Quality & Metrology worked example

Sigma Shift with short-term sigma of 2.25 sigma: a worked example

Suppose short-term sigma falls to 2.25 sigma. This page works the full calculation at that level so you can see exactly which result moves and by how much. Convert a short-term process sigma to a long-term sigma by subtracting the standard 1.5 sigma shift.

The inputs for this scenario

  • Short-term sigma (Zst): 2.25 sigma (the input this scenario stresses; the baseline uses 4.5)
  • Sigma shift (typically 1.5σ): 1.5 sigma (held at the documented default)
  • Additional process drift: 0 sigma (held at the documented default)
  • Further sigma adjustment: 0 sigma (held at the documented default)

Working through the calculation

  • The calculation starts from the formula this tool documents: Total shift = sigma shift + additional drift + further adjustment.
  • Long-term sigma (Zlt) works out to 0.75 sigma at these inputs, and this is the headline figure for the scenario.
  • Total sigma shift works out to 1.5 value at these inputs.
  • Short-term sigma (Zst) works out to 2.25 value at these inputs.
  • Utilization works out to 33.33 % at these inputs.

How this compares with the baseline

  • Against the tool's baseline example, where short-term sigma sits at 4.5 sigma and the headline result is 3 sigma, this scenario comes in 75% below the baseline at 0.75 sigma.
  • It subtracts a total sigma shift (the 1.5σ convention plus any additional drift you specify) from short-term sigma to give the long-term sigma level Zlt. 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

  • Long-term sigma (Zlt): 0.75 sigma (headline result)
  • Total sigma shift: 1.5 value
  • Short-term sigma (Zst): 2.25 value
  • Utilization: 33.33 %

Run it with your numbers

  • To rerun this with your own numbers, open the live Sigma Shift calculator, set short-term sigma to your actual value, and adjust the remaining inputs to match your operation.

Last reviewed 2026-05-12.