How Much Data Do I Need to Calculate Control Limits?

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Thanks so much for reading our publication. We hope you find it informative and useful. Happy charting and may the data always support your position.


Dr. Bill McNeese
BPI Consulting, LLC

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Comments (24)

  • JP DubeyAugust 31, 2016 Reply

    Many thanks Dr Bill. It was an excellent article on the subject. Hope we will have more such articles on attribute data as well. 

    • billSeptember 11, 2016 Reply

      As usual, when I don’t know how to do something, I reach out to someone who does. I asked Dr. Wheeler. He said that the interpretation is the same when it comes to COV (the equation above holds). He also said:

      “I am not certain on this, but I remember the following formula:

      d.f. = (2/9)* (sum of the squared counts).

      Whether this formula is exactly right or not, I know that zero counts do not increase the d.f. Only positive counts do that. So, when the data satisfy the conditions for either a binomial or Poisson distribution, the limits for the attribute charts will gel much more rapidly than the limits for an XmR chart. But if the counts do not qualify as binomial or Poisson, then the limits rapidly converge to the wrong values. In most examples that I get to see, the failure of the assumption of binomial or Poisson counts is the problem with using attribute charts.”

  • PavelFebruary 12, 2019 Reply

    Hi, if we have large data sets of continuous individual data e.g. above > 300 values, should will still use estimated deviation or we can use normal deviation over the whole data to calculate UCL and LCL?UCL / LCL based on estimated deviation (CL+/-2.66MR) in our case are more conservative than actual deviation over general population. Due to technical advancement, we can calculate deviation on the fly for large date sets with millions of measurements.

    • billFebruary 13, 2019 Reply

      Lots of data for sure.  I would stick with the average moving range – but i imagine with all those points, a few out of control will not matter.  The question you have to answer is "is my process in control".  I believe you always use the control limit equations to judge that.  But i have not dealt with millions of data points.

  • VicenteMarch 26, 2019 Reply

    Dear Dr. Bill McNeeseFor determining the oil density in an oil field, a sample per week is taken. Do you consider approppriate to take an average of the samples taken over a time period as the oil field density value, and evaluate with control charts if a new measurement (n) is in or out the control limits. Then check with a new measurement (n+1) if the previous value (n) was wrong or if the field oil density has changed?In this case how many density samples should you consider appropriate to take the average and to conform the control limits?Thank you

    • billMarch 27, 2019 Reply

      Yes, you can plot the weekly result as in individuals control chart.  If it has changed, keep taking samples until you have five new ones.  Calculate limits then, then update the limits with each new point until you have 20.

  • KengAugust 16, 2019 Reply

    Hi Bill, thanks for sharing the knowledge about control chart. It’s really helpful for the project I am working on. I have some questions regarding the euations. How do you derive the equation of degree of freedom, df = 0.62(n – 1) for the average moving rangeand df = 0.9k(n – 1) for n less than 7df = 0.85k(n – 1) for n from 7 to 10 for the average range? Thank you.

    • billAugust 17, 2019 Reply

      I have not dervied them.  I used the information from Dr. Wheeler's book referenced above.

  • Stat-EgyOctober 10, 2019 Reply

    Hello Bill,I am trying to set a control limits for a thickness value measurements, I picked a sample size of 40 subgroups , each subgroup is 5 samples ( with total number of samples = 200 readings) so that I could obtain a diff % ~ 0.0% . However when I tried to calculate the sigma (x) in order to obtain the LCL & UCL , I obtained a very narrow tolerance limit (0.002) , which is too strict in my measurement ( usually my tolerance is 0.0x). I need to understand what mistake I made? is that because I picked too many subgroup size?Please help , thanks in advance !

  • RashidJanuary 15, 2020 Reply

    Hi. Does this number of points guide apply to all phases (learning phase, testing phase)? Thanks.

    • billJanuary 15, 2020 Reply

      Yes, I would think so.

  • RaazMarch 27, 2020 Reply

    Thank You Dr. Bill,It is very enlightenment article on control chart. I am working on process which have more variation not meeting yield spec limit(93-103) and I have 22 data point over 3 years of run. Data range is 16 (min81-max97) with overall 4.02, when I plot I-MR Chart, all data were within control limit, UCL =104.29, LCL =78.91. My objective was to assign new yield limit as 11 data points were lower than 93 and production claim there is no special cause (it is attributed to common cause of material and equipment). As control limit looks too wide 79-104, is it due to large variation and small sample size? Can I say this process is predictable as all points are within control limit? Also, Can you please elaborate in more detail of the following from your previous publication on control chart…“Individuals control charts are not as sensitive to changes as Xbar-R charts. In addition, values of X and R can have significant variation (even though the process is in control) until the number of individual data points reaches 100.”Much appreciation and thank you in advance!

    • billMarch 28, 2020 Reply

      Three years is a long time.  If the control chart is in control, then it means that the process is consistent and predictable.  There are no special causes.  Individuals control charts sensitivity can be increased by applying the other out of control test (such as the zone tests).  Now, I do not worry about the difference in sensitivity between Xbar-R and X-mR control charts.  

      • RaazMarch 30, 2020 Reply

        Thank you again Dr. Bill, How can i (at what point) say my process is more precise? if the moving range is in control means process is precise?  

        • billMarch 30, 2020 Reply

          Not precise, but it means it is predictable and consistent.  If the range chart is in control, it means the width of hte histogram is staying the same, that hte value of sigma is consistent over time.

          • RaazMarch 30, 2020 Reply

            Thank you so much Dr. Bill-really appreciate your time. Do you have any suggestion on how to know a process is precise or not?

            • billMarch 31, 2020 Reply

              Not sure what you mean by precise.  If you mean repeatable, then if the range chart is in control, I would say it is as precise as it can get for the current process.

  • EA MadsenApril 15, 2020 Reply

    Hi Bill. Thank you for the article! It sheds light on a question I have been thinking about. I would like to ask you, just to be certain: Is the advantage of locking control limits after 20/30 data points just that it saves time as compared with calculating the limits after every single measurement? Obviously, the difference in COV isn't much if we increase the number of data points, but is there any other advantage in locking the control limits after a certain amount of data points and not just calculating the limits based on the entire dataset?

    • billApril 15, 2020 Reply

      Thanks for the comment. The reason you lock the control limits is to create baseline data to judge any future changes against. If you recalculate each time, those changes could become part of the control limits and be masked. Please see this article from our SPC Knowledge Base:
      When to Calculate, Lock, and Recalculate Control Limits

  • David BennackApril 15, 2020 Reply

    Hi Dr. Bill,This article was very helpful! I am currently working on a project where the control limits are being determined based on average subgroup standard deviation. How do I determine the degrees of freedom when using this method of estimating the standard deviation?Best regards,

    • billApril 16, 2020 Reply

      Thanks David.  There is a table in Dr. Wheeler's book "Advanced Topics in Statistical Process Control" that list the degrees of freedom.  What you can do to estimate it is to use df = k(n-1) where k = number of subgroups and n = subgroup size.  For example, if you have k = 25 and n = 4 then df = 25(4-1) = 75. The table value is 70.4  So, they are close.

  • DanielMay 8, 2020 Reply

    Hello,I want to evaluate the capability of my process by measuring de brigthness in the final product. The process is batch and every month I make 1 batch and one batch takes normally 2 days. So I have 12 subgroups with diferent sizes (goes from 12 to 30 values per group). What should I do to get a control chart with diferent sizes of the subgroups?  Please, help me out. 

    • billMay 8, 2020 Reply

      You can make a control chart with different subgroup sizes, just use the different values of A2 for the different subgroups.  Our software will do it autmatically for you.

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