The table below displays operational metrics for eight semiconductor fabrication facilities (fabs).
| Fab ID | Region | Wafer Yield Rate (%) | Defect Density (defects/cm²) | Monthly Capacity (k Wafers) | Operating Cost per Wafer ($) |
|---|---|---|---|---|---|
| Fab Alpha | Asia-Pacific | 94.2 | 0.08 | 120 | 450 |
| Fab Beta | North America | 91.5 | 0.12 | 85 | 520 |
| Fab Gamma | Europe | 95.8 | 0.05 | 60 | 490 |
| Fab Delta | Asia-Pacific | 91.5 | 0.10 | 140 | 410 |
| Fab Epsilon | Europe | 93.0 | 0.09 | 95 | 475 |
| Fab Zeta | North America | 94.2 | 0.07 | 110 | 510 |
| Fab Eta | Asia-Pacific | 89.8 | 0.15 | 150 | 390 |
| Fab Theta | Europe | 95.8 | 0.06 | 70 | 465 |
Evaluate the following statement as True or False:
If the table is sorted primarily by Wafer Yield Rate (%) in descending order, and secondarily by Defect Density (defects/cm²) in ascending order to break ties, the facility ranked 4th has a lower Monthly Capacity than the facility ranked 3rd.
Answer: Answer
Answer
The statement is False.
Sorting primarily by Wafer Yield Rate (%) descending places facilities with yield in positions 1–2 and facilities with yield in positions 3–4. To break the tie for positions 3 and 4, we sort Defect Density in ascending order. Fab Zeta ( defects/cm²) precedes Fab Alpha ( defects/cm²). Thus, Fab Zeta is ranked 3rd with a capacity of k wafers, and Fab Alpha is ranked 4th with a capacity of k wafers. Since is greater than , the statement claiming the 4th-ranked facility has a lower capacity is False.
Step-by-Step Solution
Key Concept
Multi-Column Sorting and Secondary Tie-Breaking Logic