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Beyond the "Regular Guy" Control Charts: An Ode to the EWMA Chart

It's no secret that in the world of control charts, I- and Xbar- are pretty much the popular kids in school.  But have you ever met their cousin EWMA? That's him in the middle of the class, wearing the clothes that look nice but aren't very flashy. You know, when Xbar- and I- were leading the championship football team last month, EWMA won the state tennis championship?  I didn't go either -- pretty much only the player's parents go to tennis matches -- but I heard that he won it.  Someone told me he even got a scholarship to an Ivy League school to play, not that he needed it with his grades and great SAT score. 

Me? I'm going to the state university. I-, Xbar-, and I are renting a house and we're going to sublet the basement to MR- and R-.

You know, I just realized that if EWMA would just meet more people, they'd probably realize he was ever bit as capable and maybe even smarter than I- and Xbar-!

The "Regular Guys" of Control Charts

Let's call the I-Chart and Xbar-Chart "The Regular Guys."  You probably use The Regular Guys almost every time you make a control chart, without much thought as to what they are built to detect. The Regular Guys are really good charts and great for many situations: a sudden shift in process or an errant point in particular are likely to get captured as special causes fairly quickly.

But for a critical process, or one with mediocre quality to begin with, even a subtle shift in the process can have serious implications. That's where our friend the EWMA Chart comes in.

Suppose we want to track annual inflation, a good example of something that we want to capture subtle shifts in reasonably fast. First, let's plot the data (since 1983 when we last ended a "special cause" period) on an I-Chart:

I Chart of Inflation

We nearly get a signal for an unusually high point around 1990, and we get a signal for an unusually low point in 2009.  You may be looking at the chart and thinking, "It looks like things were maybe a little high during the 1980's and a little low during the 1990's, but maybe that's just random variation".

Enter the EWMA Control Chart

EWMA stands for "Exponentially Weighted Moving Averages." What does that mean, exactly? Well, the EWMA Chart uses each data point and all prior points to form the plot (so point 4 on the plot uses information from points 1-4, and point 19 uses information from points 1-19), and gives the most recent point the strongest weight. 

You can create EWMA control charts in Minitab by going to Stat > Control Charts > Time-Weighted Charts > EWMA...

Without getting caught up in all of the mathematical details, the result is that subtle but sustained shifts are made much clearer, as you can see in this EWMA Chart of the same data:

EWMA Chart of Inflation

Now it is much easier to see that we did in fact have a sustained period above the mean during the 1980's, as evidenced by the increasing values in points, followed by a period below the mean during the 1990's and stability during the 2000's...until obvious economic factors shake things up more recently.

Where Could You Use the EWMA Control Chart?

The same concept could apply to numerous metrics you're tracking at your organization. Although a signal on an I-Chart may let you know of a sudden, extreme shift or event, the EWMA will likely reveal if the process has drifted slightly from being centered (assuming it was centered to begin with) and product quality has deteriorated.  Think of where you might apply this tool on a chart you are already using, to learn more from your process!

Comments

Name: bhim prasad • Thursday, December 13, 2012

Can someone tell me what are the tools that we need to use while analysing the discreate data in minitab?


Name: Joel • Thursday, December 13, 2012

There are numerous tools in Minitab intended for discrete data - too many to list! We have had a couple of recent blog posts about discrete data that may be of interest, and the Assistant Menu will guide you to the correct test if your data are discrete. Otherwise, I recommend attending a training course - we cover both continuous and discrete data, with a little more focus on discrete data in the service-based courses.


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