Standard SPC Formulas
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SD = R/D2
Cp = USL – LSL / 6 * SD
Cpk = min (Cpl, Cpu)
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Cpl = X – LSL / 3 * SD
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Cpu = USL - X / 3 * SD
SD (n-1) (for n-1 samples) = sqrt [((X12 + X22 +…Xn2) – n (XBAR)2 ) / (n-1)]
Pp = (USL – LSL) / 6 * SD (n-1)
Ppk = min (Ppl, Ppu)
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Ppl = (X – LSL) / (3 * SD (n-1))
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Ppu = (USL – X) / (3 * SD (n-1))
FOR XbarR Chart :
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LCLx = X – (A2 * R)
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UCLx = X + (A2 * R)
UCLr = (D4 * R)
LCLr = (D3 * R)
FOR XbarS Chart :
UCLs = B4 * S