Formula & Calculator
Process Capability Index
Measures how well a process output fits within specification limits.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| C_p | Capability index | |
| USL | Upper spec limit | |
| LSL | Lower spec limit | |
| σ | Process standard deviation |
What it means
The Process Capability Index (C_p) is a statistical measure that quantifies how well a process can produce output within specified tolerance limits, assuming the process is centered between the Upper Specification Limit (USL) and Lower Specification Limit (LSL). It is calculated as the total tolerance width divided by six times the process standard deviation (6σ), which represents the natural spread of the process. A C_p ≥ 1.33 is generally considered acceptable, indicating that the process spread is narrower than the tolerance band. C_p does not account for process centering; if the mean is not centered, the actual capability is lower, which is captured by Cpk. C_p is widely used in Six Sigma, manufacturing, and quality engineering to evaluate machine performance, supplier quality, and process improvement initiatives. It provides a dimensionless metric that is independent of units, enabling comparisons across different processes. Managers use C_p to decide whether a process is capable of meeting customer requirements without excessive defects. Understanding C_p is essential for quality professionals to design control plans and to drive continuous improvement.
Worked example
Process Capability Index (Cp) – Two Examples
Real‑World| Parameter | Value |
|---|---|
| USL | 11.0 mm |
| LSL | 9.0 mm |
| σ | 0.2 mm |
| Parameter | Value |
|---|---|
| USL | 510 mL |
| LSL | 490 mL |
| σ | 3.0 mL |
Common mistakes
- USL and LSL: Upper and lower specification limits – must be in the same units as the process data.
- σ: The process standard deviation (population) – often estimated from sample data using s (use a control chart estimate).
- Interpretation: C_p measures potential capability if the process is centered. It does not account for mean shift.
- Threshold: C_p ≥ 1.33 is generally considered capable (for 4σ); C_p ≥ 1.67 is highly capable.
- Assumptions: The process is stable (in statistical control) and the data are normally distributed.
Applications
The process capability index, C_p = (USL − LSL)/(6σ), measures a process's potential to produce output within specification limits, assuming the process is centred. A C_p of 1.0 means that the process spread (6σ) equals the tolerance width, producing about 0.27% defects if centred. Quality engineers use C_p to assess whether a process is capable of meeting customer requirements, to evaluate machine selection, and to set improvement targets. It is widely used in manufacturing, healthcare, and service industries to benchmark process performance and to guide Six Sigma projects. However, C_p does not account for process centering, so Cpk is often preferred. By calculating C_p, organisations can identify processes that need improvement and validate that new equipment or methods meet capability requirements.
- Evaluation of manufacturing process capability for dimensional tolerances
- Supplier quality assessment and validation
- Design of experiments and process parameter selection
- Six Sigma project prioritisation and benchmarking
- Compliance with customer‑specified capability requirements