Quality & Metrology worked example

Control Chart Limit with process centerline of 50 units: a worked example

Suppose process centerline falls to 50 units. This page works the full calculation at that level so you can see exactly which result moves and by how much. Estimate an upper control limit by adding the process centerline and three equal one-sigma bands.

The inputs for this scenario

  • Process centerline: 50 units (the input this scenario stresses; the baseline uses 100)
  • First one-sigma band: 2 units (held at the documented default)
  • Second one-sigma band: 2 units (held at the documented default)
  • Third one-sigma band: 2 units (held at the documented default)

Working through the calculation

  • The calculation starts from the formula this tool documents: Upper control limit = process centerline + first one-sigma band + second one-sigma band + third one-sigma band.
  • Upper control limit (UCL) works out to 56 units at these inputs, and this is the headline figure for the scenario.
  • Element 1 works out to 50 units at these inputs.
  • Element 2 works out to 2 units at these inputs.
  • Element 3 + 4 works out to 4 units at these inputs.

How this compares with the baseline

  • Against the tool's baseline example, where process centerline sits at 100 units and the headline result is 106 units, this scenario comes in 47.17% below the baseline at 56 units.
  • It sums the process centerline and three successive one-sigma bands to produce the upper control limit, and reports the average band width. 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

  • Upper control limit (UCL): 56 units (headline result)
  • Element 1: 50 units
  • Element 2: 2 units
  • Element 3 + 4: 4 units

Run it with your numbers

  • To rerun this with your own numbers, open the live Control Chart Limit calculator, set process centerline to your actual value, and adjust the remaining inputs to match your operation.

Last reviewed 2026-05-12.