Process Capability and Non-Normal Data

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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 (30)

  • AnonymousAugust 12, 2014 Reply

    How did you arrive at theoritical % above USL? I am referring to the statement above: For example consider the value of Cpu above. Cpu = 1.1 and the theoretical % above the USL is 0.05%. How did you arrive at 0.05% also Ppu=0.56 (1.83%). How did you arrive at 1.83%.

    • billAugust 14, 2014 Reply

      For the normal distribution (Cpu), the % out of spec is estimated by calculating a z value.  z is the (USL – Average)/Estimated Sigma.  For the data above z = 3.299392.  Then use 1 – Normsdist(z) in Excel to find the fraction of results beyond that value of z (or above the USL in this case).  That gives 0.00005 which translates to 0.05%.
      For the non-normal, you use the cumulative distribution function for the specified distribution to find the %  above the USL.  In this example, that was the exponential distribution.  The CDF for the exponential function is 1 – Exp(X/Scale) where X = USL in this case and Scale = 1.5.  This equates to 0.981684.  Subtracting from 1 gives the 0.0183.

  • rolMarch 16, 2019 Reply

    A very useful article! Very clear! thanks

  • SigalApril 18, 2019 Reply

    Thank you for the article , what is that can be done to calculate Ppk if no distribution is found that fits the data? 

    • billApril 18, 2019 Reply

      In this case, I would simply use the histogram and compare it to the specs for a long period of time.  And then just note the PPM out of spec.  No calculation really for Ppk can be done.

  • Jimmy Hood June 11, 2020 Reply

    I have a Good CP and CPK yet still shows law is not normal, Distribution is Good,Process OK and Setting Ok and yet still telling me law is not normal. 

    • billJune 11, 2020 Reply

      I am not sure i understand what you mean by "law".  Please send me that data to look at.  [email protected]

  • RamachandiranSeptember 5, 2020 Reply

    If my Cpk is <1, but data is normally distributed for one of the process. whether we can start to monitor the Control chart such X Bar R or IMR or we need to make the process to meet capability of cpk >1.33 then only we can make SPC monitoring. Please confirm.Also, if SPC monitoring in place how to know wheher CPk is improving or remains same. what is the suggestion?

    • billSeptember 7, 2020 Reply

      We discussed this on your post on LinkedIn.  Let me know if you have more questions.

  • Chennakesava ReddyOctober 12, 2020 Reply

    Hi, Good Evening.As thumb rule, before calculating process capability (Cpk), data should be normally distributed.I have a case where, data points are not normally distributed (P-value is less than 0.05 in probability plot). But, process capability (CpK) is very high i.e 50(more than 1.33). In this case, I do not have lower specification limit and histogram is fallen left side.Can you interpret the above please.

  • SalahOctober 14, 2020 Reply

    Hello, i  want to calculate the Ppk of a truncated gaussian distribution . (The lower spec of the distribution is 0 and the upper sup is 0.8).Do you know the formula to calculate the Ppk in this case? Thanks 

    • billOctober 14, 2020 Reply

      Is 0 a natural boundary?  If so, you would have no lower specification and just calculate is based on the upper spec.  

      • SalahOctober 21, 2020 Reply

        Sorry for the late response, do you mean i can use the classical formula ppk= (USL-Average)/(3Soverall).Thanks you so much for your answer !

        • billOctober 21, 2020 Reply

          Yes I think so.  Send me the data if you would like me to look at it.  [email protected]

  • AnonymousFebruary 11, 2021 Reply

    General quries,In the above senario,My assumption , As shopkeeper suggested 6 min is the time max that the customer as to wait.I start collecting data , and verified my data follow exponential distribution.then i go for normal capabilty analysis chart in minitab and i click distribution as exponential .and verified for cpk value is it fine , for our estimation.what is the need of non -normal data analysis chart in minitab as mention above calculate. i can do it in normal capability analysis by selction of distribution as exponential in drop down list.can u pls clarify the same.thank in advance.    

    • billFebruary 12, 2021 Reply

      Not sure I understand you.  In SPC for Excel, like Minitab, if you select the Exponential distribution, you are not doing a capability analysis with the normal distribution, but  with the exponential distribution.  so it is not a "normal" distribution process capability.  You get different results from assuming you have a normal distribution.

  • Gaurav April 7, 2021 Reply

    If my data has Largest extreme distribution (non-normal distribution) with mean of 50, maximum value = 55. minimum value = 45. If i calculte Ppk, it comes out to be 0.83 (even when my specification limits are 40 and 60). Ppk of 0.83 means process is not able to produce within the specification limits of 40 and 60. How is it possible if all my data poiunts fall [45    55] ?  

    • billApril 7, 2021 Reply

      Please send me the data and I will look at it ([email protected]).    All the data can be in specs, but not the entire theoretical distribution.

  • BrendanAugust 18, 2021 Reply

    Hi,I have variable data not meeting normality and fits a Largest extreme value distribution.  So, now to determine ppk. I am using only a one sided lower spec which is a good bit below my data set.Minitab cannot give ppk but just an Astrix. I think its because the lower spec is so far from the distribution.  Anyways, what is the ppk formula for non normal largest extreme value?Any help appreciated 

    • billAugust 19, 2021 Reply

      Is there a reason  you believe the data should fit the largest extreme value distribution?  How many data points do you have?  Please send me the data and I will show you how the calculation is done.  You simply need the pdf for the largest extreme value distribution so you can calculate the limits.  But if you data are far from the lower spec, why does it matter?  You are capable.  Please send it to [email protected]

  • Leo YangNovember 5, 2021 Reply

    How to find a non-normal distribution can be fitted with my data? Do we still need to have a p value >0.05 for the goodness of fit test?

      • Leo YangNovember 9, 2021 Reply

        Hi Bill, Thanks for your reply. I have used Minitab to analyse my data and assessed 15 distribution models (Weibu, Exponential, etc). However, through the Goodness of Fit Test for the 15 distribution models, all of the p values are small and Weibu achieved a highest p value <0.01. Do I have to get a p value >0.05 for the distribution fitting before calculating the cpk or ppk? Is the SPC for Excel able to solve my issue? I can send my data to you if you do not mind. 

        • billNovember 9, 2021 Reply

          Send me the data and I will look at it.  It is possible none of the distributions fit the data.  IN that case, you just compare the histgoram to the specs.  Not much else to do there.  [email protected]

  • Steve JonesAugust 24, 2022 Reply

    For MS Excel analysis, what is a very simple and fairly reliable method for determining good normal distribution of your data?  If Cp and Pp comparison is a good method (they should be almost identical), then how close is good enough… 95%, 90%, 85%, etc?  Thanks.

    • billAugust 24, 2022 Reply

      If your process is in control, the Cpk and Ppk values will close for the normal distribution.  Not sure I have a number that means close.

  • AnonymousAugust 14, 2023 Reply

    Thank you so much for this article. But I want to ask something. In my case, my data is negative binomial distributed, which is not included in 14 distributions in Minitab. How to solve that problem, is there any other method ?. Thank you very much

  • NAugust 14, 2023 Reply

    thanks for the article. What if in my case, the data is negative binomial distributed. which is not included in the 14 distributions in Minitab for non normal ? Or there is any different method for this problem ? Thank you so much.

  • billAugust 16, 2023 Reply

    Hello, in this case, i think you just have to consruct a histogram and compare the specifictions to the histogram.

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