Bimodal Capability in an Eight-Cavity Mold
An injection molder produces a 12 mm retention clip from an 8-cavity tool; specification is 12.00 ± 0.15 mm. The Green Belt collects 200 consecutive parts over one shift, records the cavity number for each, and plots an Xbar-R chart using subgroups of 5 parts taken in sequence. The chart shows no out-of-control points and no trends. Overall capability is Ppk = 0.80 against a 1.33 target. The histogram of all 200 parts is visibly bimodal. Splitting the data by cavity shows that cavities 1–6 are centered at 11.98 mm with a within-cavity standard deviation of 0.012 mm, while cavities 7 and 8 are centered at 12.11 mm with a standard deviation of 0.013 mm. Cavities 7 and 8 were reworked last month after a water-line repair. The tool shop proposes grinding all eight cavities to a single nominal, at a cost of two days of downtime. The production manager wants instead to tighten the incoming resin specification, saying 'resin lot variation must be causing that bimodal shape.'
1. Calculate within-cavity capability and explain why the overall Ppk of 0.80 misrepresents the process.
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Limits are LSL 11.85 and USL 12.15.
- Cavities 1–6: Cpk = (12.15 − 11.98) / (3 × 0.012) = 0.17 / 0.036 ≈ 4.7 (lower side not limiting).
- Cavities 7–8: Cpk = (12.15 − 12.11) / (3 × 0.013) = 0.04 / 0.039 ≈ 1.03.
The overall Ppk of 0.80 is produced almost entirely by the between-cavity shift, not by within-cavity spread. The pooled standard deviation of the mixed stream is about 0.058 mm, roughly four times the within-cavity value, because the mean difference of 0.13 mm between the two cavity groups is large relative to their spread. This is a mixture distribution: two capable-ish populations superimposed give a bimodal histogram and a misleadingly poor single capability index.
It also explains the quiet control chart. The limits come from within-subgroup variation, so a shift that occurs between parts inside a subgroup never appears as a point beyond the limits - the subgroup average just wobbles inside limits that are too wide for the real problem. The chart is answering 'is the process stable within a few minutes?' while the dominant variation source is cavity identity.
2. Evaluate the two proposals (grind all eight cavities vs tighten the resin specification) and recommend an action with a justification.
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Neither proposal survives contact with the evidence.
- Resin specification: resin lot variation would affect all eight cavities roughly equally. It cannot create a clean split between cavities 1–6 and 7–8, and the split appears immediately after the water-line repair on 7 and 8. The timing and the pattern both point to the tool, not the material. Tightening resin spec adds cost and incoming-inspection burden with no mechanism to fix the observed shift.
- Grinding all eight cavities: over-scoped. Cavities 1–6 already have Cpk ≈ 4.7 and a mean of 11.98 - essentially on nominal. Their surface does not need rework. Grinding them adds two days of downtime and risk for zero benefit.
Recommendation: re-center cavities 7 and 8 only - restore the cooling/water-line condition from the repair, adjust the cavity trim or gate, then verify. If 7 and 8 land on 11.98–12.00, expected Cpk is roughly (12.15 − 11.99)/(3 × 0.013) ≈ 4.1, and the mixed-stream Ppk rises above the 1.33 target with no tool downtime across all cavities. Run a short capability study on 7/8 alone, then re-run the full stratified study across all cavities before signing off. Escalate the resin claim only if a stratified study still shows lot-to-lot shifts within a single cavity.
3. What must change in the ongoing monitoring approach so the team can see this kind of problem in future?
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The current chart is structurally blind to the largest variation source. Three changes:
- Stratify by cavity. Plot cavity means on a multi-vari or slot chart, or run separate I-MR charts per cavity group. Alternatively use a subgroup that deliberately includes all eight cavities so the chart's between-subgroup component reflects tool variation - but then the limits must be understood as 'mixed-cavity' limits, not process capability.
- Track the right metric. For a multi-cavity tool, the key control metric is the cavity mean spread (max minus min cavity average) plus the within-cavity sigma, not a single pooled Cpk. Put a limit on cavity-to-cavity offset.
- Tie the reaction plan to the tool. Any step change in one or two cavities triggers a tool check, not a chart annotation. Include cavity identification on every sample so the data can be split.
Add the post-repair verification to the control plan: after any tool maintenance, a capability check on the affected cavities is required before production release. Without that step, the same shift will reappear after the next repair and the team will relearn the same lesson.