Statistics & SPC — Cheat Sheet
Descriptive stats, normal distribution, Cp/Cpk, control-chart limits and Six-Sigma DPMO.
Descriptive
| Mean | x̄ = Σx / n |
| Sample variance | s² = Σ(x−x̄)² / (n−1) |
| Std deviation | s = √s² |
| Range | R = x_max − x_min |
| Std error | SE = s / √n |
Normal distribution
| Z-score | z = (x − µ) / σ |
| Empirical rule | 68 / 95 / 99.7% within 1 / 2 / 3σ |
| Confidence (95%) | x̄ ± 1.96·σ/√n |
Process capability
| Cp | (USL − LSL) / 6σ |
| Cpk | min[(USL−µ), (µ−LSL)] / 3σ |
| Target | Cpk ≥ 1.33 (≈ 4σ); 1.67 for safety-critical |
| Pp/Ppk | same, using long-term σ |
Control charts (X̄–R)
| X̄ limits | X̄̄ ± A₂·R̄ |
| R chart | UCL = D₄·R̄, LCL = D₃·R̄ |
| n=2 | A₂=1.880, D₃=0, D₄=3.267 |
| n=4 | A₂=0.729, D₃=0, D₄=2.282 |
| n=5 | A₂=0.577, D₃=0, D₄=2.114 |
Six Sigma
| DPMO | defects / (units × opps) × 10⁶ |
| Yield | (1 − DPMO/10⁶) × 100% |
| 6σ level | 3.4 DPMO (with 1.5σ shift) |
Formula reference — verify against the governing standard. Not a substitute for engineering judgment.