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Quick reference
Plackett-Burman DOE
The Plackett-Burman Fractional Factorial DOE is the most efficient method to conduct a screening study. It minimizes the runs by restricting factors to two-level factors and eliminating the analysis of any interaction effects.
When to use
This technique is used in the screening phase when there is a large number of control factors.
Instructions
Plackett-Burman DOE is the most efficient method for conducting a screening phase of a Fractional Factorial DOE. This technique reduces the number of test runs to the absolute minimum that will provide main effect calculations using a balanced and orthogonal matrix.
The test runs will always be in blocks of four – that is how it is able to maintain the balanced and orthogonal aspect of the analysis. The number of factors can be up to one less than the number of rungs. So, 11 factors can be analyzed with 12 runs. However, 12 factors will need to jump up to the next block of four so that many factors will require 16 runs.
The Plackett-Burman DOE only determines main effects. All interaction effects are confounded with a main effect. This does lead to a risk that if the true significant aspect of the product, process or system design was an interaction effect, this analysis would point to an otherwise irrelevant factor as the main effect. However, for a screening study, the risk is low that critical effects will be missed.
Attempting to create the test matrix by hand is very difficult. Therefore, use a statistical analysis application such as Minitab to set up the test matrix for you. One constraint for the Plackett-Burman factors is that they can only be two-level factors, no multi-level factors. However, since the screening study is normally completed with only two-level factors this constraint is not a barrier to the use of the technique.
Hints & tips
- If you have more than ten factors, you should seriously consider using Plackett-Burman.
- If you have less than four factors, don’t use Plackett-Burman, just do a full factorial and be done.
- Normally, if an interaction effect is significant, at least on or more of the interacting factors will be significant.
- 00:04 Hello, I'm Ray Sheen.
- 00:05 I want to discuss a special case of fractional
- 00:10 factorial DOEs known as Plackett-Burman.
- 00:14 You may be wondering what is a Plackett-Burman DOE?
- 00:18 Well, it's a very effective fractional factorial DOE that can analyze
- 00:23 dozens of factors with very few runs.
- 00:25 It's named after the gentlemen who developed the approach, Robin Plackett and
- 00:29 J.P. Burman.
- 00:30 They created the methodology way back in the 1940s when all the calculations and
- 00:35 set up had to be done by hand because there was no computers available to do it.
- 00:39 In fact, their study was based upon an agricultural problem where they wanted to
- 00:43 understand what were the major effects on crop yield.
- 00:46 And they had over 30 factors that they wanted to study.
- 00:49 The key principle they applied, which earned them some ridicule from
- 00:53 the mathematical gurus who were the gatekeepers of DOE at the time,
- 00:57 was that they ignored the interaction effects.
- 00:59 They only wanted to know what were the main effects.
- 01:02 Frankly, that's an eminently practical question when working with agriculture in
- 01:07 the 1940s.
- 01:07 The mathematicians may find the coefficient for
- 01:10 third order effects highly interesting.
- 01:12 But the farmer wants to know,
- 01:14 what are the top four or five things that they need to worry about each year?
- 01:18 And that is why I love to use Plackett-Burman for
- 01:21 screening studies, especially if I have lots of potential factors.
- 01:25 It boils those down to the vital few that I need to concentrate on.
- 01:29 I can then take these to a refining phase of my study.
- 01:32 So how do we setup or design one of these studies?
- 01:36 One thing to understand is that the number of experiments or
- 01:40 runs will always be a factor of 4, things like 8, 12, 16, 20, 24, and so on.
- 01:46 The reason for this is that you need to have a multiple of 4s to have a balanced
- 01:51 and orthogonal test matrix.
- 01:53 The number factors that can be analyzed is one less than the number of test runs.
- 01:59 So 12 runs can analyze up to 11 factors.
- 02:03 And 20 runs can analyze up to 19 factors.
- 02:07 This approach does not come free; an issue to recognize is that all of
- 02:10 the interaction effects are compounded, you only have main effects.
- 02:14 But that maybe okay for a screening phase.
- 02:17 One thing that you have available to you that Plackett-Burman did not is Minitab.
- 02:22 When you select create study design from the DOE menu, you get this panel.
- 02:26 Well, instead of using the first line which is the default,
- 02:30 select the Plackett-Burman design.
- 02:32 Notice that you could have up to 47 factors with this approach.
- 02:37 Next, select the number of factors that you have, and
- 02:40 Minitab will create the matrix.
- 02:41 This is the matrix for
- 02:43 the 11-factor Plackett-Berman that I had selected on the previous slide.
- 02:48 Notice, one of the constraints is that you can only use 2-level factors.
- 02:53 But that's what we normally do with screening phase anyways, so
- 02:56 really isn't a problem for us.
- 02:58 And we have 12 runs, a number that is a factor of four, and
- 03:02 that means the matrix is balanced and orthogonal.
- 03:05 You can check for balance quickly by seeing that if you add all the columns,
- 03:09 they total 0.
- 03:10 Orthogonal will require you to multiply each of the columns together and
- 03:14 then add the result.
- 03:15 And I'll just leave that for you to do on your own time at your leisure.
- 03:19 Let's wrap this up with a discussion of the pros and
- 03:22 cons of using the Plackett-Burman approach to fractional factorial DOE.
- 03:27 First, we must acknowledge that this is a special case DOE design and
- 03:31 should only be used under certain conditions.
- 03:33 That means we only use it in screening studies with two-level factors.
- 03:37 Typically, at this point we're not worried about interaction effects.
- 03:42 Which is okay because Plackett-Burman won't give us those.
- 03:45 And it only makes sense to use this when you have more than four factors and
- 03:49 usually a lot more than four.
- 03:51 If there are less than four factors, just do a full factorial DOE.
- 03:55 Finally, if money or time is short,
- 03:58 use this approach to at least understand the main effects.
- 04:02 Which brings us to the advantage of using this approach, it's fast and cheap.
- 04:06 The more factors you want to analyze, the more important this becomes.
- 04:11 And we've already mentioned the downside.
- 04:13 But let me quickly summarize.
- 04:14 No interaction effects are identified.
- 04:16 Everything is treated like its a main effect.
- 04:18 And that means that if one of the true main effects is interaction effect,
- 04:23 it will be confounded with something else which may not be at all important.
- 04:27 That means you could wind up trying to analyze something in your
- 04:31 refining study that is actually irrelevant.
- 04:34 When you have lots of factors and you need to isolate down to a vital few,
- 04:39 the Plackett-Burman fractional factorial DOE approach is the one that
- 04:44 best fits that bill.
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