Quality & Metrology worked example

Process Capability Cpk with distance from mean to nearest spec limit of 1 spec units: a worked example

Push distance from mean to nearest spec limit up to 1 spec units and the picture changes. This example computes every intermediate figure at that operating point. Use it when a feature may be off-center and you need a capability number that reflects the worst-case spec limit for a go or no-go review.

The inputs for this scenario

  • Distance from mean to nearest spec limit: 1 spec units (raised for this scenario; the documented default is 0.4)
  • Required clearance buffer: 0.04 spec units (unchanged)
  • One-sided process spread (3 sigma): 0.27 spec units (unchanged)

Working through the calculation

  • Applying the documented formula (Adjusted distance to limit = distance to nearest spec limit − required clearance buffer) to the inputs above produces each figure below.
  • At this operating point the engine returns 3.56 Cpk for cpk, the number this scenario is built around.
  • At this operating point the engine returns 0.96 spec units for effective distance to limit.
  • At this operating point the engine returns 0.27 spec units for one-sided spread (3σ).

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 167% above the baseline at 3.56 Cpk.
  • It computes Cpk as the centering-adjusted distance to the nearest spec limit divided by the one-sided three-sigma process spread. The value of this scenario is the size of the gap it exposes: that gap, priced out over a year, is the budget you can justify spending to close it.

Results at a glance

  • Cpk: 3.56 Cpk (headline result)
  • Effective distance to limit: 0.96 spec units
  • One-sided spread (3σ): 0.27 spec units

Run it with your numbers

  • Every input above is editable in the live Process Capability Cpk calculator, which recalculates instantly and can be shared with the inputs intact.

Last reviewed 2026-05-12.