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Beyond the ‘Regular Guy’ Control Charts

An ode to the EWMA chart

Joel Smith
Tue, 11/27/2012 - 09:18
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It’s no secret that in the world of statistics, the individuals chart and X-bar chart are pretty much the popular kids in school. But have you ever met their cousin EWMA? He’s all about exponentially weighted moving averages (EWMA). That’s him in the middle of the class, wearing the clothes that look nice but aren’t very flashy.

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You know, when X-bar and individuals were leading the championship football team last month, EWMA won the state tennis championship. I didn’t see him play; usually only the player’s parents attend tennis matches, but I heard that he won it. Someone told me he even won a scholarship to an Ivy League school, not that he needed it with his grades and great SAT score.

Me? I’m going to the state university. Individuals, X-bar, and I are renting a house, and we’re going to sublet the basement to mR chart and R chart.

You know, I just realized that if EWMA would just meet more people, they’d probably realize he was every bit as capable and maybe even smarter than individuals and X-bar.

 …

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Comments

Submitted by Steve Moore on Thu, 11/29/2012 - 10:18

*sigh* Here We Go Again

The EWMA chart will virtually always lag behind the Shewhart control chart for detecting a signal. In fact, it may obscure sudden shifts in the process due to the long rolling averaging going on. EWMA is no more sensitive that the standard control chart when used with the four Western Electric Zone Tests. The EWMA chart is more complex and more difficult to understand (especially for operators) than the Shewhart chart. Increased complexity does not necessarily make something more useful. While EWMA does have its uses, it is not a viable alternative to the Shewhart chart. These points and others can be reviewed in detail in Wheeler's "Just What Does An EMWA Do?". "Dr. Shewhart contrived and published the rule in 1924 – 65 years ago. Nobody has done a better job since.” - W. Edwards Deming (1989)
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Submitted by Joel Smith on Thu, 11/29/2012 - 12:44

In reply to *sigh* Here We Go Again by Steve Moore

EWMA and Western Electric

Nowhere in the article was it suggested that EWMA Charts should replace Shewart charts...they are a valuable tool to detect certain kinds of shifts just as Shewhart Charts are. A EWMA Chart uses a single test - one point more than 3 standard deviations from center - whereas you are suggesting using four tests. It is more difficult for operators to use one test than to use the same test PLUS three others? The only complexity is in calculations that are done by computer, invisible to the user. Just as more complexity does not necessarily make something more useful, more simplicity does not either. A car is more complex than a skateboard for a reason. As long as the car is simple to operate, it does not matter that what's behind the dash is complex. Additionally, the "sensitivity" you suggest is obtained by doing more tests and increasing the false alarm rate as well. Simulation demonstrates that the rate of catching small, sustained shifts is similar between the two charts, but on an I Chart with the four Western Electric rules the real signals are hidden in a sea of false alarms that are occurring at a higher rate than the real signals. The boy who cried wolf was also good at detecting real wolves.
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Submitted by rderoeck on Fri, 11/30/2012 - 08:56

In reply to EWMA and Western Electric by Joel Smith

Explanning your Analysis

The beauty of the XmR is its simplicity. It is so important to be able to explain your analysis to your audience (management) so that they (management) can take the proper action. Believe me from years of experience, it's difficult enough explaining what that funny Moving Range chart is or, aren't those spec limits on your graph? An appalling ignorance of understanding variation and special vs. comon causes is management's #1 diesese. To think you could explain the EWMA chart to them is simply laughable. In addition to that, most real world processes are very unpredictable with 3-4-6 sigma shifts common. You don't need a jackhammer when a simple pick and shovel will do.

Rich 

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Submitted by kkbari on Fri, 11/30/2012 - 13:29

In reply to *sigh* Here We Go Again by Steve Moore

Niche for EWMA

Well, in an effort to make things simple, we get things confused.  An EWMA chart has specific uses.  Its derivation is from a non-stationary IMA (1,1) model (integrated moving average).  Blah, blah, blah, but the key is the fact that the assumption is that the underlying model has a non-stationary mean.  This is entirely plausible for something like business data.  It is absurd to assume something like inflation resets itself year after year just because Jan 1 first rolls around and each point is independent of each other.  Rather it rises and falls somewhat independently of an arbitrary time subgrouping.  Unemployment is another example – you can go out to the BLS website and find serial data to your heart’s content! 

 

Within manufacturing, chemical process data can often benefit from using an EWMA chart rather than a IX chart, because of mixing, residence time, consumption, etc.  If you want to use a IX-chart effectively here, you can solve the issue of the sample rate (how often to sample) by looking at such things as autocorrelation function plots (ACF) and partial autocorrelation function plots (PACF) but that is beyond most engineers knowledge.  Simple lag plots, seeking for no correlation, is a simple enough tool to get close to determine how often to sample.  But now to balance the sample rate with the IX-chart effectiveness, you may increase risk of not seeing a real shift/trend and that’s a business decision. 

 

Sticking one's head in the sand and saying the IX chart is a universal tool for all data is problematic at best.  If the data is non-stationary, then it is non-stationary.  An IX chart with any set of rules will flag all the time and people will also look at you funny when you say it's always out of control.  You are looking at a significant rate of change, not for "stability".

 

I don’t use EWMA very often, but I do use it when it is appropriate for data that have non-stationary means by definition.  And I think that was the point of Joel’s article, which is “here is another tool for specific moments.” 

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Submitted by willy@qsconsult.be on Fri, 11/30/2012 - 09:32

Comparing charts

It always surprises me how emotional discussions can become on essentially very technical and even mathematical issues. There is also no need to be vague when exact numbers are available. For instance, in this discussion the ARL curves (Average Run lengths) for the charts in this discussion are available and have been published.With a weight of 0,2 (the value that Minitab proposes and that probably has been used for the example given - author?) the ARL0 (which is the false alarm run length) is about 550, which is indeed very robust. Using the four rules on a classical control chart will lead to an ARL0 of about 90. So yes, you will have more false alarms. Whether this has to be described as "a sea of false alarms", I have no idea. Off course, the classical chart with the 4 rules is more sensitive to changes. As an example ARL 0,5 (0,5 sigma shift) about 27 vs 45. ARL1 9 vs 11 and ARL2 3 vs 4. 

As most charts are run on software these days, checking 4 rules is no longer more difficult than checking 1 rule.With this knowledge, it is up to the owner of the process to decide which chart he finds the most adequate to use as a continuous improvement tool for his process.

Kind regards,

Willy Vandenbrande (willy@qsconsult.be)

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