spc capability
**Process capability** in SPC measures a process's **ability to produce output within specification limits** — it quantifies how well the natural variation of the process fits within the required tolerance window. High capability means the process consistently produces results well within spec; low capability means the process frequently approaches or exceeds the limits.
**Key Capability Metrics**
- **Cp (Process Capability Index)**:
$$C_p = \frac{USL - LSL}{6\sigma}$$
Compares the specification width to the process spread. **Does not consider process centering** — it measures potential capability if the process were perfectly centered.
- **Cpk (Process Capability Index, Centered)**:
$$C_{pk} = \min\left(\frac{USL - \bar{X}}{3\sigma}, \frac{\bar{X} - LSL}{3\sigma}\right)$$
Accounts for **how close the process mean is to the nearer spec limit**. Always ≤ Cp. Cpk = Cp only when the process is perfectly centered.
**Interpreting Capability Values**
| Cpk Value | Interpretation | PPM Defective |
|-----------|---------------|---------------|
| < 1.0 | **Not capable** — significant out-of-spec production | >2,700 |
| 1.0 | Barely capable — 3σ limits touch spec limits | 2,700 |
| 1.33 | **Acceptable** — standard industry minimum | 63 |
| 1.67 | **Good** — typical target for critical steps | 0.6 |
| 2.0 | **Excellent** — 6σ process | 0.002 |
**Why Capability Matters in Semiconductors**
- A CD process with Cpk < 1.33 produces too many out-of-spec features — directly causing yield loss.
- **Critical steps** (gate CD, overlay, film thickness for thin films) often require Cpk ≥ 1.67.
- **Non-critical steps** may accept Cpk ≥ 1.0, but improvement is expected.
- **Cp vs. Cpk Gap**: If Cp is high but Cpk is low, the process has adequate precision but is off-center — a simple **target adjustment** can improve Cpk.
**Improving Process Capability**
- **Reduce σ**: Tighten the process spread through equipment improvements, recipe optimization, or better raw materials. This improves both Cp and Cpk.
- **Center the Process**: Adjust the process mean to the midpoint of the specification range. This improves Cpk without changing Cp.
- **Widen Specifications**: If the specs are unnecessarily tight, relaxing them improves capability — but this requires design validation.
Process capability is the **ultimate measure** of process quality — it directly connects manufacturing variation to product specifications and defect rates.