Keeping the Process on Target: CUSUM 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 (14)

  • AnonymousSeptember 1, 2014 Reply

    It is somewhat related to weighted average chart ? I feel this is very nice chart to keep eye on when our results are going off-track. Thanks a lot for sharing.

  • janSeptember 5, 2016 Reply

    Hi,please from the formula σ =R /1.128 = 0.0279,were did you get the 1.128 ? what is that number ?Thanks

    • billSeptember 6, 2016 Reply

      In general, sigma is Rbar/d2 where d2 is a constant that depends on subgroup size. With a moving range of 2, d2 is 1.128.

  • alexDecember 18, 2016 Reply

    hi, please from "we know the target is 0,16", how do you know the target? thanks 

    • billDecember 18, 2016 Reply

      It is just an example for this newsletter.  You would use whatever the target is for your process.

  • AndreyJanuary 19, 2019 Reply

    Should be there SH(2)= Max[0, 0.001 + 0.152– 0.16 – 0.01395] = Max[0, -0.021] = 0 ? And the same for the SL. Is it correct? The second sample result is 0.152. Note that this result is below our aim. It if is far enough away, then it should add to the low side value of SL.SH(2)= Max[0, 0.001 + 0.175 – 0.16 – 0.01395] = Max[0, -0.021] = 0SL(2) = Min(0, 0 + 0.175 – 0.16 + 0.01395] = Min[0, 0.035] = 0

    • billAugust 6, 2019 Reply

      Thank you for pointing that out to me.  It has been corrected in the article.

  • SelenKAugust 6, 2019 Reply

    Hi, i calculated Std Dev in minitab as 0,02588, so why don't we take 0,02588 (instead of 0,0279) when we're calculating H and k? Is it a wrong way?

    • billAugust 6, 2019 Reply

      This paper uses the moving range to estimate the standard deviation.  Using the moving range chart makes sure that the process is consistent.  You an use the standard deviation if you want as long as the process is consistent ( in control).  There is not much difference between them in that case.

  • Andrew WardFebruary 6, 2020 Reply

    Many thanks for this. I found this extremely useful as I wanted to understand how to do this 'by hand' as opposed to the other searches that I encountered that signposted to packages / programs. 

  • Trần Thị Hạnh TrangMay 11, 2020 Reply

    Dear Bill McNeese!Do you have an example of cusum chart for subgroups with sample size of n>1?Thanks alot for your feedback!!

    • billMay 11, 2020 Reply

      What are you looking for?  Please let me know at [email protected] and I will see what i can do.

  • sooraj123gptAugust 20, 2020 Reply

    if the standard deviation is not known then how to calculate it to draw CUSUM chart? 

    • billAugust 20, 2020 Reply

      You can use the moving range as shown above to estimate the standard deviation.  

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