Cpk is the process capability index that measures how well a process fits within its specification limits, accounting for where the process mean is centered. It equals min(Cpu, Cpl) where Cpu = (USL − mean) / (3σ) and Cpl = (mean − LSL) / (3σ). A higher Cpk means fewer defects.

What is the difference between Cp and Cpk?

Cp measures overall process spread relative to the tolerance band — (USL − LSL) / (6σ) — without considering where the mean falls. Cpk adjusts for centering: it equals Cp only when the mean is exactly centered between USL and LSL. Cpk is always ≤ Cp. A large gap between Cp and Cpk signals a centering problem.

What Cpk is acceptable?

A Cpk below 1.0 means the process produces defects outside specification. Values from 1.0 to 1.33 are marginally capable and often accepted for non-critical features. Values from 1.33 to 1.67 are capable and are a common minimum requirement. A Cpk of 1.67 or higher is excellent and required for safety-critical or high-volume processes.

How is PPM estimated from Cpk?

PPM is computed by integrating the normal distribution tails beyond the spec limits. Total PPM = (1 − Φ((USL − mean) / σ) + Φ((LSL − mean) / σ)) × 1,000,000, where Φ is the standard normal CDF. This assumes a stable, normally distributed process without a sigma shift.

What does sigma level mean here?

Sigma level = Cpk × 3. It represents the distance from the process mean to the nearest specification limit, measured in standard deviations. A Cpk of 1.33 corresponds to a 4-sigma process; Cpk of 1.67 corresponds to 5-sigma. This uses the short-term definition without the 1.5-sigma drift correction used in DPMO tables.

What inputs do I need?

You need four values: USL (upper specification limit), LSL (lower specification limit), the process mean (average of your sample measurements), and the process standard deviation (σ). These come from your measurement data — typically from a control chart study or a capability study with at least 30–100 parts.

Cpk Process Capability Index Calculator

Name: Cpk Process Capability Index Calculator
Availability: InStock
Author: Nham Vu

Calculate Cpk, Cp, sigma level, and estimated PPM defect rate from your process mean, standard deviation, and specification limits.

Process Parameters

Upper Specification Limit (USL)

Lower Specification Limit (LSL)

Process Mean

Process Std Dev (σ)

Cpk Reference Guide

Cpk Range	Sigma Level	Est. PPM	Rating
< 1.00	< 3.0	> 2,700	Not capable — process produces defects
1.00 – 1.33	3.0 – 4.0	63 – 2,700	Marginally capable — monitor closely
1.33 – 1.67	4.0 – 5.0	0.57 – 63	Capable — meets most quality standards
≥ 1.67	≥ 5.0	< 0.57	Excellent — required for critical features

PPM estimates assume a stable, normally distributed process with no long-term sigma drift.

Summary

Calculate Cpk, Cp, sigma level, and estimated PPM defect rate from your process mean, standard deviation, and specification limits.

How it works

Enter the Upper Specification Limit (USL) and Lower Specification Limit (LSL).
Enter the process mean (average of measurements) and process standard deviation.
The calculator computes Cpu = (USL - mean) / (3 × sigma) and Cpl = (mean - LSL) / (3 × sigma).
Cpk = min(Cpu, Cpl) — the smaller of the two one-sided indices.
Cp = (USL - LSL) / (6 × sigma) measures total spread relative to the tolerance band.
Sigma level = Cpk × 3; PPM is estimated from the normal distribution tail beyond each spec limit.

Use cases

Verify a machining process meets dimensional tolerances before a production run.
Determine whether a chemical fill process needs re-centering or tighter control.
Report capability to a customer as part of a PPAP (Production Part Approval Process).
Compare Cp and Cpk to diagnose whether variation or centering is the primary issue.
Set process improvement targets by seeing what mean shift or sigma reduction is required.
Train quality engineers on the relationship between Cpk, sigma level, and defect rate.

Frequently Asked Questions

Last updated: 2026-07-22 · Reviewed by Nham Vu