# Question : HISTOGRAM WITH CP AND CPK ANALYSIS

## Answer : HISTOGRAM WITH CP AND CPK ANALYSIS

##### Hello JohnSrinivassan,Based on http://en.wikipedia.org/wiki/Process_capability_index ...1) Your data are not even close to be normally distributed, and one of the underlying assumptions for theprocess capability index is that the data are at least approximately normally distributed2) You did not provide a mean or a std deviation for the data.  Based on the histogram, the followingformulae *estimate* the mean and std deviation for your sample:Mean: =SUMPRODUCT(A2:A110,B2:B110)/B111Std Dev: {=SQRT(SUM(B2:B110*(A2:A110-C1)^2)/(B111-1))}Note that the std dev formula is an array formula, and not a normal formula.  To enter an array formula, do not enter the curly braces, and hit Ctrl+Shift+Enter instead of Enter to finish it off.   Excel will then display those braces to indicate that it's an array formula.3) If you create Names Mean, SD, Lower, and Upper for the mean, std deviation, lower specification bound,and upper specification bound, respectively, then these formulas get CP and CPK:CP: =(Upper-Lower)/(6*SD)CPK: =MIN((Upper-Mean)/(3*SD),(Mean-Lower)/(3*SD))Regards,Patrick
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