Quality & Metrology worked example

Control Chart Limit with process centerline of 250 units: a worked example

What does the result look like when process centerline reaches 250 units? The full calculation is worked below with real intermediate numbers. Use it to set a three-sigma control limit for a chart when you already know the centerline and the standard deviation.

The inputs for this scenario

  • Process centerline: 250 units (raised for this scenario; the documented default is 100)
  • First one-sigma band: 2 units (unchanged)
  • Second one-sigma band: 2 units (unchanged)
  • Third one-sigma band: 2 units (unchanged)

Working through the calculation

  • Applying the documented formula (Upper control limit = process centerline + first one-sigma band + second one-sigma band + third one-sigma band) to the inputs above produces each figure below.
  • At this operating point the engine returns 256 units for upper control limit (ucl), the number this scenario is built around.
  • At this operating point the engine returns 250 units for element 1.
  • At this operating point the engine returns 2 units for element 2.
  • At this operating point the engine returns 4 units for element 3 + 4.

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 142% above the baseline at 256 units.
  • A figure at this level is achievable when process centerline is genuinely sustained, not just peaked for a shift. It only builds the upper limit from bands you supply — it does not estimate sigma from data, and it assumes an in-control, roughly normal process, so garbage-in sigma yields a meaningless limit.

Results at a glance

  • Upper control limit (UCL): 256 units (headline result)
  • Element 1: 250 units
  • Element 2: 2 units
  • Element 3 + 4: 4 units

Run it with your numbers

  • Every input above is editable in the live Control Chart Limit calculator, which recalculates instantly and can be shared with the inputs intact.

Last reviewed 2026-05-12.