Quality & Metrology worked example

Process Capability Cpk with distance from mean to nearest spec limit of 0.2 spec units: a worked example

Suppose distance from mean to nearest spec limit falls to 0.2 spec units. This page works the full calculation at that level so you can see exactly which result moves and by how much. Estimate process capability Cpk as the distance from the process mean to the nearest specification limit, divided by the one-sided process spread.

The inputs for this scenario

  • Distance from mean to nearest spec limit: 0.2 spec units (the input this scenario stresses; the baseline uses 0.4)
  • Required clearance buffer: 0.04 spec units (held at the documented default)
  • One-sided process spread (3 sigma): 0.27 spec units (held at the documented default)

Working through the calculation

  • The calculation starts from the formula this tool documents: Adjusted distance to limit = distance to nearest spec limit − required clearance buffer.
  • Cpk works out to 0.59 Cpk at these inputs, and this is the headline figure for the scenario.
  • Effective distance to limit works out to 0.16 spec units at these inputs.
  • One-sided spread (3σ) works out to 0.27 spec units at these inputs.

How this compares with the baseline

  • Against the tool's baseline example, where distance from mean to nearest spec limit sits at 0.4 spec units and the headline result is 1.33 Cpk, this scenario comes in 55.56% below the baseline at 0.59 Cpk.
  • It computes Cpk as the centering-adjusted distance to the nearest spec limit divided by the one-sided three-sigma process spread. When the numbers land here, the stressed input is the lever to work; the walkthrough above shows exactly how much each output recovers as it climbs back toward the baseline.

Results at a glance

  • Cpk: 0.59 Cpk (headline result)
  • Effective distance to limit: 0.16 spec units
  • One-sided spread (3σ): 0.27 spec units

Run it with your numbers

  • To rerun this with your own numbers, open the live Process Capability Cpk calculator, set distance from mean to nearest spec limit to your actual value, and adjust the remaining inputs to match your operation.

Last reviewed 2026-05-12.