What Is the Process Capability Index?
The process capability index is a number that expresses how stably a production line is making products. On the quality management floor, it is one of the most commonly used indicators for answering "is this process safe to run?"
In a single sentence: it shows how much room exists between the spread of your product variation and the tolerance band on the drawing. The larger the index, the more margin you have.
To understand process capability, you need two concepts: the normal distribution and the standard deviation (σ, sigma). Product variation usually follows a bell-curve normal distribution. When it doesn't, that itself can be a sign that something abnormal is happening in the process.
Fig. 01 — Normal distribution and specification limits (UCL / LCL)
The diagram evaluates how much room the product variation (normal distribution) has within the upper (UCL) and lower (LCL) specification limits.
Calculating Cp
Cp is the simplest process capability index. It is just the specification width divided by the spread of variation (6σ).
For example: suppose a target dimension is 5 cm, with a tolerance of ±1 cm (so the range is 4–6 cm). The specification width is 6 − 4 = 2 cm. If the variation spread (6σ) is also exactly 2 cm, then Cp = 1.0. A higher Cp means more margin — the variation is smaller relative to the specification.
Left: curve reaches the specification limits. Right: variation fits inside the specification with room to spare.
Why Is the Threshold 1.33?
The standard pass/fail threshold widely used for process capability is Cp ≥ 1.33. Let's verify what this means numerically.
According to normal distribution probability theory, the chance of a value falling outside ±4σ is approximately 0.006% — about 6 defects per 100,000 parts. That is the level of robustness the 1.33 threshold represents.
| Cp value | Sigma span | One-side margin | Approx. defect rate | Verdict |
|---|---|---|---|---|
| 1.00 | 6σ | ±3σ | ~0.27% (2,700 ppm) | Minimum |
| 1.33 | 8σ | ±4σ | ~0.006% (63 ppm) | Standard requirement |
| 1.67 | 10σ | ±5σ | ~0.00006% (0.6 ppm) | High-reliability |
| 2.00 | 12σ | ±6σ | 0.0000002% (6σ quality) | World-class |
| < 1.00 | — | — | Defects may be occurring now | Needs improvement |
Quick floor check
Take the Cp value required of your process and multiply by 6. The result tells you how many sigma of margin that requirement represents — instantly.
The Weakness of Cp — and Why Cpk Is Needed
Cp has one major hidden assumption: that the center of the product distribution perfectly coincides with the center of the specification.
In real manufacturing, a process targeting 5.0 cm almost never sits exactly at 5.0 cm day after day. The actual mean drifts — perhaps to 5.1 cm, perhaps to 4.9 cm. Ignoring this offset (bias) means Cp alone cannot accurately evaluate true process capability.
Fig. 03 — Distribution mean shifted from specification center
The actual mean (μ) is shifted right from the specification center. The distribution is dangerously close to the UCL — even if Cp looks fine.
Cpk is the index that corrects for this offset. Cpk is always ≤ Cp. It equals Cp only when the mean is perfectly centered on the specification.
Cp vs Cpk in one line
Cp = potential. Cpk = actual performance.
High Cp but low Cpk means: "the process could perform well — but it's running off-center."
Calculating Cpk — Two Methods
First calculate how far the actual mean is from the specification center, expressed as the offset factor k. Then apply it to correct Cp.
Calculate the one-sided capability toward each limit separately, then take the smaller of the two as Cpk.
Which method to use?
Both methods always give the same result — use whichever is more convenient. For one-sided specifications (upper or lower limit only), Method 2 is the natural choice.
Summary
A number showing how much margin product variation has within the specification width. A higher value means a more stable process.
Cp ≥ 1.33 is the standard requirement. This represents ±4σ of margin from center — roughly 6 defects per 100,000 parts.
The actual mean is rarely centered on spec. Cpk corrects for offset and reflects what the process is truly delivering — not just what it could deliver.
When reviewing quality data from your own processes, make it a habit to check both Cp and Cpk. A large gap between them is a signal: "the process has low variation — but it's running off-center." That points directly toward setup adjustment as a path to improvement.