What this calculator does
Cp compares the width of the specification to the spread of the process; Cpk additionally accounts for where the process is centred. When the process sits exactly in the middle of its limits the two are equal, and a spread of 0.15 against a one-unit specification gives 1.111 for both.
The gap between them is the diagnostic. Shift the mean from 10 to 9.8 and Cp stays at 1.111 while Cpk falls to 0.6667, because the process has moved closer to the lower limit. Cp says the process is capable of fitting; Cpk says whether it currently does.
The formula
Cp is the specification width divided by six standard deviations, which covers the range a stable process occupies. Cpk takes the smaller of the distances from the mean to each limit, divided by three standard deviations. Both assume the process is stable and roughly normal, and a capability index calculated on an out-of-control process is meaningless.
| Term | Meaning |
|---|---|
| Cp | Potential capability: specification width over process spread, ignoring centring. |
| Cpk | Actual capability, accounting for how far off-centre the process runs. |
| 1.33 | The usual minimum for a capable process. 1.67 is a common target and 2.0 is the six sigma goal. |
| Stability | Statistical control, which must be established before capability means anything. |
The inputs explained
| Field | What to enter |
|---|---|
| Upper spec limit (USL) | Upper specification limit. |
| Lower spec limit (LSL) | Lower specification limit. |
| Process mean (μ) | Process mean from the measured data. |
| Process std deviation (σ) | Process standard deviation. This should come from a stable process in statistical control. |
When to use it
Qualifying a process
Customers and standards frequently require a demonstrated Cpk above a threshold before production is approved.
Diagnosing a capability problem
Cp well above Cpk points to a centring problem, which is usually far easier to fix than reducing variation.
Tracking improvement
Capability indices over time show whether process changes actually reduced variation.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What happens when the process drifts off centre?
The same process spread at different mean positions.
| Process mean | Cpk | Cp | Rating |
|---|---|---|---|
| μ = 9.8 | 0.6667 | 1.111 | Not capable (Cpk < 1) |
| μ = 9.9 | 0.8889 | 1.111 | Not capable (Cpk < 1) |
| μ = 10 | 1.111 | 1.111 | Marginally capable (1 ≤ Cpk < 1.33) |
| μ = 10.2 | 0.6667 | 1.111 | Not capable (Cpk < 1) |
Questions
What is the difference between Cp and Cpk?
Cp measures whether the process spread could fit inside the specification; Cpk measures whether it actually does, given where the process is centred. Cp is always at least Cpk, and they are equal only when the process is perfectly centred.
What Cpk is acceptable?
1.33 is the usual minimum for a capable process, corresponding to roughly 63 defects per million. Many industries target 1.67, and 2.0 is the six sigma goal. Below 1.0 the process is producing out-of-specification output at a meaningful rate.
My Cp is good but Cpk is poor. What does that mean?
The process is off centre. The variation is small enough to fit the specification comfortably, but the mean has drifted toward one limit. This is usually the easier problem to fix, since adjusting a setpoint is simpler than reducing variability.
Does the process need to be in control first?
Yes, and this is the most commonly ignored requirement. Capability indices assume a stable, predictable process. Calculating Cpk on a process with trends, shifts or special-cause variation produces a number that describes nothing, because there is no single process to describe.
For the normal distribution behind the six-sigma width, see the empirical rule calculator. For the underlying spread measure, see the descriptive statistics calculator.