Control Charts (Statistical Process Control)
Control Charts monitor whether a process is in statistical control over time. Points outside control limits or non-random patterns signal special-cause variation that warrants investigation.
Step 1 — Choose chart type
Continuous (variables) data:
| Chart | Use when |
|---|---|
| X-bar-R | Subgrouped data, small subgroups (n=2-10) |
| X-bar-S | Subgrouped data, larger subgroups |
| Individuals (I-MR) | Single measurements (subgroup size = 1) |
Attribute (counts) data:
| Chart | Use when |
|---|---|
| p chart | Proportion defective, variable sample size |
| np chart | Number defective, constant sample size |
| c chart | Defect count per unit, constant opportunity |
| u chart | Defects per unit, variable opportunity |
Step 2 — Results
- Centre line (CL) — process average
- UCL / LCL — +/-3 sigma boundaries
- Estimated process standard deviation
- Control chart plot
- Out-of-control violations with Nelson Rule cited
- In-control verdict
A UniversalChatBot is available for discussion.
Statistical methods used
X-bar-R formulas:
- UCL(X-bar) =
X-double-bar + A2 * R-bar - LCL(X-bar) =
X-double-bar - A2 * R-bar - UCL(R) =
D4 * R-bar, LCL(R) =D3 * R-bar - Sigma =
R-bar / d2
Individuals (I-MR):
- UCL/LCL =
x-bar +/- 2.66 * MR-bar
Attribute charts: Based on binomial (p, np) or Poisson (c, u) distributions.
Nelson Rules checked: Rule 1 (beyond 3 sigma), Rule 2 (9 consecutive same side), Rule 3 (6 trending), Rule 5 (2 of 3 beyond 2 sigma).
Control limits at +/-3 sigma give ~0.27% false alarm rate per point.
In control != meeting specifications. Use Process Capability for that assessment.