# 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