Question 1: Problem Statement: In a semiconductor manufacturing facility, the thickness of silicon wafers is critical for achieving precise circuitry. Variations in wafer thickness can lead to defects and yield loss. Your task is to perform Statistical Process Control (SPC) analysis on a dataset of silicon wafer thickness measurements and draw conclusions based on your analysis. Data: Below is a dataset of silicon wafer thickness measurements (in micrometers, μm) collected over 25 production runs: 725, 730, 735, 720, 732, 727, 733, 728, 722, 729, 734, 731, 726, 724, 730, 728, 723, 727, 732, 736, 725, 730, 735, 726, 731 Assignment Tasks: 1. Calculate Control Limits: - Compute the mean (X-bar) and standard deviation (σ) of the silicon wafer thickness measurements. - Determine the Upper Control Limit (UCL) and Lower Control Limit (LCL) using the mean and standard deviation. 2. Construct X-bar Chart: - Plot the silicon wafer thickness measurements on a time-ordered X-bar chart. -Add the UCL and LCL lines to the chart. 3. Analyze the Chart: - Interpret the X-bar chart by examining the plotted data points relative to the control limits. - Identify any points that fall outside the control limits or exhibit unusual patterns. 4. Draw Conclusions: - Based on your analysis, make a decision regarding the stability of the silicon wafer thickness process. - Provide recommendations for further action if necessary.
Question 1: Problem Statement: In a semiconductor manufacturing facility, the thickness of silicon wafers is critical for achieving precise circuitry. Variations in wafer thickness can lead to defects and yield loss. Your task is to perform Statistical Process Control (SPC) analysis on a dataset of silicon wafer thickness measurements and draw conclusions based on your analysis. Data: Below is a dataset of silicon wafer thickness measurements (in micrometers, μm) collected over 25 production runs: 725, 730, 735, 720, 732, 727, 733, 728, 722, 729, 734, 731, 726, 724, 730, 728, 723, 727, 732, 736, 725, 730, 735, 726, 731 Assignment Tasks: 1. Calculate Control Limits: - Compute the mean (X-bar) and standard deviation (σ) of the silicon wafer thickness measurements. - Determine the Upper Control Limit (UCL) and Lower Control Limit (LCL) using the mean and standard deviation. 2. Construct X-bar Chart: - Plot the silicon wafer thickness measurements on a time-ordered X-bar chart. -Add the UCL and LCL lines to the chart. 3. Analyze the Chart: - Interpret the X-bar chart by examining the plotted data points relative to the control limits. - Identify any points that fall outside the control limits or exhibit unusual patterns. 4. Draw Conclusions: - Based on your analysis, make a decision regarding the stability of the silicon wafer thickness process. - Provide recommendations for further action if necessary.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 1:
Problem Statement:
In a semiconductor manufacturing facility, the thickness of silicon wafers is critical for achieving
precise circuitry. Variations in wafer thickness can lead to defects and yield loss. Your task is to
perform Statistical Process Control (SPC) analysis on a dataset of silicon wafer thickness
measurements and draw conclusions based on your analysis.
Data:
Below is a dataset of silicon wafer thickness measurements (in micrometers, μm) collected over
25 production runs:
725, 730, 735, 720, 732, 727, 733, 728, 722, 729, 734, 731, 726, 724, 730, 728, 723, 727, 732,
736,
725, 730, 735, 726, 731
Assignment Tasks:
1. Calculate Control Limits:
- Compute the mean (X-bar) and standard deviation (σ) of the silicon wafer thickness
measurements.
- Determine the Upper Control Limit (UCL) and Lower Control Limit (LCL) using the mean
and standard deviation.
2. Construct X-bar Chart:
- Plot the silicon wafer thickness measurements on a time-ordered X-bar chart.
- Add the UCL and LCL lines to the chart.
3. Analyze the Chart:
- Interpret the X-bar chart by examining the plotted data points relative to the control limits.
- Identify any points that fall outside the control limits or exhibit unusual patterns.
4. Draw Conclusions:
-
Based on your analysis, make a decision regarding the stability of the silicon wafer thickness
process.
- Provide recommendations for further action if necessary.
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VIEWStep 2: Compute the mean and standard deviation(σ) of the silicon wafer thickness measurements.
VIEWStep 3: Determine upper control limit(UCL) and lower control limit(LCL) using mean and standard deviation.
VIEWStep 4: Construct X-bar chart for the obtained UCL and LCL lines.
VIEWStep 5: Interpret the X-bar chart by examining the plotted data points relative to the control limits.
VIEWStep 6: Make a decision regarding stability of the silicon wafer thickness process based on the analysis.
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