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Control Chart Process Limit Calculation

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  • #253708

    gunabalan
    Participant

    The UCL (Upper Control Limit) and LCL (Lower Control Limit) for a numerical column calculated in excel is differ from the UCL and LCL calculated by minitab for the same numerical column.

    The formula that is used in excel is
    UCL = Mean + 2 * (S.D)
    LCL = Mean – 2 * (S.D)

    This is the column:
    col =
    742
    744
    720
    835
    824
    801
    767
    796
    827
    811
    878
    826
    785
    859
    879
    798
    743
    785
    859
    846
    890
    870
    859
    901
    887
    929
    896
    913
    893
    880
    867
    943
    956
    971
    894
    849
    927
    926
    1037
    902
    997
    897
    888
    768
    757
    831
    835
    837
    831
    849
    788
    748
    839
    791
    839
    806
    889
    866
    865
    937
    967
    900
    919
    934
    842
    810
    877
    886
    1005
    1036
    1191
    1090
    1046
    1147
    1180
    1042
    1007
    1002
    951
    950
    950
    928
    953
    858
    767
    789
    713
    760
    713
    709
    655
    664
    674
    665
    706
    734
    760
    759
    679
    643
    661
    697
    771
    776
    799
    780
    712
    777
    814
    792
    751
    770
    776
    724
    777
    803
    792

    Excel UCL 1063.451853 Minitab UCL 922.7

    Excel LCL 628.9584035 Minitab LCL 769.7

    can anyone please clarify me why there is difference?

    1
    #253718

    Robert Butler
    Participant

    It looks like excel is just computing the standard deviation of the sample and then giving you the plus/minus 2 standard deviations of the sample whereas Minitab looks like it is computing USL and LSL spec limits

    0
    #253750

    Strayer
    Participant

    The control limits per Shewhart are +/- 3 standard deviations from the mean and there is sound reasoning for this. You might inquire why whoever wrote the Excel formulas used a narrower range.

    0
    #253771

    Benjamin Sagalovsky
    Participant

    Minitab does not use the formula for “s” that Excel uses for calculating those limits, it uses a different formula which is based on the values of the differences between adjacent points. You can see more at:
    https://blog.minitab.com/en/marilyn-wheatleys-blog/methods-and-formulas3a-how-are-i-mr-chart-control-limits-calculated

    This is what Shewhart prescribed, and for good reason: you don’t want to take into acount the trends and long-time swings in the data, but the short-time variation (common cause variation) so that anything that goes beyond short-time variation is highlighted on the chart. For the same reason, you do not want to square values (which would give a strong influence to outliers) because you want an estimate of the standard deviation that makes outliers stand out.

    Still, the esimate of SD that Minitab (Shewhart) uses is a ‘good’ (unbiased) estimator of the SD and would be very close to the one that Excel uses for large data sets, if there are no long-term trends or deterministic “swings” in the values.

    1
    #253782

    Savaria
    Participant

    At an individual chart Minitab estimates sigma (std dev) by moving range. Calculate the mean of moving ranges by excel divide by d2 constant and you can receive the same std. dev value as was shown Minitab

    1
    #253931

    gunabalan
    Participant

    The link gives me detailed knowledge about this, thanks

    0
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