Process capability (Cp and Cpk) calculator
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KEY POINTS
Cp is the specification width divided by the spread (6σ); Cpk is the distance from the mean to the nearer limit divided by 3σ, so it reflects both spread and centering. Fabs typically require a Cpk of at least 1.33 (±4σ, about 63 ppm for both tails) for key parameters such as film thickness, CD and sheet resistance, and target 1.67 or higher for critical steps.
Inputs
The out-of-spec rate assumes normally distributed measurements. It will differ from the real defect rate for skewed distributions such as film thickness, or for defect counts that pile up against zero.
Cpk and defect rate
| Cpk | Distance to limit | Out-of-spec rate (centered process) | Assessment |
|---|---|---|---|
| 0.67 | ±2.0σ | 44,400 ppm | Inadequate (below 1.00) |
| 1.00 | ±3.0σ | 2,700 ppm | Marginal (1.00 to 1.33) |
| 1.33 | ±4.0σ | 66.1 ppm | Good (1.33 or higher) |
| 1.50 | ±4.5σ | 6.8 ppm | Good (1.33 or higher) |
| 1.67 | ±5.0σ | 544.30 ppb | Excellent (1.67 or higher) |
| 2.00 | ±6.0σ | 1.97 ppb | Excellent (1.67 or higher) |
Cp versus Cpk
Cp only measures how small the spread (6σ) is relative to the specification width, and it does not change if the mean drifts off center. Cpk divides the distance from the mean to the nearer limit by 3σ, so it reflects both spread and centering. When Cp and Cpk differ widely, centering the process does more good than reducing variation.
Semiconductor fabs often require a Cpk of 1.33 or higher (±4σ) for key parameters such as film thickness, CD and sheet resistance, and target 1.67 or higher (±5σ) for critical steps. In statistical process control (SPC), Cpk is calculated only after control charts show that the process is stable. The Cpk of an unstable process says nothing about the quality of the next lot.
FAQ
What defect rate does a Cpk of 1.33 correspond to?
With the mean at the center of the specification, a Cpk of 1.33 puts each limit 4σ from the mean, for a combined out-of-spec rate of about 63 ppm. A Cpk of 1.67 (±5σ) corresponds to about 0.57 ppm.
What does a high Cp with a low Cpk mean?
The spread is small enough but the mean is off center. Centering the process usually does more good than reducing variation in this case.
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Last updated: October 23, 2026