By Ron Pereira Updated on April 1st, 2013

No matter if you call yourself a “lean practitioner” or “six sigma practitioner” or some combination of the two… one “tool” you should have a deep understanding of is the control chart.

I’ve written about control charts before so if you’re not familiar with what they are I’d suggest you check these articles out before pressing on with this article.

**Control Charts Part 1**: Learn what control charts are, their history, and why control limits are +/- 3 standard deviations from the mean.**Control Charts Part 2**: Learn about Attribute Data Control Charts (P chart, C chart, and U chart)**Control Charts Part 3**: Learn about Variables Data Control Charts (I MR chart)

With this said, what I’ve discovered is that there are a few “details” related to control charts that many lean and six sigma practitioners aren’t aware of.

As such, I’d like to discuss 5 of these details in this article.

First, the “power” of any statistical test is directly related to sample size. The greater the sample size the greater the statistical power.

So, in order to ensure your control limits – which are calculated at +/- 3 Sample Standard Deviations from the mean – you should collect at least 100 data points.

If you don’t have at least 100 data points you can still calculate control limits but you should consider the results preliminary.

Next, when working with the I-MR or Xbar-R Charts we should always study and interpret the MR and R Charts before the I or Xbar Charts.

The reason this is so critical is because both the I and Xbar Control Limits assume the variability in the process is in statistical control.

So, even though the MR and R charts are shown below the I and Xbar charts we need to look at them first.

Furthermore, if we see any special cause variation in the MR and R charts we should seek to understand and counter the root cause of that variation before we take any action on the I and Xbar charts.

Most Statistical Software packages, such as Minitab, allow you to test for 8 different types of special causes.

These tests were originally developed by Walter Shewhart and are sometimes referred to as the Western Electric Rules.

As it turns out, the statisticians at Minitab have done extensive testing and discovered that tests 1, 2, and 7 are the most useful for evaluating the stability of the Individuals and Xbar charts.

- Test 1 checks to see if any 1 point is greater than 3 standard deviations from the mean.
- Test 2 checks to see if there are at least 9 points in a row on the same side of the mean.
- Test 7 checks to see if there are 15 points in a row within 1 standard deviation of the mean.

Of course you’re definitely free to use any of these 8 tests but, as a starting point, we’d encourage you to at least start with these 3.

Next, while the I-MR Chart is extremely powerful it is limited since each data point is created from a sample size of 1.

So, if we’re able to collect more than one sample we should since doing this will allow us to minimize any noise, for lack of a better word, within each subgroup while maximizing our ability to spot any signals, or special causes, between subgroups.

And this is where Rational Subgroups come in.

Formally defined, a Rational Subgroup is one in which multiple samples are collected so that the chance for variation due to special causes occurring within a subgroup is minimized, while the chance for identifying special cause variation between subgroups is maximized.

Finally, if we’re able to collect data in Rational Subgroups the “variation chart” we choose depends on the size of the subgroups we collect.

- Xbar-R Chart: We should use the Xbar-R (Range) Chart when our Rational Subgroups are less than 8 but greater than 1.
- Xbar-S Chart: We should use the Xbar-S (Standard Deviation) Chart when our Rational Subgroups are greater than 8.

Now, since the Xbar-S chart uses the Standard Deviation it is more powerful than the Xbar-R chart which simply uses the Range.

If you’re interested in learning much more about control charts and any other lean or six sigma topic I’d encourage you to check out the **Lean and Six Sigma Training** we’re continuously developing over at Gemba Academy.

## Beth Sampson

September 25, 2012 - 10:09 amThank you for posting this. In all my training I have never heard that the R chart should be examined first but upon reflection it does make perfect sense. If your R chart is out of control then the I chart control limits will obviously be unstable. I definitely learned something new today. Thank you again.

## Ron Pereira

September 25, 2012 - 10:26 amYou’re very welcome, Beth. Thanks for the kinds words and comment!

## Mark Reynolds

September 25, 2012 - 10:59 pmNice article. I have used MR charts for over 20 years, it’s very easy to become complacent in your activities.

Key point articles, like this one, bring you back to the core objectives of the management of process variation, rather than just ticking along. Thanks

## Ron Pereira

September 26, 2012 - 7:18 amThanks for the comment and for reading, Mark. Glad you liked the article!

## Mohammad Ajlouni

September 28, 2012 - 1:24 amThis is a great article. I would like to comment on the 100 data points issue.

Dr. Donal Wheeler has written many books on statistical control charts and their use in QC, finance and business in general. Dr. wheeler called them Process Behaviour Charts. These charts are based on R and X charts and are called XmR charts.These charts can be created starting from as few as 12 data points.

In his book “Short Run SPC”, Dr. Wheeler describes a number of statistical control charts that can be adapted to short prodcution runs. These charts require only a few data points, which in reality what you can get from a short production run. Examples on these charts are the “:difference” chart and the “zed” chart. These are very useful for small-lot manufacturing.

Mohammad Ajlouni

## Ron Pereira

September 28, 2012 - 7:11 amThanks for the comment, Mohammad. Yes, Wheeler’s book is one of my all time favorites and I link to it in the earlier articles I wrote.

Regarding sample sizes… yes, you can definitely use control charts with small sample sizes but, as with anything related to “power and sample size” the more data the greater your statistical power which is why you can create them with less than 100 data points but, in my opinion, extreme care must be taken if you make major decisions based on the data.

Also, if you use software like Minitab they also recommend having at least 100 data points. See the notes in the Minitab Assistant related to control charts and you’ll see where they give huge warnings when sample size is less than 100.

## John Hunter

September 29, 2012 - 7:14 amI really think you can get quite solid results with far fewer than 100 data points. I think, often 30 data points can be plenty to treat results as useful. I would be more willing to distrust an indication at 30 data points than points than one at 100. It depends on the situation, of course, but I I would trust most control charts way before 100 points, normally way before 50.

Short run SPC is a very good book by Don Wheeler on drawing conclusion from very short runs of data.

I certainly would suggest including a special cause indication with 7 points in a row, all increasing or decreasing. I also prefer an indication at 7 points in a row above or below the mean.

## Ron Pereira

September 29, 2012 - 7:23 amThanks for the comment, John.

Here is a good paper written by the folks at Minitab I’d encourage you to check out: http://www.minitab.com/en-US/support/documentation/Answers/Assistant%20White%20Papers/VariablesControlCharts_MtbAsstMenuWhitePaper.pdf

I am also a huge Wheeler fan but tend to side with Minitab on this one and really feel like small sample sizes (less than 100) often lead practitioners in wrong directions far more than they realize.

Plus, since Control Charts should be dynamic in nature collecting at least 100 data points shouldn’t be that hard to do. Sure, start with 30… but don’t stop. SPC isn’t a one and done activity.

And, again, like I said, you can still create control charts with 30 data points but should – in my opinion – consider them preliminary and not bet the house on the results. Doing so could be reckless statistics.

## John Hunter

September 29, 2012 - 8:19 pmI completely agree the control chart should be continuous (as in you just keep collecting data).

I agree you don’t treat a “special cause” signal after 30 data points as TRUTH. The thing many people forget is a signal anytime (after 100 or whenever) is NOT PROOF of a special cause. It is a signal that there seems to be a high likelihood of a special cause and using special cause thinking is a profitable strategy given this signal.

One of my pet peeves is people saying that a point outside the control limits (for example) IS a special cause. It is not. It is an indication that likely a special cause exists and special cause thinking is the correct strategy to use. But that doesn’t mean there definitely was a special cause – it could be a false signal.

I do agree you would be wise to temper your conviction of how aggressively to invest in investigating the special cause signal depending on your knowledge of the situation (and a relatively small number of data points would be one factor, as would the cost of the investigation, the impact that such a signal may indicate [if it has little impact on the customer, maybe waiting to get more conviction is fine…]).