Measure process capability and centering using Cp and Cpk — so you can see whether your process consistently meets specification limits and where it sits relative to them.
Enter your specification limits, process mean and standard deviation on the left, then press Calculate.
A shaft at 50mm ±0.5mm. Mean 50.15mm, StDev 0.12mm. Enter the lab and find out if this process is truly capable — and whether it is centred.
Use the calculator above to compute Cp and Cpk from your process mean, standard deviation and specification limits. Cp measures whether the process spread fits within the spec; Cpk measures whether the process is also centred. Together they form the standard process-capability indices for short-term performance.
Cp and Cpk are short-term process capability indices. Cp compares the width of the specification to the width of the process spread (6 standard deviations). Cpk additionally accounts for how off-centre the process mean is from the spec midpoint. Cp says "can it fit"; Cpk says "does it fit where it sits".
Cp = (USL − LSL) ÷ (6σ). Cpk = min((USL − x̄) ÷ (3σ), (x̄ − LSL) ÷ (3σ)). Both indices use the short-term σ from a stable sample. Cpk is always ≤ Cp; the gap between them tells you how much capability you would gain by centring the process.
A process has a mean of 10.4, standard deviation of 0.3, and specs of 10 ± 1. Cp = 2 ÷ (6 × 0.3) = 1.11 — the spread fits comfortably inside the spec. Cpk = min((11 − 10.4) ÷ 0.9, (10.4 − 9) ÷ 0.9) = 0.67 — much lower, because the process is off-centre.
The Cp / Cpk gap (1.11 vs 0.67) tells you the process is producing defects only because it is not centred. Re-centring to 10 would deliver Cpk = 1.11 with zero variation-reduction effort. That is the practical diagnostic Cp and Cpk together provide.
Cp / Cpk show whether the process can meet spec and whether it currently does. They convert the abstract idea of "in control" into a number that maps directly to defect rates.
Use Cp / Cpk to validate process capability before sign-off, qualify new equipment, or to gate a process for release. They are central to PPAP, IATF and most quality-management standards.
Cpk = 1.0 corresponds roughly to 3σ; Cpk = 1.33 to 4σ; Cpk = 2.0 to 6σ. The capability index directly converts to Sigma Level and to DPMO at the specification limits.
If Cp is high but Cpk is low, centre the process. If both are low, reduce variation — chart the data, identify special-cause vs common-cause variation, and run a DMAIC project on the largest common cause.
Pair Cp / Cpk with Ppk, control charts and DOE to convert capability scores into a structured improvement plan.
Cp measures whether the process spread fits within the spec at all. Cpk additionally measures whether the process is centred. Cpk is always ≤ Cp; the gap shows the cost of being off-centre.
1.33 is the common industry minimum for non-critical features. 1.67 is typical for critical features. 2.0 corresponds to 6σ. Anything below 1.0 means defects are being produced at the specification limit.
Cpk uses short-term standard deviation (sub-grouped data) and represents potential capability. Ppk uses long-term standard deviation across all data and represents actual performance. Ppk is always ≤ Cpk.
Usually because the process is off-centre. Cp will be higher than Cpk in that case. Re-centring delivers the gap with no variation reduction.
Standard Cpk assumes normality. For non-normal data either transform the data, use percentile-based capability indices, or use non-normal Cpk methods (Pearson, Box-Cox).
Want to know when to use Cp vs Cpk — and how to act on the result? The Green Belt covers this in full.
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