The table below displays quality assurance metrics for six semiconductor lithography tools operating in a fabrication facility: | Tool ID | Process Node (nm) | Defect Density (defects/cm²) | Operational Uptime (%) | Calibration Status | | :--- | :--- | :--- | :--- | :--- | | TL-01 | 3 | 0.24 | 95.8%

The table below displays quality assurance metrics for six semiconductor lithography tools… — GMAT

The table below displays quality assurance metrics for six semiconductor lithography tools operating in a fabrication facility:

Tool ID	Process Node (nm)	Defect Density (defects/cm²)	Operational Uptime (%)	Calibration Status
TL-01	3	0.24	95.8%	Certified
TL-02	5	0.18	96.4%	Pending
TL-03	3	0.32	92.1%	Certified
TL-04	7	0.15	97.2%	Certified
TL-05	5	0.28	94.6%	Pending
TL-06	10	0.09	98.1%	Recalibrated

Based on the data provided, is the following statement True or False?

"For all lithography tools operating at a process node of $5\text{ nm}$ or smaller that also have a defect density strictly less than $0.30\text{ defects/cm}^2$ , the median operational uptime is greater than $95.0\%$ ."

Answer: Answer

Answer

True. The median operational uptime for the filtered subset of tools (TL-01, TL-02, and TL-05) is 95.8%, which is greater than 95.0%.

The statement is correct (True) because applying the two compound criteria (Process Node

\le 5\text{ nm}

AND Defect Density

< 0.30\text{ defects/cm}^2

) selects tools TL-01, TL-02, and TL-05. The operational uptimes of these three tools are

95.8\%

96.4\%

, and

94.6\%

. Arranged in numerical order, the median value is

95.8\%

, which exceeds

95.0\%

Step-by-Step Solution

Identify the compound logical criteria specified in the statement.

Filter 1: Process Node

\le 5\text{ nm}

. Filter 2: Defect Density

< 0.30\text{ defects/cm}^2

. Target metric: Median Operational Uptime.

Both conditions must be met simultaneously (conjunction AND) before analyzing the operational uptime column.

Filter the rows based on the Process Node criterion.

Candidate tools meeting Process Node

\le 5\text{ nm}

: TL-01 (3 nm), TL-02 (5 nm), TL-03 (3 nm), and TL-05 (5 nm). Tools TL-04 (7 nm) and TL-06 (10 nm) are eliminated.

Only tools operating at 3 nm or 5 nm satisfy the condition of being 5 nm or smaller.

Apply the second criterion (Defect Density

< 0.30\text{ defects/cm}^2

) to the candidate tools.

Qualifying subset: TL-01 (

0.24

), TL-02 (

0.18

), and TL-05 (

0.28

). TL-03 is excluded because

0.32 \ge 0.30

Strict inequality requires excluding values equal to or greater than 0.30.

Extract operational uptime values for the qualified subset and compute the median.

Values: TL-05 (

94.6\%

), TL-01 (

95.8\%

), TL-02 (

96.4\%

). Ordered values:

94.6\%, 95.8\%, 96.4\%

. Median =

95.8\%

For

N = 3

, the median is the 2nd value in sorted order.

Compare the calculated median against the target threshold.

95.8\% > 95.0\%

, verifying that the statement is True.

The calculated median of

95.8\%

strictly exceeds the benchmark value of

95.0\%

Key Concept

Compound Conditional Filtering and Descriptive Statistics on Subsets

Estimated Time:2m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic