Cpk Alone is Not Sufficient

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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 (17)

  • AnonymousApril 30, 2014 Reply

    Very good article. Why are the natural process limits of your Step 1 control chart different than those of your step3 calculation?

    • billMay 2, 2014 Reply

      The Xbar chart control limits are based on +/- three standard deviations of the subgroup averages.  The standard deviation of subgroup averages is equal to the standard deviation of the individual values divided by the square root of the subgroup size (4 in this example).  So, the subgroup averages always have less variation thatn the natural limits – in this cae, by a factor of 2.

  • AnonymousMay 1, 2014 Reply

    Cp & Cpk are two terms which are used in day to day life of any manufacutring plant. We use it daily and believe me the ocnfusions are always there, nobody is fully sure of what exactly it is and how to use it in real terms. Your article have clreaed many of my doubts and i am sure it will help our plant performance as well.Thanks again for the wonderful article.

  • AnonymousMay 1, 2014 Reply

    The details about steps to be followed for Process capability were very valuable to me.It provided fantastic information.Thanks for the update and look forward for more.BR

  • Joanna HanNovember 19, 2014 Reply

    Glad that I found this wonderful website. If I have a set of data where the subgroup size is different, how should I determine which d2 value to be used for the Cpk calculation? If I perform a Ppk calculation, is the Ppk value going to be affected by the difference in subgroup size? Thanks.

    • billApril 21, 2020 Reply

      The value of Ppk is not affected by the difference in subgroup sizes. It is based on the calculated sigma value which simple takes all the data in one group. For Cpk with varying subgroup sizes, you cannot use one value of d2. You have to determine sigma using a formula. That formula is given here. Of course, the easiest way to do is to purchase SPC for Excel. It does that for you automatically. 🙂

      • Joanna HanNovember 20, 2014 Reply

        Thank you so much. Your articles are great!

  • L.J. HannaAugust 10, 2015 Reply

    Good Read. All aspects are reflective of proper identification of Statistical Control in a process. I do differ on 1 belief however, and that is that Normality of your data is not a requirement to efficiently understand the capability of the process.1. In step one you Created a control chart to identify process stability: Process stability (special causes) are identified based on the distribution of the process. A skewed distribution analyze as a normal distribution would create false flags of special events causing you to fail your first step.2. If by chance the non-normal process passes through the original stability screen. In step 2 it is stated that the calculation for process yield can be completed using Failed Parts/Total Parts. This is TRUE for actual yield but your article is based on Cp and CPK which is not actual yield it is expected yield with the assumption of no shifts or drifts. The yield statement can not apply to a NON-normal distribution because you are using Normal approximations to predict future yield.3. In step 3 for Cp/Cpk you mention that a distribution estimate is 3 standard deviations from the mean (Cpk: to the nearest limit). This is also TRUE, but only applys when the distributions are spread evenly across the mean. If you have a Non-normal population the +3s calculation from the mean does not reflect distribution probability. Thus the Cp/Cpk which are population ESTIMATES can not be considered accurate reflection either.All in All great Article. I believe Normality should be added as your first step. Please provide feedback.

    • billMay 19, 2020 Reply

      Thanks for your comment. There is a not a requirement for data to be normally distributed to be used in a control chart. Control charts are empirically based – not based on the assumption of data following a normal distribution. Dr. Wheeler has addressed this in detail in a number of his books. It is true that Cpk is based on the assumption of the data being normally distributed. See this link for a discussion of individual charts and non-normal data,

  • Michael B.November 1, 2017 Reply

    First of all thank you very much for the informative article, it is clear, concise, and not overly cluttered with statistical terminology.  I have been doing a lot of reading into Cpk and Ppk recently as we begin to qualify our process for volume production.  I have seen in many instances a mention of confidence intervals on Cpk based upon the sample size.  To take the data used in the example the sample size is 120 and the calculated Cpk is 1.19.  Then I can say with 95% confidence that the Cpk value is actually between 1.03 and 1.35.  My question is, why add a confidence interval to Cpk if you have already proved that the process is in control?  Is it conventional to target a Cpk of 1.33 or greater even though there is a chance at some confidence level that value could fall below 1.0 based upon the sample size used?  I'd love to hear your insight into confidence intervals on Cpk and when to apply them.  Thanks!

    • billNovember 2, 2017 Reply

      Thanks for the comments on the article.  I am not a fan of confidence intervals on Cpk.  Simply complicating things unnecessarily.  Once your process is in statistical control and you have enough data in the control chart, there is no need to recalculate control limits, Cpk or anything.  Enough data means two things to me:  sufficient individual dad ta points (100 is a good number) and sufficient time that the vast majority of sources of variation have had an opportunity to occur.  There is always variation, so you will always have a different result if you take another 100 data points.  But if your process is in control, those differences are not statistically significant – and probably not significant for your process either.  Most important to me is using your knowledge of the process and the key question is has there been enough time for most of the sources of variation to occur in my process.

  • Ian Flawn OrpanaJanuary 2, 2019 Reply

    Hi Bill, again a very nice article.I just wanted your view on the choice of using an XbarR as opposed to calculating the the mean and range and then plotting a Xm chart for both.  The XbarR will normally give you more tightnened control limits and thus there is a great chance that the process is showing points outside the the control limits.  The Xm chart is more forgiving in this repect and thus the process will be in control but may lead to a lower Cpk as the control limits will be wider (more forgiving).  I raise this point as I was a heavy XbarR user until I read an chapter from Wheelers book "Making sense of data" 2003, section 16.1.  It details that Shewhart predominantly used XbarR charts but this was because he was looking mostly at manufactruing issues where they were "collecting multiple measurements within a short period of time".  Therefore is it correct to use a XbarR chart when you look at 4 values per day, even if it is for 15 days?RegardsIan 

    • billJanuary 2, 2019 Reply

      Hello Ian,
      You are correct that the control limits are tighter for an Xbar-R control chart than for the individauls control chart.  However, the Cpk value will essentially be the same whether you group the data or use individuals value assuiming hte proces is stable.  The variation in the indiviual values (the standard deviation) will be the same. 
      You say you get 4 values a day, but only every 15 days?  I would probably go with the Xbar-R chart.  With indiviuals chart it is best to have somewhat of a constant time frame between points.

      • AnonymousJanuary 3, 2019 Reply

        The readings that were provided was 4 readings every day for 15 days.  Given the comment that Wheeler made that XbarR charts be used for situations as per monitoring manufacturing processes (ie rapid sampling frequencies taken over short time periods, and taken under essentially the same conditions), I was wondering if the XbarR in this case was appropriate as 4 samples each day had the potential to be operating under “different’ conditions. I guess it’s the thing about the data context and rationale sub grouping.  But if you do not know is the XbarR dangerous as it has the potential to identify “strong signals” points outside the control limitsI think the problem with with Cp/Cpk and Pp/Ppk is that people quote these without looking at control charts first.  I have seen people quoting these indices based upon 3 points, the low number is not obvious as the indices are presented in dashboards and the number of batches is conveniently missed.  That’s why I liked the confidence intervals, but I take on board your point mentioned in a previous thread above

        • billJanuary 4, 2019 Reply

          You can definitely us e the Xbar-R chart for 4 readings every day for 15 days.  The range chart is the within day variation and the Xbar chart is the between day variation.  If it is widely out of control, then the variation between days is much larger than the variation within days.  This maybe natural – in that case use the Xbar-mR-R within/between charts.
          You should always use control charts to ensure that the process is stable – otherwise Cpk and Ppk have no meaning – not to mention those two values will be close if the process is in control.
          You need enough degrees of freedom so the estimate the variation is valid.  3 points is ridiculously low – but that is someone wanting to fill in a dashboard and not taking time to learn what those value mean – if anything.  For degrees of freedom, please see this link:

  • Akash July 30, 2021 Reply

    In step 1, graph no.1 – process subgroup average. How did you calculate UCL:113.29 & LCL:84.66 ?? 

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