Six Sigma: X Bar and R Charts

X Bar and R charts are probably the most powerful control/process behavior charts available. In the video below we help explain how you can use them for your own Six Sigma projects.




The original control chart, invented by Walter Shewhart, was the X bar and R chart and that depends on what we call rational subgroups of data. Now, frequently X bar charts are done wrong and the most common failure, is failure to form rational subgroups. So these five data right here 100.6, 103.6, 97.1, 102.3, and 104.7 need to be a rational subgroup. Well, what’s a rational subgroup? That’s a set of items that were produced under conditions that are as nearly identical as possible, so these maybe five sequential items that came off one machine.

What we’re going to plot is the average. That’ll be the X bar. That’s the average of these five data and the lower chart will be the range chart, which will simply be the largest of these minus the smallest. That 7.62. Now, what I’ve done for you is I’ve opened up QuikSigma and under baseline and capability, which happens to include the behavior charts, I’ve opened up the X bar and R chart, and I’ve taken this first rational subgroup, here, and I placed it in the column here, and I’ve indicated that it’s subgroup number one. Now, alternatively, if I can leave this column blank and just click here and tell it that my sub groups are all size 5 and by the way, you may wonder, does it have to be five? No, it doesn’t. 2, 3, 4, 5, up to possibly as many as 10. Depends on what you want to do.

Now, the next thing that I will do after I open that back up, is I will bring this next subgroup over and maybe that’s a set of samples that we’re taking an hour later. Then I’ll take the third one and the fourth, and I’ll start to fill out the column over here. So I’ll do that, and then come back and show you the result. What I’ve done is I’ve transferred over all 25 subgroups that were generated in the random number generator. You can see that here I have checked
the four Western Electric rules and I’ve clicked calculate. So that produces my chart and I look at my subgroup means here and they’re nice and stable and predictable. Well, that’s kind of what you get when you get your data out of a random number generator and below here the ranges we’ve got a couple of points that are showing rule violations. You will occasionally get a false positive. So every time you get a a rule violation doesn’t necessarily mean there’s a problem. It just means you ought to look and see if there is a problem.

So there you have X bar in R charts. The key is rational subgroups. The reward is these are more sensitive than I-MR charts. They’re a little harder to do, but they give a better result.

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