Eight Points Above the Centerline: Recenter or Investigate?
A filling line targets 500 mL with specs of 495-505 mL. Subgroups of n = 5 are taken every 30 minutes. The X-bar chart limits, computed from three months of stable operation, are UCL = 503.0, LCL = 498.6, centerline = 500.0. The R chart is in control at R-bar = 2.3 mL (d2 = 2.326 for n = 5). The last eight subgroup averages, covering four hours, read: 501.7, 501.5, 501.9, 501.6, 501.8, 501.4, 501.7, 501.6. No point is outside a limit. Seeing the points drifting toward the upper limit, the operator wants to dial the filler down by 2 mL. The supervisor wants to let it run: 'Nothing is out of spec.' The customer requires Cpk of at least 1.33.
1. Calculate the process standard deviation and Cpk. Does the process meet the customer requirement?
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From the in-control R chart:
- sigma = R-bar / d2 = 2.3 / 2.326 = 0.989 mL
- Recent mean (8 subgroups) = 501.65 mL
Cpk is the smaller of the two half-distances to the specs, divided by 3 sigma:
- Upper side: (505 - 501.65) / (3 x 0.989) = 3.35 / 2.97 = 1.13
- Lower side: (501.65 - 495) / 2.97 = 2.24 (not limiting)
So Cpk is about 1.13 against a 1.33 requirement - the process does not meet it, even though not one point is outside a control limit. That is the key lesson: control limits describe the voice of the process, specification limits describe the voice of the customer, and a chart that is in control can still be incapable.
Roughly, an upper-tail z of 3.35/0.989 = 3.39 corresponds to about 350 ppm over 505 mL, which is a real reject stream the supervisor is not seeing.
2. Interpret the eight consecutive points. What is the chart telling you, and what is the first thing to check before touching the filler?
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Eight consecutive points on one side of the centerline is a non-random pattern (a run), which is a special-cause signal even though every point sits inside the limits. The mean has shifted upward by about 1.6 mL and stayed there for four hours - that is a level change, not the ordinary wiggle of common-cause variation.
Before adjusting anything:
- Confirm the R chart is in control (it is, at R-bar = 2.3). If the R chart had been out of control, the X-bar limits would be meaningless and you would fix variation first, not the mean.
- Verify the measurement: check the scale or check-weight, confirm the tare/zero, and confirm the sample is taken the same way as during the baseline period.
- Look for an assignable cause at the time the shift began: nozzle change or wear, product viscosity or temperature change (a warmer product fills lighter), pump or valve drift, a new lot of containers, or a change in fill time/speed.
Adjusting the filler in response to a signal without identifying the cause is guessing, and a guess of 2 mL is not even the measured shift of 1.6 mL.
3. The cause is found to be a product temperature change. What action do you take, and how does it affect capability?
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Because a specific assignable cause has been identified, correcting the level is now justified - it is no longer a blind tweak.
- Correct the fill level so the mean returns to about 500 mL, and confirm with a check standard and a fresh subgroup before releasing the line.
- Recalculate capability after the correction. With the mean centered at 500:
- Cp = (505 - 495) / (6 x 0.989) = 10 / 5.93 = 1.68
- Cpk = 1.68, comfortably above 1.33.
- Note what changed and what did not. Recentering fixed off-centering; it did not change the variation. Cp was already 1.68 - the process spread is fine. The 1.13 Cpk was entirely a centering problem of about 1.65 mL.
Going forward: put product temperature (or fill weight by net content) on a check sheet or add it to the startup checklist, since the shift was traceable and will recur. Do not loosen specs and do not accept a 'nothing is out of spec' argument - at Cpk 1.13 the process was shipping rejects.