Control chart
Warm-up
Production monitoring
Production records
Signal rule: a point outside the 3-sigma limits, or eight consecutive points on one side of the centre line, signals investigation.
Live x̄ control chart
Subgroup means and your selected limits update live.
Examine the process and check your decision.
The maths
Each subgroup mean x̄ is the arithmetic average of n measured fill weights, in grams.
Known process mean μ and individual standard deviation σ give SE = σ/√n.
Centre line CL = μ.
Upper control limit UCL = μ + 3σ/√n.
Lower control limit LCL = μ − 3σ/√n.
The total control-band width is UCL − LCL = 6σ/√n.
Signal: one point strictly outside the control limits, or eight consecutive subgroup means strictly above or below the centre line.
A point exactly on a limit is not beyond it. A point on the centre line interrupts a run.
These are x̄ control limits, not product specification limits or confidence intervals.