The Estimated Standard Deviation and Control Charts

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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 (28)

  • AnonymousDecember 10, 2012 Reply

    Good morning, Bill -The newsletters are great but it would be nice to be able to print them and HTMLs do not print well. Any chance that you could either publish in PDF format or add a "printer friendly" option?Thanks.dave  

    • billJanuary 12, 2013 Reply

      Hi Dave,I will take a look at doing the PDF format.  You can always copy the newsletter and paste into Word in the meantime.  Thanks for the comment on the newsletters. Bill

  • Sachin BakshiMarch 12, 2016 Reply

    Very informative article , had observed the difference in control its but known the reason yet..thanks for sharing the underlying reason..

  • CIESFebruary 24, 2017 Reply

    How do you calculate the 1461.15?? From the initial data, how should I interpret the Xij???

    • billFebruary 24, 2017 Reply

      There should really be a second summation sign in the numerator. Below are the calculations. Xij is the ith observation in the jth subgroup.

  • Carlos EFebruary 28, 2017 Reply

     How to calculate C4?? Is there a ful table available??

    • billMarch 1, 2017 Reply

      There is a table in the article. What are you looking for?

  • Viet NguyenJune 18, 2017 Reply

    Dear Dr. Bill McNeeseI have a question about Control Limit UCL & LCL, Sigma = Rbar/d2 ,and Theory is Control Limit is 3Sigma (+/-) so, Can we just use UCL=Xbar+3*Rbar/d2 and LCL=Xbar-3*Rbar/d2 ( 3*Rbar/d2 = 3Sigma), Hope you can help me to have more clear about it ,I known that correct Formula shows ,Formula  ,UCL = Xbar + 3 Sigma/SQRT(n)  ,LCL = Xbar-3Sigma/SQRT(n) ,But it will not be 3Sigma because still devide to SQRT(n), Why is it? ,Thank you so much  

    • billJune 27, 2017 Reply

      Please see this link for information on where control limits come from:
      Control limits are +/- three standard deviations of what is being plotted.  So, with subgroup averages, it is +/- three standard devations of the subgroup averages.  The subgroup averages standard devaition comes from sigma/sqrt(n) where n is the subgroup size and sigma is the standard devaition of the individual values (estimated by Rbar/d2).

  • Viet NguyenJune 20, 2017 Reply

    Understood now, thanks so much Dr Bill

  • M. Senthil KumarAugust 21, 2017 Reply

    Dear Sir,     Greetings,   I have a doubt, is it calculate the control limits for population method.I have 125 nos samples. i will not seperate this for sub groups. How to calculate the UCL & LCL. Is it possible. 

  • MarcusOctober 14, 2017 Reply

    Hi there, i was wondering if u could help me in the following problemI have been given 50 numbers in an excel sheet.. each number represents an average of 5 subsample observations. I have not been given the individual 5 numbers, just their average. and therefore am unable to calculate the range.Ive also been told the 50 average of subsamples follow a normal distribution following N(2,3), sample size n = 5 , the standard deviation = 3, and to follow a 2-sigma deviation.The average of the 50 averages i calculated =1.94How would i go about calculating the LCL and UCL, given the information i have.? many thanks in advance mate

    • billOctober 15, 2017 Reply

      All the information you need in the article.  You have the average.  Are you saying the distribution of subgroup averages has a standard deviaiton of 3?  Or is the individual values?  What do you mean by a 2 sigma deviation?

  • Ratul November 29, 2017 Reply

    In X-R chart the value of A2R is 1.8 calculate the value of sigma i.e standard deviation?

    • billNovember 29, 2017 Reply

      Not clear to me what you are asking.

  • EaglesDecember 12, 2017 Reply

    Why don't we estimate standrad deviation by using standard deviation of all samples?

    • billDecember 12, 2017 Reply

      If you use the calculated standard deviation of all the range, it will inflated when the data are not in control. The purpose of a control chart is to determine if the data are homogeneous. Calculating the standard deviation assumes that the data are homogenous.

  • siddharthMay 30, 2018 Reply

    For PpK calculation, overall standard deviation is used. Can you please explain how to calculate for above datas.

    • billMay 30, 2018 Reply

      The calculated standard deviation is the same as the STDEV function in excel.  It is the square root of the sum of the (Xi-Xavg)^2 divided by n – 1.

  • suresh kumar CJanuary 21, 2020 Reply

    Request you all to explain how we get 20 for summation of n-1That is degrees of freedom is 20

    • billJanuary 21, 2020 Reply

      There are 10 subgroups. The subgroup size is 3 for each subgroup (ni = 3). Those three values are used to calculate a subgroup average. So, if you have the subgroup average and two values, the third value is set in the subgroup. So the degrees of freedom for each subgroup is two. There are ten subgroups, so 10X2 = 20.

  • peyton maggieDecember 16, 2020 Reply

    is sigma the same thing as standard deviation? so if the CL is 2, UCL is 5, and LCL is -1, is the standard deviation 1 or 3?

    • billDecember 16, 2020 Reply

      Sigma is the estimated standard deviation from a range chart.  If the average is 2 and control limits -1 and 5 then the estimated sigma value is (UCL – Avg)3sigma or sigma  = 1

  • selbyJune 28, 2022 Reply

    what is the relationship between standard deviation and upper & lower limit?

    • billJune 29, 2022 Reply

      The upper and lower control limits are three sigma away from the average.  Where sigma is given as shown above.

  • YCAugust 9, 2022 Reply

    For Individuals data (i.e. subgroup size = 1), UCL= Mean (˭X) + 3σ; LCL = Mean (˭X) – 3σ. For the below data, Mean is 5.9848 and Standard deviation is 0.1959. But UCL and LCL calculated by Minitab is 6.39 and 5.579 respectively. Why they are different from the calculations using the above equation?6.05, 5.99, 6.11, 6.13, 5.87, 6.05, 6.23, 6.49, 6.15, 5.89, 5.87, 5.99, 6.07, 6.17, 5.86, 6.07, 6.01, 5.87, 5.66, 5.58, 5.62, 5.89, 6.02, 5.93, 6.05

    • billAugust 9, 2022 Reply

      Control limits are not based on +/- 3 standard deviations where the standard deviation is the calculated standrade deviation (like STDEV in excel).  The limits are base on +/- 3 sigma where sigma is estimated from the range chart.  For individual values, sigma = average moving range/1.128.

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