Multivariate Control Charts: The Hotelling T2 Control Chart

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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 (10)

  • Walt WilsonNovember 23, 2019 Reply

    Bill, you are a great teacher and mentor through my journey of process, continuous improvement, and applying statistical knowledge.   Your articles continue to challenge, teach and train.  Thank you for the history, background and application of Hotelling's T2.  Thank goodness for modern analytical tools was my first thought.  Appreciate the article and a focus on the tools available to understand and control our process. 

  • XDecember 16, 2020 Reply

    How did you multiply a 2×1 matrix (x-xbar)' into S-1 which is a 2×2 matrix !!? 

    • billDecember 18, 2020 Reply

      The prime means transponse so it tranposes the 2 by 1 to a 1 by 2

  • DouSeptember 2, 2021 Reply

    Great article, thanks Bill. Can you comment on the reason for calculating the covariance using the moving difference of the data (i.e., V), rather than on the original data (i.e., X)?

    • billSeptember 2, 2021 Reply

      Thanks for the kind comments.  I will have to do some digging on your question though because I don't have an answer off the top of my head.

  • Jeff LancasterDecember 14, 2021 Reply

    Bill-Bill- Could I use this example in a course (Jet Engine Basics) that I give at the U. of Hartford?Also, I have an Excel file of Airfoil Dimensional Parameters (15 airfoils, 9 parameters, each parameter at 10 different section locations) and was wondering if this data case lends itself to multvariate analysis. Would you be willing to comment on it? I'd be glad to send it to you.Thank you very much!!

    • billDecember 14, 2021 Reply

      The example i use is from Dr. Wheeler's book referenced above.  I will be glad to look at it if you send me the data.

  • T. ReiterOctober 18, 2022 Reply

    This tutorial is without a shadow of doubt the clearest and most followable explanation on Hotelling T2 control charts that I have come across within weeks of search!!! — Many thanks for this!

  • TamasOctober 24, 2022 Reply

    Hi Bill, thanks for the great tutorial!May I ask if you could double check your covariance matrix S'S = …..I think it should be: [0.5625, 0.375 ; 0.375,0.25] 

  • TamasOctober 24, 2022 Reply

    Apologies! Your covariance matrix is perfectly done! No errors!

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