Off to the Milky Way

Use moving ranges to redirect a vague meeting about a vague problem

Published: Tuesday, April 9, 2013 - 10:20

I received the following note from a physician who is very interested in improvement: “I am not sure I understand what a process behavior chart and a moving range chart do to the discussion, and what do the colored lines represent? aka ‘Still confused.’”

His comment was in response to my column, “What Are You Tolerating?”, which included the two graphs in figure 1. I’d like to take a step back and address his question in the hopes of helping him (and you) avoid yet another vague meeting about a vague problem with some vague data. “Off to the Milky Way,” incidentally, was one of W. Edwards Deming’s favorite expressions and describes that scenario very well.

Figure 1: No. of falls, year-over-year, and last 12 months

When you are at meetings like this and don’t have your computer, there are still some very useful, simple things you can do by hand that will take all of 10 to 20 minutes and could drastically change the room’s conversation and the project's direction.

Ellis Ott: “First, you plot the data. Then you plot the data. Then, you plot the data.”
Good improvement practice frames any situation as a process. One needs to assess the process stability to determine whether a common cause and/or special cause strategy should be used. How is this done? Plot the dots!  You could easily sketch a run chart (i.e., a time-ordered plot with the median of the 23 observations shown in figure 2 drawn in as a reference line). Here are the actual data, the data sorted to find the median, and the resulting run chart: 

Figure 2: Run chart  (Click here for larger image)

Only because the run chart shows no evidence of any shifts, one can now take the average of all the data. During these 23 months, there were a total of 125 falls: Process average = 125 / 23 = 5.4.

So there are now two key questions:
1. Given that the process average is 5.4, what is the expected range of observed falls for any given month?
2. Of course, most of the time, two consecutive months will probably have different numbers, but how much of a difference between two consecutive months is “too much?”

To answer these, we must calculate the moving ranges. The moving range is defined as the absolute value of the difference between any time-ordered observation and its immediate predecessor. Its value is always positive, and it turns out to have very nice statistical properties. In finding the moving ranges of a set of time-ordered data, the average moving range or median moving range contains the information needed to understand the inherent variation (i.e., common cause) of a process (see figure 3).

Figure 3: Moving range

The moving ranges for these 23 values are shown in the table (Note: 23 values yield 22 moving ranges). They are also sorted to find the median value; in a boring meeting without a calculator, this is much easier to do than calculate an average.

Many of you have learned to make process behavior charts using the average moving range, which, theoretically, is considered (slightly) more “accurate.” For most purposes, however, using the median moving range is usually good enough. The procedures are identical, except when using the average moving range, one uses the constant 2.66 in place of 3.14 and 3.268 instead of 3.865 in the calculations below. These are all derived from statistical theory and can be used with the moving ranges from pretty much any time-ordered set of data, regardless of length.

So, to answer question one for these data, the common cause range of expected values is:

5.4 +/– (3.14 x median moving range): 5.4 +/– (3.14 x 3)

Or approximately -4 to 15. But, since you can’t have negative falls the lower limit would be zero, not -4.

(If we were using the average MR our limits would be approximately 0 – 14.)

In chart form, this looks like the graph in figure 4. The red-line (15) is the largest value that could be expected from common cause variation for this process “centered” at 5.4:

Figure 4: Common cause range of expected values (Click here for larger image)

Many of you have been taught the classic nine Western Electric tests for special causes. They are programmed into many software packages and were applied to this process behavior chart:
1. Using these standard tests for special cause patterns, there are none.
2. They are averaging 5.4 falls a month, but for any one particular month, a value between zero and 15 (upper red-line limit) will manifest as a natural result.
3. All the data fall within this common cause range.
4. Getting people pizza for the month where zero was obtained was most probably treating a common cause as if it were special.

Now, about that increase from zero (seen in October 2012) to nine (in November 2012). To answer question two, the maximum expected difference between any two consecutive months due to common cause is:

(3.865 x median moving range): (3.865 x 3)

Or approximately 12 (approximately 11 if using average MR)

Figure 5 shows this in chart form:

Figure 5: Maximum expected difference (Click here for larger image)

The charts have demonstrated that the variation is common cause. So, while the meeting was “off to the Milky Way,” poring over useless and inappropriate analyses (perhaps month after month?), you did all this in about 10 to 20 minutes. How would this now change the conversation? Do you dare?

Of course, they’re going to ask you what they should do instead. What do you tell them? You could start with one of Brian Joiner’s favorite expressions, “Don't just do something, stand there!”

About The Author

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.