Calculating Cp

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    I understand that Cp = (USL-LSL)/6 SigmaR
    where SigmaR = Rbar/d2
    If I have a subgroup size of 1, how is the Rbar calculated? I am told that the default in Minitab is an Average Moving Range of length 2. What about the value of d2? I dont think I understand how Cp is calculated in such a scenario. Also, am I better off tracking Pp and Ppk instead?



    Hi Rahul,
    With a subgroup size of 1, you should use an IX & MR chart to monitor the process output.  Individual readings (the IXs) are plotted on the IX chart while the moving ranges (the MRs) are plotted on the MR chart.  Moving ranges are computed as the absolute value of two consecutive IX values.  For example, if your first IX is 25 and the second IX is 23, the first moving range is 2.
    MR1 = | IX1 – IX2 | = | 25 – 23 | = 2
    If the third IX is 27, the second moving range is 4.
    MR2 = | IX2 – IX3 | = | 23 – 27 | = 4
    When control is established, add up the moving ranges and divide this total by the number of MRs included in this sum to get the average moving range, MR-bar.  To estimate the short-term process standard deviation, sigmaST, divide the average moving range by a d2 factor for a subgroup size of 2 (two IX values are used to compute each moving range).  The d2 factor for a subgroup size of 2 is 1.128.
    Estimate of sigmaST = MR-bar / d2 = MR-bar / 1.128
    With this estimate of sigmaST, you can estimate the Cp index with the formula you gave at the beginning of your post.
    As an alternative method of tracking process capability, you could pool all the in-control IX values into one large sample and calculate s, the sample standard deviation of these measurements.  s is a good estimate of the long-term process standard deviation, sigmaLT.  Using this estimate, you can estimate the Pp index, which is a measure of the long-term potential process capability.
    Pp = (USL – LSL) / (6 sigmaLT)
    Hope this helps.



    Hi Ross, Thanks for the exhaustive reply.
    I am not fully satisfied with the way the average moving range is calculated. I’m looking at finished parts coming out of a machining process. An AMR of 2 presumes that consecutive values have the greatest chance of being alike. I would not like to make this assumption about my process due to the special cause variation in it. I would say that my proces is in control, with a lot of operator interaction (undesirable). It is for this reason that I am looking at alternative statistics to give me an understanding of the capability of the process.

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