Formula & Calculator
Process Capability Index (Cpk, Accounting for Centering)
Measures process capability while also accounting for how well the process is centered within its specification limits, unlike the simpler Cp.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Cpk | Process capability index (centered) | |
| USL | Upper specification limit | |
| LSL | Lower specification limit | |
| μ | Process mean | |
| σ | Process standard deviation |
What it means
The Cpk index is a process capability measure that accounts for both the spread of the process (via σ) and the centering of the mean (μ) relative to the specification limits (USL and LSL). It is defined as the minimum of the upper and lower capability indices: Cpk = min[(USL−μ)/(3σ), (μ−LSL)/(3σ)]. A Cpk of 1.0 means that the process spread is exactly 3σ from the mean to the nearest limit, implying that 0.27% of output is outside the limits (assuming normality). Higher Cpk values indicate better capability; typically, a Cpk ≥ 1.33 is desired for new processes. Unlike C_p, Cpk penalises off‑center processes. This metric is widely used in Six Sigma and quality engineering to evaluate whether a process can meet specifications, to compare suppliers, and to prioritise improvement efforts. It helps in setting quality targets and in acceptance decisions. Understanding Cpk is essential for quality professionals to ensure that products meet customer requirements consistently.
Worked example
Process Capability (Cpk) – Two Examples
Real‑World| Parameter | Value |
|---|---|
| USL | 20 |
| LSL | 0 |
| μ | 11 |
| σ | 1.5 |
| Parameter | Value |
|---|---|
| USL | 14 |
| LSL | 10 |
| μ | 8 |
| σ | 0.8 |
Common mistakes
- USL and LSL: Upper and lower specification limits.
- μ: Process mean – use the estimated mean (e.g., from sample).
- σ: Process standard deviation (estimated from control charts).
- Interpretation: Cpk accounts for process centering – it is the smaller of the two capability indices to the nearest spec limit.
- Threshold: Cpk ≥ 1.33 is generally acceptable; Cpk < 1 indicates the process is not capable.
- Assumptions: Process is stable and normally distributed.
Applications
Process capability index Cpk = min[(USL − μ)/(3σ), (μ − LSL)/(3σ)] accounts for process centering, unlike Cp. It provides a more realistic measure of process capability, indicating how well the process output falls within specification limits. A Cpk of 1.33 or higher is typically considered acceptable, meaning the process is capable. Quality engineers use Cpk for process certification, for supplier evaluation, and for assessing the impact of process improvements. It is widely used in automotive (AIAG), medical devices, and other regulated industries where product quality is critical. By calculating Cpk, organisations can identify processes that need adjustment, reduce scrap, and ensure customer satisfaction. Cpk is often reported in PPAP (Production Part Approval Process) submissions.
- Process performance evaluation for product specifications
- Supplier quality validation (PPAP, APQP)
- Equipment acceptance and process qualification
- Reduction of scrap and rework through centering
- Compliance with industry quality standards (ISO, IATF)