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The following statistics are calculated from values stored in the configuration and from values stored in the standard:
The upper limit used for this equation depends on the Acceptance limit based on setting for this configuration.
The Upper individual limit, Upper gate, and Upper spec are stored in the standard.
The Target is stored in the standard as Target X (Nominal).
A = Acceptance limit
A = Upper limit – Target
S = Starting value
S = k * A
where
k = Start value constant
T = Sample unit tolerance
T = ( k * A) / h
where
h = Decision interval value
k = Start value constant
C1 = Target – T
C2 = Target + T
The C1 and C2 values are used to display the C1/C2 Zone on CuSum charts. They are also used to calculate the Upper and Lower CuSum values for each data subgroup.
The following statistics are calculated for each data subgroup entered.
QU(n) = Upper CuSum value for nth subgroup
QU(n) = QU(n-1) + XBar(n) - C2
where
if n = 1, then QU(n-1) = S
if subgroup n-1 caused a real-time CuSum failure (QU(n-1) > A), then QU(n-1) = S
if QU(n-1) < 0, then QU(n-1) = 0
n = sequential number of the subgroup (subgroup 1, subgroup 2, etc.)
QU(n-1) = Upper CuSum value for previous subgroup
XBar(n) = subgroup average for nth subgroup
QL(n) = Lower CuSum value for nth subgroup
QL(n) = QL(n-1) - XBar(n) + C1
where
if n = 1, then QL(n-1) = S
if subgroup n-1 caused a real-time CuSum failure (QL(n-1) > A), then QL(n-1) = S
if QL(n-1) < 0, then QL(n-1) = 0
n = sequential number of the subgroup (subgroup 1, subgroup 2, etc.)
QL(n-1) = Lower CuSum value for previous subgroup
XBar(n) = subgroup average for nth subgroup
If QU(n) > 0, the top of the CuSum bar is plotted at QU(n) + Target
If QU(n) < 0, the top of the CuSum bar is plotted at the Target
If QL(n) > 0, the bottom of the CuSum bar is plotted at Target - QL(n)
If QL(n) < 0, the bottom of the CuSum bar is plotted at the Target
During data entry, a data subgroup where QU(n) > A or QL(n) > A fails the real-time test for CuSum failures.