Process Capability (Cp/Cpk) Simulator

Process Settings

Process mean μ 50.0

Process σ (variation) 1.50

Spec width (USL−LSL) 18.0

Capability Indices

Capable process

Cp (potential)

—

Cpk (actual)

—

Pp (overall)

—

Ppk (overall)

—

Sample n

Defect rate

0 PPM

How it works

Process capability compares how much a process could vary (its natural spread, 6σ) against how much room the specification allows (USL − LSL), and separately checks whether the process is actually centered inside that spec window.

Cp  = (USL − LSL) / (6σ)
Cpk = min( (USL − μ) / (3σ),  (μ − LSL) / (3σ) )
Pp, Ppk : same formulas using the sample's overall (long-term) mean/σ instead of a subgroup estimate
Defect rate ≈ 2·Φ(−3·Cpk) · 1,000,000 PPM (parts per million out of spec)

Cp — the process's raw potential if it were perfectly centered; ignores where μ actually sits.
Cpk — the real-world capability, penalized whenever μ drifts off-center toward either spec limit.
Cp > Cpk always, unless the process is perfectly centered (Cp = Cpk).
Rule of thumb: Cpk ≥ 1.33 is "capable", Cpk ≥ 1.67 approaches Six-Sigma quality, Cpk < 1.0 means the process is already producing out-of-spec parts.
Corrective action — the classic quality-engineering response to a low Cpk: re-center the mean on target and tighten (reduce) the process variation σ, exactly as a real SPC/DMAIC improvement cycle would.

This is the core index used on real production lines (automotive, semiconductor, pharma) to decide whether a process is fit to ship parts against a customer's tolerance, and to quantify how much a corrective action actually improved it.

In-spec part Out-of-spec part Spec limit plane

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.