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This lesson builds on the previous factor selection lesson. However, now it addresses how the factor selection process changes as a fractional factorial DOE progresses through two or three levels of studies.

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Quick reference

Factor Selection

The Fractional Factorial DOE factor selection must consider several key items. One is the phase of the DOE.  The results of each phase influence the decisions for the factors of the next phase. The second is the level of each factor. 

When to use

Fractional Factorial DOE factor selection must be done at three different times within the typical DOE study. First at the screening phase, then the refining phase and finally the optimizing phase. The number of factors selected normally reduces with each phase although the number of levels may increase.

Instructions

The criteria for a control factor in a Fractional Factorial DOE are the same as for a Full Factorial DOE; the factors should be practical, feasible, and measurable. However, the number of factors and factor levels will often change as the Fractional Factorial DOE progresses from one phase to the next. 

The screening phase will have the most factors and these will virtually always be two-level factors. The purpose of this phase is to determine significance. The two level factors will provide that level of insight. Those factors that are not significant should be locked into a setting that is the best business value (cost, quality, performance) for that factor during the remaining two phases. Any significant qualitative factor should be set at the level that has an optimum performance as the study moves to the next phase.

The refining phase will normally have less than half the number of factors as the screening phase. In addition, these factors are usually all quantitative factors. Often these will be multi-level factors – the most commonly chosen number of levels is three.  Depending upon the number of factors and the number of runs the study can accommodate, this will be a full factorial or as close to it as possible. This allows the team to get an excellent understanding of the non-linear effects of a factor. Adding the additional points of multi-level factors will help to define zones of sensitivity and inflection in the system performance.

The final phase is the optimizing phase. Sometime this phase is not needed because the analysis of the refining phase has already determined the optimal settings for factors.  However, even then I recommend a final confirming run. If the phase is needed it is normally to investigate one or two factors for sensitivity within a relatively narrow range.  This can be done by varying that one factor and setting all others to their optimal settings, similar to what is done in an OFAAT analysis.

A debate often occurs over whether to use two-level factors or multi-level factors. Each has its good points and weak points. Two-level factors will result in a smaller simpler study and great insight into primary effects. But it provides little insight into non-linear effects and almost no useful help with designing tolerances for the factors.  The multi-level factors do provide insight into non-linear effects which will help to identify inflection points in the system performance. The disadvantage with these factors is that it will be a bigger an more complex study and these cannot be used with the qualitative attribute factors.

Hints & tips

  • When selecting factors for the screening study, be sure the factors are really control factors that can be used to drive performance.
  • You may want to retain a qualitative factor for the refining study if the factor was involved in a significant interaction effect with a quantitative factor. Minitab can create a DOE study design with a mixture of two-level and multi-level factors.
  • I prefer to always do a confirming run as part of the optimization phase, even if that run configuration was done as part of the refining phase and showed excellent performance. The additional confirmatory run adds credibility to the design decisions.
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  • 00:01 Hello, I'm Ray Sheen.
  • 00:05 Well, let's look again at factor selection.
  • 00:08 And this time with a focus on the fractional factorial DOE study.
  • 00:13 The fractional factorial factor selection process has some additional
  • 00:18 levels of complexity as compared to the full factorial process.
  • 00:22 The basic attributes of the control factors are similar to what we've
  • 00:26 discussed when looking at full factorial factor selection, things like practical,
  • 00:31 feasible and measurable.
  • 00:32 But one big difference in fractional factorial DOE is
  • 00:36 that there are often more factors, and possibly many more factors.
  • 00:40 Remember, the fractional factor DOE does not need as many runs so when the cost or
  • 00:45 time for the number of test runs is limited on the size of the study,
  • 00:49 the fractional factorials DOE can study many more factors with the limited
  • 00:54 number of test runs.
  • 00:56 Another characteristic is that typically all the factors in the screening
  • 01:00 phase of the study, are tested as two level factors.
  • 01:03 That keeps the number of runs small, and yet
  • 01:06 can still show significance of the factors.
  • 01:08 And the refining study will normally have multi-level quantitative factors.
  • 01:13 The qualitative factors normally are not studied in the refining study since their
  • 01:17 significance has already been determined.
  • 01:20 They're just set at the proper level based upon the results of the screening study.
  • 01:24 This refining study then uses quantitative factors to find their sensitivity,
  • 01:30 and any performance limits.
  • 01:32 The optimizing study is often only one run of ideal settings, or
  • 01:36 several runs, but usually with only one or maybe two factors that are varying.
  • 01:40 This is to confirm the optimal performance point, and
  • 01:44 I have occasionally used it to help with setting tolerances.
  • 01:47 Let's take a moment to discuss why you would want to use
  • 01:50 multi-level factors instead of two-level factors in the refining study.
  • 01:55 Two-level factors focus on significance.
  • 01:57 As you can see in the chart, a low factor level is much more significant than a high
  • 02:02 factor level for this example.
  • 02:04 But real word effects are seldom precisely linear.
  • 02:07 So a three-level factor, or higher, will be better able to approximate the actual
  • 02:12 impact of the factor on the operational system performance.
  • 02:16 You can see that by adding the middle point in this factor with an exponential
  • 02:20 effect, the approximation becomes very close.
  • 02:23 It should be obvious, but I will state it anyway.
  • 02:27 Multi-level factor settings are only used with quantitative
  • 02:31 factors whose values can vary in small increments.
  • 02:34 Multi-level factors, and just to be clear, that usually means three-level factors,
  • 02:39 model the factor behavior with more accuracy which means that they can do
  • 02:43 a better job of predicting the response behaviour.
  • 02:47 But of course, three-level factors will require many more runs.
  • 02:50 We saw that in an earlier lesson.
  • 02:52 Let's do a quick pro and con assessment of two and three double factors.
  • 02:57 Two-level factors have the advantage of a simpler study design because there
  • 03:02 are fewer tests.
  • 03:03 Also, these are very well suited to identify which factors have a major effect
  • 03:08 on response and which have a minor effect.
  • 03:10 For this reason, they are very well suited to the screening phase of a DOE.
  • 03:14 But the strengths also provide insight into the weaknesses or
  • 03:18 cons with these factors.
  • 03:20 All effects are assumed to be linear, yet
  • 03:22 most real-world effects are not perfectly linear.
  • 03:25 In addition, these factors are not good for determining sensitivity, and
  • 03:30 therefore they don't provide much insight for
  • 03:32 when trying to set tolerances to minimize costs or maximize performance.
  • 03:37 Now let's consider multi-level factors.
  • 03:40 These do provide insight into non-linear effects of the factor on system response.
  • 03:45 That means that hey can identify zones in the factor that have little impact on
  • 03:49 response, and zones that have major impact on response.
  • 03:53 Knowing the inflection point when the factor changes its effect is
  • 03:56 useful from both system design and tolerancing.
  • 03:59 That is why these are ideal for refining and optimizing.
  • 04:02 And that is why my preference is for
  • 04:04 using multi-level factors with the refining phase.
  • 04:07 But I recognize that opinion is not universally shared.
  • 04:10 If your organization has a policy, follow it.
  • 04:13 Let's translate what we have been discussing into ground rules for
  • 04:17 each phase of a fractional factorial DOE study.
  • 04:20 First, the screening phase, in this phase you're analyzing many factors,
  • 04:24 for that reason you'll want to do a fractional factorial DOE, and
  • 04:28 normally a pretty small fraction to keep that phase small and fast.
  • 04:32 Use two-level factors in order to check for significance.
  • 04:35 Now in the refining phase, all the qualitative factors and insignificant
  • 04:40 factors from the screening phase should be set as constants for this phase.
  • 04:44 If the qualitative factor was significant, pick the best technical performance level.
  • 04:49 For all insignificant factors, pick the level of best business impact.
  • 04:54 That may be driven by cost or quality or scheduling or customer satisfaction.
  • 04:58 That means that the only thing you are varying are the most significant
  • 05:02 quantitative factors.
  • 05:04 And if the number of factors permits,
  • 05:06 I will do this with a full factorial study and often with multilevel factors to
  • 05:11 maximize my understanding of the impact on system performance.
  • 05:15 Finally, the optimizing phase.
  • 05:18 This may not be needed, depending upon the size and
  • 05:21 results of the refining phase.
  • 05:22 Normally, this is a confirming test of the optimal factor settings.
  • 05:26 You may still be doing some focused analysis of one or
  • 05:30 two factors to nail down sensitivity, which leads to tolerances.
  • 05:34 For that reason,
  • 05:35 if you are testing a factor it will probably be in a multilevel mode.
  • 05:40 It should be clear by now, that factor selection, whether it's for
  • 05:45 a full factorial study, or a fractional factorial study,
  • 05:49 is a key to the design of the study and the validity of the results.

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