# SPC Formulas

Standard SPC Formulas

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1. SD = R/D2

2. Cp = USL – LSL / 6 * SD

3. Cpk = min (Cpl, Cpu)

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4. Cpl = X – LSL / 3 * SD

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5. Cpu = USL - X / 3 * SD

6. SD (n-1) (for n-1 samples) = sqrt [((X12 + X22 +…Xn2) – n (XBAR)2 ) / (n-1)]

7. Pp = (USL – LSL) / 6 * SD (n-1)

8. Ppk = min (Ppl, Ppu)

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9. Ppl = (X – LSL) / (3 * SD (n-1))

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10. Ppu = (USL – X) / (3 * SD (n-1))

FOR XbarR Chart :

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11. LCLx = X – (A2 * R)

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12. UCLx = X + (A2 * R)

13. UCLr = (D4 * R)

14. LCLr = (D3 * R)

FOR XbarS Chart :

15. UCLs = B4 * S