Statistical
Individuals control chart: moving-range three-sigma limits
Estimate individual-observation control limits using average adjacent moving range, then compare a new reading with the fixed baseline.
Voice of the Process (UCL / LCL) vs Voice of the Customer (USL / LSL)
For an individuals chart, estimate sigma from the average absolute difference between successive baseline observations, divided by 1.128. Limits are baseline mean plus or minus three times that estimate. Preserve the time order and keep the new reading separate from the baseline.
Control limits describe process behavior; specification limits describe requirements. They must be labeled separately. An outside point is a signal to investigate, not proof of a particular cause. A point inside the limits does not establish control; runs, trends and the moving-range chart also matter. Five baseline observations here are only a small teaching example, not a reliable production calibration.
| SPC Control Limit Metric | Formula on Baseline [48,50,52,49,51] | Result |
|---|---|---|
| Center | AVERAGE(B2:B6) | 50 |
| Average moving range | AVERAGE(C3:C6) | 2.25 |
| Upper limit | =ROUND(AVERAGE(B2:B6)+3*AVERAGE(C3:C6)/1.128,4) | 55.9840 |
| Lower limit | =ROUND(AVERAGE(B2:B6)-3*AVERAGE(C3:C6)/1.128,4) | 44.0160 |
3-Sigma Upper Control Limit (UCL), Lower Control Limit (LCL), and Excursion Check
Adjacent moving ranges are 2, 2, 3 and 2; their mean is 2.25. Divide by 1.128 to estimate sigma, then use the mean of 50 as the center.
=ROUND(AVERAGE(B2:B6)+3*AVERAGE(C3:C6)/1.128,4)Compare a new observation with the baseline limits
This implements only the outside-limit rule. Zero moving-range variation is reported explicitly rather than treated as a calibrated zero-width process. Do not apply this continuous-measurement chart to defect counts without selecting an appropriate chart model.
=IF(OR(COUNT(B2:B6)<>5,NOT(ISNUMBER(D2))),"Invalid readings",LET(center,AVERAGE(B2:B6),sigma,AVERAGE(C3:C6)/1.128,IF(sigma=0,"Insufficient baseline variation",IF(OR(D2>center+3*sigma,D2<center-3*sigma),"Outside limits","Within limits"))))Try the example
Use the original values or change them to test your understanding.