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Davis Balestracci

Health Care

Your ‘Swiss Army Knife’ of Control Charts

Why the Individuals chart is good enough for purposes of improvement

Published: Monday, February 26, 2018 - 13:03

The Individuals chart is the “Swiss Army knife” of control charts. It usually approximates the supposedly “correct” chart under most conditions, and its use is much easier to understand and explain. It can also save you a major side trip into the swamp of unnecessary calculation minutiae, especially avoiding square roots!

Based on real data

Suppose a quality analyst (QA) comes to you saying, “We’re trying to reduce this particular infection, and I had some data: the number of infections and patient days for the past 30 individual months. My software led me down its decision tree and told me to do a u-chart, which you can see in figure 1:

Figure 1: U-chart of infection rate

“It’s obvious I need to investigate that special cause at month 22. And month seven got a zero! But since it’s right on the limit, it would probably be advantageous to investigate it anyway, right?”

A good consultant would reply...

GC: I’m more interested in what might be a significant reduction right after what seems to be the special cause at month 22. Did you notice that the most recent eight months’ performances are all below the average?
QA: But they’re between the limits!
GC: Which is why you should always do a run chart first and be aware of the eight-in-a-row rule.
QA: But the Nelson rules for control charts say you should use nine-in-a-row.
GC: Sigh… I think investigating these past eight months, especially month 23, would be a higher-yield strategy than digging into the zero at month 7, which wasn’t necessarily a special cause.
QA: Would the chart need to be recalculated to take this into account? Maybe month seven is a special cause!
GC: That’s the least of your worries at the moment. The run below the median of the last eight data points is gold. What I would do is aggregate those 19 infections that occurred during those months and brainstorm various ways to categorize them, then see how these tallied patterns are different from the same categorizations of the 134 infections of months one to 21. [This is the basic idea of stratification.] Unfortunately, it’s not much data at this point, but it’s all you’ve got.

Right now, the most fruitful approach might be asking what happened during month 23.

It also wouldn’t hurt to investigate what happened during month 22, but it was something outside of normal circumstances that doesn’t seem to affect routine performance. Is it something worth preventing in the future?

In any case, you can then use these last eight data points as a baseline, should you make more interventions.

QA: But that’s only eight data points. I was taught that you need 20 to 25 data points for a good baseline! Can I still use a u-chart?
GC: If it’s all you’ve got, it’s all you’ve got. Besides, you start to get reasonable limits with as few as seven to 10 points.
QA: No way! You didn’t answer my question about the u-chart. You probably can’t use an Individuals chart either because eight points can’t tell you whether the data are normally distributed.
GC: That normal distribution nonsense is a myth. Let me show you. Figure 2 is your u-chart adjusted for the shift, and figure 3 is the Individuals chart for the last eight data points:

Figure 2: U-chart of infection rate adjusted for shift

Figure 3: Individuals chart for the last eight data points

Note the similarity in limits. I’d say it’s a good enough approximation to move ahead in your improvement effort, as I suggested, without fretting about and getting seriously sidetracked about “accuracy” issues. It also gets rid of the annoying distraction of the stair-step limits, which never fail to cause a predictable tangent from what should be the main issue of keeping your focus and everyone else’s focus on the process needle.

By the way, also note that recalculation of the limits still shows that month seven’s zero was common cause.
QA: That’s still not a very long baseline. Do I need to recalculate my limits after every new data point? When can I stop?
GC: Sigh… let the data be your guide. It’s not a bad idea to keep recalculating for now. The more important question of the moment is, “How will you know if your intervention is effective?”

Need more proof?

Figure 4 is another u-chart showing 30 months of stable behavior for a different facility where nothing has changed (and once again, zero is not necessarily a special cause to celebrate). Figure 5 is an Individuals chart approximation of the same data. Note the similarity of the limits. Those of the Individuals chart are a good enough approximation for purposes of improvement.

Figure 4: U-chart of infection rate for a different facility

Figure 5: Individuals chart using the data from figure 4

Rather than waste precious meeting time over which chart is more correct, the time would be much better spent aggregating the 109 infections produced by this system during this stable 30 months of behavior and brainstorming ways to stratify them to do a Pareto analysis. That would also be far more productive than investigating the (nonexistent) “disturbing upward trend” during months 15 to 19 and the “high” performance (> 20!) of months five and 14.

The wisdom of Dr. Donald Wheeler:
“The purpose is not to have charts. The purpose is to use the charts.... You get no credit for computing the right number—only for taking the right action. Without the follow-through of taking the right action, the computation of the right number is meaningless.” (From “When Do I Recalculate My Limits?” Quality Digest, May 1996.)


About The Author

Davis Balestracci’s picture

Davis Balestracci

Davis Balestracci is a past chair of ASQ’s statistics division. He has synthesized W. Edwards Deming’s philosophy as Deming intended—as an approach to leadership—in the second edition of Data Sanity (Medical Group Management Association, 2015), with a foreword by Donald Berwick, M.D. Shipped free or as an ebook, Data Sanity offers a new way of thinking using a common organizational language based in process and understanding variation (data sanity), applied to everyday data and management. It also integrates Balestracci’s 20 years of studying organizational psychology into an “improvement as built in” approach as opposed to most current “quality as bolt-on” programs. Balestracci would love to wake up your conferences with his dynamic style and entertaining insights into the places where process, statistics, organizational culture, and quality meet.


Nice Job, as usual

"There are people who are afraid of clarity because they fear it may not seem profound."

Thanks Davis for a very nice illustration of what is important and what is not.

Thank you, Dr. Wheeler

I appreciate your kind comments. I have so much gratitude for what you have taught me over the years.



Detecting "small" changes quickly

No beef about not obsessing over the use of the "correct" attribute chart in this case.  But, I continue to be wary of the idea that all that is needed for SPC are I/MR charts.  In many manufacturing cases, we want to detect process changes (e.g. 1-2 sigma shifts) that are not likely to be detected quickly using I-MR charts. 

So, I think it's important to consider each process and ask the question, what kind of process change would we be interested in detecting since the purpose of the control charts is to detect process changes.  The answer could be very different depending on the risk, current capability, etc.

The answer may lead to using Xbar charts of sufficient sample size to produce signals (and detect changes) in a TIMELY basis, or CUSUM/EWMA charts for individuals. 

I think we are too quick to say we must make it simpler for everyone by using using I-MR charts for everything.

Great point, Davis!

As usual, an excellent article, Davis. I didn't actually see where you said to use an XmR chart exclusively, just that it does often work. 

What I have found effective, given software such as JMP or Minitab, is that if you have counts of items ("binomial" data) or counts of events ("Poisson" data), the XmR chart is more robust to any assumptions associated with it than the P, nP, C or U charts are to the many assumptions associated with them. The XmR chart is an empirical tool that does not rely solely on theory for the calculation of its limits. An nP chart, for example, cannot tell the difference between a data set containing all twos and eighteens and a data set containing all nines and elevens; the averages will (of course) be the same, and so will the limits! That is not true of an XmR chart, that takes its limits empirically from the data. 

So, when I have counts of items or events, I will usually run the XmR chart as well as the appropriate count chart. For one thing, the count charts (as Don Wheeler points out) "build up degrees of freedom faster" than XmR equivalents. For that reason, I always use an nP chart with the Red Bead. It also helps to find those cases where a small area of opportunity (denominator) creates what appears to be a special cause in the individuals chart. 

Thanks, Rip...

...as always, for your thoughtful additions. I totally agree.

Steven: I agree with you!

Thanks for reading and commenting. Many times, manufacturing has unique issues where the use of ICharts exclusively is indeed silly. I'm mainly addressing the rampant expansion of charts into service industries, especially healthcare, where I-MR charts are one's only option.

But, if I may challenge you a bit:  I still see people obsessed with the classic "BUT WHAT IF my process goes out of control?"  Perhaps put some of that obsession into trying to design processes that are more robust and don't go out of control so often -- and that includes working with suppliers to send more consistent material (or paying more for it!).  "WHAT IF" that were the approach instead?

And then there are the problems inherent in using X bar/R (or S) charts -- many people who should understand them don't!  This is especially obvious when specification lines are drawn in on them.

Conversations like I describe in my article are rampant on factory floors as well.

I/MR Charts


I completely agree on the needed emphasis on process understanding and optimization.  Most of our consulting work is applying tools like DOE, Reliability Methods to optimize product designs and processes. 

I agree there is a shocking lack of understanding of some basics like how individuals differe from averages, and we make a huge deal in our training classes of how misleading it is to put spec limits on Xbar charts.  But I worry that avoiding these tools because they are not understood is to use less effective simpler methods.  It just is a cycle of dumbing down. 

2nd class chart

Davis, You talk about XmR as though it is a "2nd class" chart with words like "approximates".  As Dr Wheeler noted:As Shewhart wrote in 1943 [17], “Classical statistics start with the assumption that a statistical universe exists, whereas [SPC] starts with the assumption that a statistical universe does not exist.”  We can never know the distribution of process data.  Therein lies the brilliance of Shewhart Charts ... which is lost on the SS mob.I can't find the reference but I also read from Dr Wheeler wherein he claimed you'd need a PhD in statistics, like him, to determine if it was reasonable to use a p, np, c, u chart in a particular process.Furthermore, if you are taking square roots, or letting some unnecessary software do it for you, you are not control charting correctly. (See Ch3 "Advanced Topics in SPC")Dr Wheeler has shown XmR is great for all situations. 

Of course XmR is great for all situations

A lot of my use of the word "approximate" is tongue-in-cheek.  I defer to Dr. Wheeler's expertise whenever possible.

We agree!

We agree. Don’t get caught up in minutiae, and don’t let perfect be the enemy of good.