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Davis Balestracci

Six Sigma

Yet Another Predictable Question

How many data points do I need to have a good chart?

Published: Monday, May 12, 2014 - 08:50

In my last column, I considered two of the most common questions faced by a statistical educator and the deeper questions that need to be addressed. I encouraged people to consider their everyday reality for the necessary context. Predictably, some become frustrated by my lack of concise answers and try to distract me by asking, “Well, even though I can’t think of a situation, how many data points do I need to have a good chart?”

This predictable question is once again met by my predictably vague reply, “How much data do you have?” It’s usually not very much.

Despite the pedantic proclamations many of you have encountered in favor of waiting for anywhere from 15 to 25 data points, I have found that useful limits may be computed with much less data. As few as seven to 10 observations are sufficient to start computing limits, especially if it’s all you have—something that happens to me frequently. What else are you going to do? I dare you to find a more accurate way to assess the situation.

Limits do begin to solidify when 15 to 20 individual values are used in the computation. To argue semantics, when fewer data are available, the limits can be considered “temporary limits,” subject to revision as additional data become available. When more than 50 data are used in computing limits, there will be little point in further revisions of the limits.

When to recalculate limits… sort of

The purpose of limits is to provide a reasonable range of expected performance due to common cause. For the I-chart, as long as the limits are computed correctly—via the moving range between consecutive observations in time order—and three sigma are used, then they are “correct limits.” As Donald Wheeler likes to point out, notice that the definite article is missing—they are just “correct limits,” not “the correct limits.”

Ready for a blinding flash of the obvious? The time to recompute the limits for your charts comes when they no longer adequately reflect your experience with the process. There are no hard and fast rules. It is mostly a matter of deep thought analyzing the way the process behaves, the way the data are collected, and the chart’s purpose.

If the process has shifted to a new location and you don’t think there will be a change in its common-cause variability, then you could use the former measure of variation with the new average to obtain temporarily useful limits. Meanwhile, it would probably be a good idea to keep track of the moving range on an MR-chart to note any obvious changes. There is no denying that you will need to ponder recalculating the limits. With today’s computers, it’s less of an issue, but still requires good judgment.

The following questions by Donald Wheeler and Perry Regier are a wonderful road map:

• Do the limits need to be revised for you to take the proper action on the process?
• Do the limits need to be revised to adequately reflect accurate process performance?
• Were the current limits computed using the proper formulas?

Still not sure? Look at the chart and ask:

1. Do the data display a distinctly different kind of behavior than in the past?
2. Is the reason for this change in behavior known?
3. Is the new process behavior desirable?
4. Is it intended and expected that the new behavior will continue?

• If the answer to all four questions is yes, then it is appropriate to revise the limits based on data collected since the change in the process.
• If the answer to question 1 is no, then there should be no need for new limits.
• If the answer to question 2 is no, then you should look for the special cause instead of tinkering with the limits.
• If the answer to question 3 is no, then why aren’t you working to remove the detrimental special cause instead of tinkering with the limits?
• If the answer to question 4 is no, then you should again be looking for the special cause instead of tinkering with the limits.

The objective is to discover what the process can do, or can be made to do.

So, stop getting sucked into the swamp of calculation minutiae. Instead, put that energy into using your charts to understand and improve your processes. The first time you use “It depends” in answer to someone’s question, congratulations—you’ve had a major breakthrough in thinking. Let me know and we’ll both celebrate what will certainly be one of the biggest leaps in your effectiveness.

I nearly forgot the issue of, “Which chart do I use for which situation?” I’ll deal with that next time. Between now and then, if you take the advice from my last two columns, you’ve got plenty to keep you out of trouble—or maybe even help you create some (needed) trouble!

Discuss

About The Author

Davis Balestracci’s picture

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.

Comments

Iterations

Hi Davis,

We're never trained to operate in the realm of uncertainty. All formal education focuses exclusively on certainty - well defined problems with closed-form solutions. Even our managers ask for one-button-solutions. Is it any wonder then that in the face of a real world problem we look for "the formula"; to plug-n-chug numbers to get the "right answer?" Most have us have never learned how to learn, so I think understand why people ask the types of questions they do. My exposure to the learning cycle (Plan-Do-Study-Act) came very late. It's very decent of folks like Dr. Donald Wheeler and you, among others, to suffer fools and patiently guide them in their journey of understanding.

New and experienced workers need to learn through experience guided by mentors the reality of uncertainty and how to minimize it using the learning cycle. Like you asked: When you don't have "enough" data "what else are you going to do?" You need to make the most of the data you have...until you get more, if you can get more. The only way to build confidence about your knowledge i.e. reducing uncertainty is by replicating results. There is no one question, therefore there is no one answer. You grow your knowledge about a process over time and through experimentation by deeply considering what you're observing. You have to expend brain energy.

Best regards,

Shrikant Kalegaonkar (Twitter: https://twitter.com/shrikale, Blog: http://shrikale.wordpress.com)

Thank you for your kind words and additional comments

There's really nothing more to be said. You've said it well. When we try to help people who are sincerely trying to learn and accept our challenges, they are hardly "fools." It's the arrogant "fools" who try their best to play "got'cha" with us for whom I have no patience. It's nice to have "colleagues" such as you joining us in our quality "journey."

Kind regards, Davis