Fractional Factorial Pros and Cons

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About this lesson

This lesson compares the difference between the full factorial approach and fractional factorial approaches. It explains the pros and cons of using a fractional factorial methodology.

Quick reference

Fractional Factorial Pros and Cons

Fractional factorial reduces the number of runs needed to complete the analysis.  There are both pros and cons to this approach.  When the limitations are understood, the technique can be used to gain excellent results with lower cost and time.

When to use

The more factors and complexity within the system or problem, the greater the advantage of using a fractional factorial DOE.  When time and money are significant factors in the analysis, this approach will be more efficient.

Instructions

Fractional factorial DOE studies are exactly what their name implies. A DOE that only uses a fraction of the runs that are used with a full factorial DOE. Which runs used must be carefully selected and that will be covered in another lesson. However, the reduction in the number of runs can save a great deal of time and money.

The disadvantage with the fractional DOE is that the analysis of interaction effects is limited based upon the level of the fraction used. This is not a problem when a system is dominated by primary or main effects. In a complex system, a multi-phase approach is often used. The first phase, a screening phase, uses a high fraction and many factors to determine which are significant and which are not. Next is a refining phase which sets the insignificant factors at the best business value and further analyzes only the significant factors with either a full factorial analysis or a small fractional factorial analysis. Based upon these final results, an optimizing phase is often done that sets the factors at the optimum level and confirms the expected performance. Even though this takes three phases, the total number of runs is often much less than the number required for a full factorial DOE. For this reason, the middle or refining phase will often have multi-level factors and replicates and center points to improve the statistical analysis of these critical factors that are analyzed in this phase.

The tables below show the reduction in number of runs needed for 2-level and 3-level factors.  Note that 2-level factor fractions are always divisible by 2 and 3-level factor fractions are always divisible by 3.

Hints & tips

  • The multi-phase approach reduces the number of runs and can actually increase the statistical accuracy and confidence.
  • Use 2-level factors for the initial screening portion of the study and see which factors have a high coefficient.  These factors are often studied in the refining portion of the study but with narrower limits or multi-level factors to clarify the effect on performance.
  • Even adding replicates or center points, a fractional factorial study can reduce the number of runs by half.
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  • 00:05 Hi, I'm Ray Sheen.
  • 00:06 I now wanna discuss the Design of Experiments approach known as
  • 00:09 Fractional Factorial DOE in more detail.
  • 00:11 And I'll explain some of the pros and cons of using this approach.
  • 00:16 I need to start by defining my term.
  • 00:19 What do I mean by fractional factorial?
  • 00:22 Well, fractional factorial DOE is a more efficient form of DOE than
  • 00:26 the full factorial method.
  • 00:28 It still tells us what is most important and we still get a design space
  • 00:32 equation but we can do this with only a fraction of the number of test runs.
  • 00:37 And that is where it gets its name.
  • 00:39 Only a fraction of the runs of a full factorial DOE are used.
  • 00:43 It maybe a half fraction, a third fraction, a fourth fraction,
  • 00:47 we'll look at those in a few minutes.
  • 00:49 One major change in how we do fractional factorial DOEs as compared to full
  • 00:54 factorial DOEs,
  • 00:55 is that we often do a fractional factorial with all the control factors.
  • 00:59 And then you use the results to do a follow-up fractional or
  • 01:03 full factorial DOE with just those factors that had a major effect.
  • 01:07 The first set of experiments screens the analysis to determine
  • 01:12 what we will refine in the second set.
  • 01:14 The fractional factorial approach is typically used with a complex system that
  • 01:19 has many factors.
  • 01:20 Since it is much more efficient than full factorial, you can
  • 01:23 sift through all those factors with an efficient fractional factorial DOE and
  • 01:28 then focus on a select few.
  • 01:30 Since a major difference of the fractional factorial DOE is that there are fewer runs
  • 01:34 required, let's look at the amount of reduction.
  • 01:37 First we'll look at the two level factors.
  • 01:40 The number of experiments that we do will be a fraction of the full factorial,
  • 01:44 which is shown on the leftmost column.
  • 01:46 Since these are two level factors, the reduction is occurring by a factor of two.
  • 01:51 So a full factorial, seven-factor study is 128 runs.
  • 01:54 A half factorial, seven-factor study is only 64 runs.
  • 01:59 A one-fourth factorial, seven-factor study is 32 runs, and
  • 02:03 one-eighth factorial seven-factor study is only 16 runs.
  • 02:07 Again, we'll need to do a statistical analysis of the results to
  • 02:11 determine which factors are significant.
  • 02:14 And one of the cons that we will look at more in another lesson is that we
  • 02:18 must carefully choose which runs we do, it's not just any 16 runs.
  • 02:23 Another con is that when we do fractional factorial DOE,
  • 02:26 we lose some of our ability to calculate the interaction effects.
  • 02:30 The main effects can still be determined but not all of the interactions.
  • 02:35 We looked at two-level factors, let's jump now to multi-level factors, and
  • 02:39 I'll use the three-level factor in my example.
  • 02:42 A multi-level factor accounts for a relationship between the control
  • 02:46 factor and the response variable that is not a straight line effect.
  • 02:50 The extra point in the middle will help to shape the curve.
  • 02:54 You could use four or five levels if you felt you needed them to get a detailed
  • 02:59 shape of the control factor versus response variable curve.
  • 03:03 Frankly, I've never used more than three.
  • 03:05 One of the challenges with multi-level factors is that it increases
  • 03:10 the number of runs by a lot.
  • 03:12 Look at this table, with seven three-level factors, we need 2,187
  • 03:16 runs to do the DOE, and not just 128 runs that we needed with two-level factors.
  • 03:21 So its no surprise that the amount of reduction in runs for
  • 03:25 a fractional factorial with three-level factors is also much higher.
  • 03:29 A one-third fraction seven-factored DOE is down to just 729 runs.
  • 03:34 A one-nineth fraction seven-factor DOE is 243 runs.
  • 03:38 And one-twenty seventh fraction seven-factor DOE is only 81 runs.
  • 03:44 So let's take a look at the difference in runs when actually doing the DOE
  • 03:49 study between a full factorial and a fractional factorial.
  • 03:53 To illustrate this, I will use a study with seven control factors,
  • 03:57 five of these are quantitative and two are qualitative.
  • 04:00 The full factorial DOE is 128 runs, but
  • 04:03 the fractional factorial DOE can be done with only 71 runs.
  • 04:08 And frankly,
  • 04:09 I will have a better study statistically with the fractional factorial.
  • 04:13 Let me explain.
  • 04:15 For full factorial, I would do a seven-factor two-level DOE,
  • 04:18 which is 128 runs.
  • 04:19 With this I can calculate my design space equation, but
  • 04:23 all the effects are straight-line effects since they are only two-level factors.
  • 04:29 Now for the fractional factorial, I will do the study in three phases,
  • 04:34 but only 71 runs.
  • 04:35 First I will do a one-eighth fraction,
  • 04:38 seven-factor two-level fractional factorial DOE for a screening phase.
  • 04:43 No replicates, no center points, that only takes 16 runs.
  • 04:48 And let's say that those results show me the best levels to use for
  • 04:52 my two qualitative factors, and
  • 04:54 it shows that two of the quantitative factors are not significant.
  • 04:59 That leaves me with three significant quantitative factors.
  • 05:02 Now I will do the refining phase, but
  • 05:05 I really wanna understand those three factors.
  • 05:08 I will set the other factors at their best value determined by the screening study,
  • 05:13 and not change them.
  • 05:14 But I will take those other three factors and
  • 05:17 do a three-level full factorial study with replicates.
  • 05:21 Doing this with just three control factors takes 54 runs.
  • 05:25 So now, I did 16 runs in the first phase,
  • 05:28 54 in the second phase which adds up to 70 runs.
  • 05:31 I will now do one more run at the optimum values that I get when solving the design
  • 05:36 space equation for those three factors just to confirm that there are no errors.
  • 05:41 It's 71 runs.
  • 05:43 That's 57 runs less than full factorial and I did three-level factor study on
  • 05:48 the most significant factors to get better insight into the relationship, and
  • 05:53 with a full set of replicates I minimized noise around those three factors.
  • 05:58 Fractional factorial DOE will usually require significantly fewer runs,
  • 06:04 saving both time and money, but
  • 06:06 you lose the ability to fully capture the interaction effects.

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