trend the display that won’t die - balestracci

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Trend: The Display That Wont Die

By Davis Balestracci on Aug 18, 2011 | Categorized under: General

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As time goes on, I have an increasing affection for the much-neglected run chart

Any article about control charts leads to inevitable (and torturous) discussions ofspecial cause testsall nineof them. No wonder confused people continue to usethings like trend lines. But Im getting ahead of myself.

First of all, before you take another tools seminar or read another bookexcept,

perhaps, Brian Joiners Fourth Generation Management(McGraw-Hill, 1994)pleasetry Dr. Donald Berwicks admonition at the end of my Aug. 2, 2011, article, A NewConversation for Quality Management: Find something important, and plot it overtime. This is probably the best way to learn the most important lesson of qualityimprovement: That everything is a process, and effective improvement means havingnew conversations around the crucial distinction between common and special causes.As I have relentlessly tried to make clear, you are swimming in everyday opportunity.

Most of my articles are concerned with statistical thinking in the context of an overallimprovement process. This is much different from control charting, say, a machine onthe manufacturing floor, which could indeed show a trend as in the classic case of toolwear. Im sure there are others, but once again, thats an application for the 1 to 2

percent of people who need advanced statistics. Im trying to counteract the effects ofRule No. 4 of Demings Funnel Experiment, as it has manifested in the process ofstatistical training for the masses.

Treating every special-cause signal as a special cause?

Many people have the misconception that each special-cause signal on a chart must betreated as a special causei.e., needs to be uniquely investigated. Have you everthought, Might there be oneunderlying explanation generating allof these signals?

How ironic that a lot of people teaching control charts as a tool dont understand thismore subtle manifestation of common vs. special cause. As I continually emphasize,

quality improvement is a mind-set that knows how to ask the right questions.

But the test for trend is statistically significant

Someone once presented me with the graph in figure 1. (Yes, the y-scale started atzero.) It almost convinces you there is a trend, eh? (p-value < 0.001.)

Some of you could be wondering, What insight might a control chart give? Figure 2shows you, with the resulting tests for special causes:

Fig. 1: Percent conformance to goal




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Test 1: One point more than 3.00 standard deviations from center line.Test failed at points 9, 50, 51, 52.

Test 2: Nine points in a row on same side of center line.Test failed at points 9, 1.

Test 5: Two out of 3 points more than 2 standard deviations from center line (on oneside of CL).Test failed at points 4, 6, 7, 9, 15, 48, 49, 50, 51, 52.

Test 6: Four out of 5 points more than 1 standard deviation from center line (on oneside of CL).Test failed at points 5, 6, 7, 8, 9, 10, 17, 18, 20, 50, 51, 52.

Test 8: Eight points in a row more than 1 standard deviation from center line (aboveand below CL).Test failed at points 9, 10.

Yikes! Sixteen of the 52 data points generate special-cause signals. Some data pointseven generate multiple signals. Thats 30 special-cause signals total .Where does onebegin?

Unfortunately, the way I see control charts generally taught, obviously one shouldinitially investigate, individually, the four points outside the three standard deviationlimits, in this case observations points 9 and 5052 not!

As time goes on, I have developed an increasing affection for the much-neglected runchart, a time plot of your process data with the median drawn in as a reference line. It isfilter No. 1 for any process data, and it answers the question, Did this process possibly

have at least one shift during this time period? This is generally signaled by:

A clump of eight consecutive points either all above or below the median Less often, six consecutive increases or decreases. This is sometimes called a

trend but more correctly, it indicates a transitionto a new process level. (Anygood software package should do this analysis and let you effortlessly togglebetween run charts and control charts.)

Heres the rationale for using the median: If special causes are observed in the runchart, then it makes no senseto do a control chart at this time because the average of allthese data doesnt exist. Sort of like, If I put my right foot in a bucket of boiling waterand my left foot in a bucket of ice water, on average Im pretty comfortable.

One of the healthiest things that a run chart can do is get you thinking in terms ofprocess needle(s), i.e., focusing on the processs central tendency.

Fig. 2: Percent conformance to goal showingtests for special causes (y-axis expanded)




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Most of the time, run charts are glossed over and taught as the boring prerequisite tolearning control charts. Isnt it far more exciting to jump right to the control chart withall its bells and whistles, look at the special-cause signals, and try to find reasons foreach individual signal?

The run chart does not find individual special-cause observations because that is not itspurpose.That is one of the objectives of the control chartcall it filter No. 2. One plots

the data incorporating the shifts detected via the run chart. This usually reduces thenumber of subsequent special-cause signals, resulting in a lot less confusion. Thecontrol chart also has an additional power to detect more subtle shifts neither obviousnor detectable in the run chart.

So, what light might a run chart shed on the current situation? Take a look at figure 3:

With the y-axis scale a lot healthier and no control limits as a distraction, doesnt it looklike the needle shifted twicearound observation points 21 and 47? In fact, when Iasked the clients about those two particular points and their corresponding dates, they

looked at me like I was a magician and asked, How did you know? Those datescoincided with two major interventions to improve this process.

As the chart in figure 4 shows, they workedtwo needle bumpsnot a continuouslyincreasing improvement trend. Making only those two adjustments, the correctresulting control chart is shown below. Theres not a special cause to be found, butthere is a possible improvement/transition in the making, as evidenced by the last fourdata points. Time will tell.

Take the challenge

1. Can you think of one or two applications like this in your everyday work ormeetings? Plot it.

Fig. 3: Run chart of percent conformance togoal

Fig. 4: Control chart of percent conformance togoal




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2. Can I also challenge you to take one routinely trended data display and plot it as arun chart?

3. Will you promise me that, before you take yet another course on more tools, you willdo a (mere) run chart of a number that makes you sweat?

4. What part of never. If someone asks you to trend some data, will you flat out

refuse? If so, be prepared: You probably will also have to refuse his valiant attempt tokeep the trend monster alive via the dreaded two-headed transplant techniquei.e.,when he predictably insists, OK, then, just put them both on the same page.

5. And beware of this monsters cousin (figure 5):

P-value for trend: < 0.001, R-squared: 51.1 percentand total rubbish!

A final clarification

For those of you who may still be slightly confused, ponder this: Suppose youre tryingto lose weight. You make a hefty cut in your calories. You start weighing yourselfevery day and plot it. During the first two weeks, you will probably lose 5 to 7 poundsof water weight. For the next two weeks, you will probably lose 1 to 1 1/2 pounds aweek. After that, physiologically, the body adjusts to your decreased caloric intake tothe weight that it is perfectly designed to get and levels off. Then, by all means, goahead and fit a trend line; I guarantee a statistically significant regression. And if yourweight loss proceeds perfectly linearly according to the line, please let me knowtheday beforeyour weight goes to zero.

For purposes of improvement: trend = transitionto the new process you are perfectlydesigned to get, given your new inputs vis--vis your old status quo.

Latest article by Davis:

The Road to Health Care Reform Is Paved with Missed Opportunities

After reading Joe De Feos July 8, 2011, Quality Digest Dailyarticle, A Positive Prognosis:Transforming Health Care in America,I took another look at the wonderful book, Escape Fire(Jossey-Bass, 2003), a compendium of Dr. Donald Berwicks inspiring plenary speeches at theInstitute for Healthcare Improvements (IHI) 19922002 annual forum. Berwick is probably theleading health care-improvement thinker in the world. He is the former CEO of IHI and, as someof you know, a controversial Obama appointee as head of the Centers for Medicare and Medicaid

Administration. In my opinion, he is most definitely the person for the job. As if it wasnt difficultenough to deal only with health care cultures, he now has the thankless job of integrating messypolitical agendas into the very serious business of health improvement.

Fig. 5: Trend control chart for percentconformance to goal.



trend the display that won’t die - balestracci

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