Observe → Predict → Investigate
Control Chart Lab
Did the process change, or are we seeing its usual variation?
Build a reference from an initial baseline. Then change the monitoring period without moving the goalposts.
Before looking at the answer
What would you investigate?
Would a change in the average, the spread, or both create a signal?
Start here
R chart · within-subgroup spread
If variation is unstable, investigate it before relying on the x-bar limits.
x-bar chart · subgroup averages
Measurements in mmShaded region: baseline. White region: monitoring. Select a numbered subgroup below to inspect its calculation. Signals use unrounded values; point-on-limit is not outside.
Follow one calculation
Two different questions
Stable does not mean acceptable.
Estimated from process data. “Is the process behaving consistently?” The x-bar chart tracks averages, not individual items.
Set by a customer or design requirement. “Does this individual item meet the requirement?” They do not move the control limits.
These are illustrative item specifications, not lines on the subgroup-average chart. This lab does not estimate Cp/Cpk or long-run capability.
Inspect every subgroup & spreadsheet bridge
CSV includes the measurements or counts, phase, observed statistic and frozen limits. Expand the formulas below to recreate the calculation in Excel.
Use this in one existing chart lesson
- Predict: Begin with “Baseline continuation.” Describe what ordinary variation looks like.
- Compare: Change only the monitoring period. Explain why the reference stays fixed.
- Check: Work through one subgroup and recreate its result in a spreadsheet.
- Decide: Name a sensible investigation or measurement check. A signal does not identify the cause.
Assumptions, limitations & references
Examples are synthetic teaching data, deliberately simple, not measurements from a real organization. A practical baseline often uses 20–25 or more representative, rational subgroups. Screen a baseline for assignable causes and measurement problems before using it prospectively; do not remove inconvenient points just to force stability.
x-bar/R: continuous measurements, independent rational subgroups, equal subgroup size 2–10, and a suitable approximately normal within-subgroup measurement distribution. The range constants are rounded tabulated values. p: each unit is conforming or nonconforming, independent Bernoulli outcomes and a common underlying probability within a stable phase. Multiple defects on one unit need a different chart. Overdispersion, clustering, autocorrelation and changing definitions can invalidate these limits.
The default rule is a point strictly beyond a 3-sigma limit. The optional eight-point rule is a selected supplementary rule, not a full Western Electric/Nelson ruleset; more rules increase false alarms. Baseline flags are retrospective diagnostics; monitoring flags are comparisons to the fixed reference. No signal is not proof of control. Out-of-limit counts are not causal diagnoses.
References: NIST: x-bar and R charts; NIST: proportions control charts; NIST: control-chart rules and interpretation.