Nordlys Components: Rework, Upgrade or Rebalance
Nordlys Components runs three production lines. Line A makes 45,000 units a month at a 2.4% defect rate; Line B makes 30,000 at 3.5%; Line C makes 25,000 at 1.2%. Every defective unit that reaches a customer costs €18 in rework and credit. Line B's defect rate can be cut to 1.6% by a vision-inspection system leased at €9,000 a month. Separately, up to 8,000 units a month of Line B's volume could be transferred to Line C, whose process is more reliable; the transfer costs nothing, and Line C's defect rate would be unaffected by the extra volume. The plant manager must make a recommendation for next month, when the volumes above are fixed and Line C has spare capacity.
1. Compute the current monthly defect rate across the plant and the monthly cost of defects. Show the line-level figures.
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Defects by line:
- A: 45,000 × 0.024 = 1,080
- B: 30,000 × 0.035 = 1,050
- C: 25,000 × 0.012 = 300
Totals: 100,000 units, 2,430 defects → 2.43% overall.
Cost: 2,430 × €18 = €43,740 per month.
Note why the plant rate (2.43%) sits below Line B's 3.5%: it is a volume-weighted average, dominated by Line A, which is the largest line. Any intervention should be judged on defects removed, not on the defect rate of the line it touches - a point that matters in the next two questions.
2. Evaluate the vision-inspection upgrade on its own. Should the manager lease it?
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Defects on Line B after the upgrade: 30,000 × 0.016 = 480. Defects removed: 1,050 − 480 = 570 per month. Saving: 570 × €18 = €10,260 per month. Lease cost: €9,000 per month. Net benefit: €10,260 − €9,000 = +€1,260 per month (about €15,100 a year).
Recommendation: yes - it pays for itself, though with a thin margin of about 14% over cost. That thinness is the important finding: the decision is sensitive to volume. If Line B's volume fell below roughly 25,000 units (saving ≈ €7,500 against a fixed €9,000 lease), the upgrade would destroy value. The manager should therefore resist a multi-year lease at this month's volumes and prefer a cancellable or volume-linked contract.
3. The manager decides to move the 8,000 units to Line C first, because it is free. Re-evaluate the upgrade *after* that move, and state the combined recommendation.
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Step 1 - the transfer. The 8,000 units move from a 3.5% process to a 1.2% process: 8,000 × (0.035 − 0.012) = 184 defects avoided, worth 184 × €18 = €3,312 per month, at zero cost.
New Line B volume: 22,000 units; Line C: 33,000 units.
Step 2 - re-evaluate the upgrade at the new volume.
- Defects on B at 3.5%: 22,000 × 0.035 = 770
- At 1.6%: 22,000 × 0.016 = 352
- Avoided: 418 → 418 × €18 = €7,524 per month
- Lease cost: €9,000 → net −€1,476 per month
Combined recommendation: take the transfer, reject the lease. The two options are substitutes, not complements: each removes defects from the same line, so the second one only earns its fixed cost on the volume the first has left behind. Evaluating them independently - as a cost-per-defect comparison would - overstates the case for doing both. Total monthly benefit of the correct plan: €3,312.