Repetitions versus Replications

Many Six Sigma practitioners struggle to differentiate between a repetition and replication. Normally this confusion arises when dealing with Design of Experiments (DOE).

Let’s use an example to explain the difference.

Sallie wants to run a DOE in her paint booth. After some brainstorming and data analysis she decides to experiment with the “fluid flow” and “attack angle” of the paint gun. Since she has 2 factors and wants to test a “high” and “low” level for each factor she decides on a 2 factor, 2 level full factorial DOE. Here is what this basic design would look like.

Now then, Sallie decides to paint 6 parts during each run. Since there are 4 runs she needs at least 24 parts (6 x 4). These 6 parts per run are what we call repetitions. Here is what the design looks like with the 6 repetitions added to the design.

Finally, since this painting process is ultra critical to her company Sallie decides to do the entire experiment twice. This helps her add some statistical power and serves as a sort of confirmation. If she wanted to she could do the first 4 runs with the day shift staff and the second 4 runs with the night shift staff.

Completing the DOE a second time is what we call replication. You may also hear the term blocking used instead of replicating. Here is what the design looks like with the 6 repetitions and replication in place (in yellow).

So there you have it! That is the difference between repetition and replication.

Note: If you call these concepts by different terms please do share by leaving a comment.

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6 Comments

  1. curiouscat

    May 9, 2007 - 9:34 pm

    It is possible cost considerations may lead you to not do the runs in a random order but that would be preferable, right (between replications, for example).

    Shouldn’t the blocked runs be randomized between the blocks? For example, the run order for the day and night shifts be different.

    George Box has some interesting reports on related matters (see what you can learn in 8,12 and 16 runs).

    And of course I think
    >Statistics for Experiments
    has good info for those interested in more info, but I am biased.

  2. Ron Pereira

    May 10, 2007 - 2:17 am

    Hi John, excellent points that I forgot to mention! We should definitely randomize runs if possible within blocks. Like you said, this may not be possible for cost or time purposes. For example, if we are heating up an injection mold machine we may get it to temp 1 and do all the runs at that temp and then move to temp 2. Of course even this is tricky as holding it at “temp 1” can be tricky. Thanks for the links. I will check them out.

  3. Jennifer Adams

    September 1, 2010 - 8:29 pm

    I was struggling with how to explain the difference between these to my 7th graders, and you just made it 100% easier for me!!…of course I probably won’t use the exact example of Sallie and her DOE, but I will use your ideas! 🙂 Thanks!

  4. Amit

    October 16, 2010 - 6:04 am

    Repetition is better than replication ? R=True or false ?

  5. Gagan

    June 6, 2012 - 3:46 am

    Thank you so much for explaining this concept with simple example. I read this concept many times but used to forget. Now I think I will remember it with the example.