjustable,
  • 05:13 you can reuse the test articles for multiple tests.
  • 05:16 If this is a process analysis, the test articles may be generic and
  • 05:21 should be as close to identical as possible, and
  • 05:23 what will be changed are the process settings for each run.
  • 05:27 While the test articles are being prepared, the test procedure for
  • 05:30 each experimental run needs to be clarified.
  • 05:33 The goal is for each run to be identical except for
  • 05:36 the factor changes, that's why the procedure is specified.
  • 05:40 You don't want different test operators to follow different procedures,
  • 05:43 unless that's one of the factors being tested.
  • 05:46 Step 6 then is to conduct the test runs.
  • 05:49 Normally these are done in a random order to minimize the likelihood that
  • 05:52 the operators or test conditions can impact the results.
  • 05:55 But even then the order must be carefully followed.
  • 05:58 The statistical software will need to know exactly which configuration is associated
  • 06:03 with each data point.
  • 06:05 So these must be carefully recorded.
  • 06:08 Often the statistical software application that's used will randomize the tests and
  • 06:12 dictate the test sequence.
  • 06:14 Step 7 is to analyze the results statistically to determine the optimal or
  • 06:18 desired settings for the product processor system.
  • 06:22 And Step 8 is a good practice to follow.
  • 06:25 The final settings are used to create another one or two tests samples and these
  • 06:29 are tested as a confirmatory test to be sure that the performance is as expected.
  • 06:34 The steps for the full factorial DOE study are logical and it's important that
  • 06:38 they're followed to ensure valid statistics and meaningful study analysis.

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