Beware the Tukey Control Chart

Another bad idea surfaces

I recently read about a technique for analyzing data called the "Tukey control chart." Since Professor John Tukey is no longer with us, it appears that someone without his brilliance has tried to adapt one of his techniques into an alternative type of control chart. To understand the inappropriateness of this approach, read on.

John Tukey was one of the foremost statisticians of the 20th century. He created many profound techniques for analyzing data of every type. So let me be clear that none of what follows is in any way a critique of Dr. Tukey or his work. However, when others adapt a technique for use in a way in that it was never intended to be used, and when that adaptation does not work as well as the standard technique, that adaptation must be judged to be a failure.

This is the case with the Tukey control chart.

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Comments

Who is advancing this?

Who is advancing the idea of a Tukey Control chart? I haven't heard of this before.

The proponents

A correspondent sent me a link to a chapter in a book coming out of George Mason University in Virginia. The authors are listed as Farrokh Alemi, Duncan Neuhauser, and Nancy Tinsley. The URL is gunston.gmu.edu/healthscience/708/book/ChartDiet.htm

ANOM like chart?

This technique sounds more like an ANOM type chart where you want a more exploratory type analysis for a finite data set?

Do we really need more techniques (inferior or otherwise) when we struggle to get folks to visualize their data using simple but powerful methods?

I don't think so.

Rich

Tukey Control Charts

I have seen this chart mentioned a couple of times in health-care related applications. Thanks for Dr. Wheeler for analyzing it in a very clear manner.

I agree with you, Rich. Why do we need more techniques when it is huge struggle just to get people to plot the data over time? It seems so simple.

Thanks Dr. Wheeler,

Bill McNeese

www.spcforexcel.com

Tukey' Control Chart

sir is tukey's chart is nt appropriate or i cant get ur point i am doing work on this chart may kindly guide m what exactly the problem with tukey's control chart. only the problemm 3 sigma limits please sir guide me

regards

This comes as no surprise

We are dealing with a binomial distribution (finite sample from a relatively infinite population, pass/fail similar to Deming's red bead experiment) which barely meets the requirements for the normal approximation (expect 4-6 occurrences per sample). The normal approximation is mediocre under these circumstances, and something that relies on medians and interquartile ranges is likely to be even worse. It is no surprise that points are above the upper control limit when the process is in control.

I do like the box and whisker plot because it is an excellent way to present data graphically, but it is a visual aid as opposed to a substitute for an analytic technique like ANOVA or a t test. I would definitely not use it as a basis for an X chart, as the author shows.

Box and Whisker Plot

The box and whisker plot does not show the Data. It uses a five statistics computed from the data as a surrogate for the data. The plot gives major emphasis to the middle two quartiles, representing them by rectangles, and then completely deemphasizes the outer quartiles, representing them by lines. I have only found the box and whisker plot to be useful one time in the past 30 years.

Typo in the text

There is a typo in the text. Near the beginning where the moving range values are listed. The last moving range value is listed as 16. It should be 1. It looks like you used the correct value in your calculations.

Fixed the typo

Thanks Andrew. We have fixed the typo.

Are the control limits the fences?

In the article, the control limits for the so called Tukey control chart are described as follows: "This inner quartile range is then multiplied by 1.5, and the product is added to the median and subtracted from the median to get the limits for the Tukey control chart."

In the GMU page that Dr. Wheeler references (in the comments section), the control limits are shown as follows:

LCL = Fourth – 1.5 * Fourth Spread

UCL = Three-Fourths + 1.5 * Fourth Spread

Essentially the fourth is the first quartile, the three-fourths is essentially the third quartile, and the fourth spread the IQR. The LCL/UCL calculations shown on the GMU page do not involve the median. The control limits rather are the inner fence values, and not based on the median. That makes them analogous to 2.7-sigma limits.

Perhaps the GMU page has changed since Dr. Wheeler wrote this column.

NT3327