Eight Points Above the Line, and a Project Due to Close
After a DMAIC project on a 500 mL fill line, the team sets up an X̄–R chart with n = 5 and 25 subgroups. Specification is 500 ± 5 mL. The chart shows no points beyond the control limits, but the last eight subgroups all fall above the centerline (X̄̄ = 500.4 mL, R̄ = 3.2 mL, so σ̂ ≈ 1.38 mL). Calculated capability: Cp = 1.21, Cpk = 1.11. The charter's exit criterion is Cpk ≥ 1.33 with a documented, owned control plan. The line supervisor's reaction plan reads: "If a point is outside the specification limits, adjust the filler." A new resin lot arrived two days ago and the night-shift crew was reassigned to this line last week. The team is scheduled to close the project on Friday.
1. Is the process in control, and what is the correct immediate response?
Read the worked answer
No - the process is out of control on a run rule, even though nothing is beyond the limits.
- Eight consecutive points on one side of the centerline is a recognized signal of a sustained mean shift (Nelson rule 2 / the classic run rules). Run rules exist precisely because they detect small shifts - on the order of 1 to 1.5 sigma - that a single point beyond 3 sigma will miss. Its sensitivity is its value and its cost: it will occasionally fire on noise, which is why the first move is investigation, not adjustment.
The supervisor's reaction plan is inverted. It responds to specification limits, which describe the customer's requirement, instead of control limits, which describe the process's own voice. Two consequences:
- A point can be out of control while well inside spec (exactly our case) - the plan says do nothing, so a real shift runs unchecked.
- A point inside control limits but outside spec is a capability problem, not an operator adjustment problem; and adjusting the filler on every spec excursion is tampering - reacting to common-cause variation, which increases variation rather than reducing it.
Correct immediate action: flag the shift, check the data entry and sample handling, then investigate assignable causes by stratification - resin lot (arrived two days ago), night-shift crew (reassigned last week), nozzle wear, temperature, scale calibration. Verify with a short targeted data collection. Do not touch the filler setting until a cause is identified.
2. Should the project close on Friday? Address the capability numbers and the exit criterion.
Read the worked answer
No. Two independent charter conditions fail, and one of them invalidates the other's number.
- Stability is a prerequisite for capability. Cp and Cpk assume one stable distribution. Our 25 subgroups contain a mean shift, so the pooled σ̂ of 1.38 mL blends at least two process states. The reported Cpk = 1.11 is neither the old process's capability nor the new one's - it describes a process that no longer exists in that form. Capability cannot be certified from an out-of-control chart.
- Even taken at face value, 1.11 < 1.33. The charter criterion is explicit, and the gap is not rounding. Cp = 1.21 vs. Cpk = 1.11 also shows a centering loss of about 0.4 mL above target - small, but it will grow if the upward shift continues, and it is pure product giveaway on a 500 mL fill.
- The shift is in the wrong direction for risk. With the mean drifting up and σ̂ ≈ 1.38, the fraction above the 505 mL upper limit rises quickly. A rising mean is both a quality risk and a cost risk.
What closing now would mean: the team would hand over a chart with a live out-of-control signal and a capability number that fails the charter, plus a reaction plan that tells operators to adjust on specification breaches. That is how gains decay - the project would show savings at closure and lose them within a quarter.
Path forward: identify and eliminate the assignable cause, restore control, collect a fresh stable baseline of sufficient length, recompute capability on stable data, and only then close - with an honest note on what was and was not achieved if 1.33 remains out of reach.
3. What must the control plan and reaction plan contain before handover?
Read the worked answer
A control plan is an operating document, not a chart taped to a wall.
- What is monitored, by whom, how often: fill volume, n = 5 every 30 minutes, operator on shift; plus resin lot verification at receipt and a nozzle inspection on a defined frequency - the two suspected assignable causes from the shift.
- Chart and limits: X̄–R, n = 5, limits frozen from the validated stable baseline and not recalculated routinely. Recalculation is allowed only after a documented, permanent process change - recalculating limits to include the shifted eight points would simply redefine the shift as normal, which is how control is lost.
- A reaction plan written in control-limit language, not specification language: e.g., one point beyond 3 sigma, 8 consecutive on one side, 2 of 3 beyond 2 sigma, or a visible trend → stop, contain product since the last known-good check, notify the line lead, investigate the listed candidate causes in order, document, restart. Name the owner and the escalation path for each step.
- Pre-authorized corrective actions for known causes, so the operator is not improvising at 03:00.
- Mistake-proofing where it pays: an automatic check-weigher with reject gate, or an interlock so out-of-tolerance fills cannot be palletized. Error-proofing beats vigilance, especially with a newly reassigned crew.
- Training and qualification for the night shift, and a named process owner accountable for chart review and monthly audits.
- Verification of the control system itself: an audit schedule and a metric (e.g., % of out-of-control signals with a documented response) so the plan can be shown to be working after the Belt leaves - which is the only evidence that the improvement will persist.