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University of Toronto Department of Mechanical and Industrial Engineering MIE304/364: Intro to Quality Control and Improvement (Winter 2024) Page 1
of 2
Assignment 2 Due: Friday, February 02, 2024, at 11:59 pm Please submit your answer as one
Jupyter file on Quercus
Please post your questions on Piazza
Please answer these following questions using Python. You may find Scipy Stats documentation helpful
1.
In a manufacturing facility, a type of microchip has an exponential time-to-failure distribution with a mean life of 36,000 hours.
1.1.
What is the probability of a microchip lasting at least 30,000 hours?
1.2.
If a microchip is already in operation at 30,000 hours, what is the probability that it will last another 10,000 hours?
1.3.
Two of these microchips are put in parallel, meaning the system will be operational if at least one of the microchips is still functioning. What is the probability of the system being operational for 45,000 hours? Assume that the microchips operate independently.
2.
In an electronics manufacturing company, the specifications for the thickness of microchips are 100.0±1.5 µm. From process data, the distribution of the microchip thickness is estimated to be normal, with a mean of 99 µm and a standard deviation of 1 µm. The rework cost per unit is $1.25, and the unit cost of scrap is $1.7. For the daily production of 12,000 microchips:
2.1.
What proportion of the microchips is conforming? What is the expected total daily cost of rework and scrap?
2.2.
The manufacturer changes the mean setting of the production machine to 100 µm. If the standard deviation is the same as before, what is the expected total daily cost of rework and scrap?
2.3.
The manufacturer is trying to improve the process and reduce its standard deviation to 0.8 mm. If the process mean is maintained at 100 µm, what is the percent decrease in the expected total daily cost of rework and scrap compared to part (2.2.)
?
3.
The following data consider random observations of the times (in weeks) required in the fabrication of 12 advanced semiconductor devices: 11.4, 14.2, 12.5, 15, 11.9, 13.6, 14.4, 14.9, 12.7, 13.5, 12.9, 13.8.
University of Toronto Department of Mechanical and Industrial Engineering MIE304/364: Intro to Quality Control and Improvement (Winter 2024) Page 2
of 2
3.1.
Find a 97% confidence interval for the mean processing time for the advanced semiconductor devices. What assumptions do you have to make to solve this problem?
3.2.
Find a 95% confidence interval for the variance of the processing times.
3.3.
Test the hypothesis that the process variability, as measured by the variance, exceeds 0.80. Use α = 0.05.
4.
Based on the dataset “A2 data”, answer the following questions: 4.1.
Does the data support a population mean of 12? What is the p-value?
4.2.
If mu = 12.00, what is the probability that we fail to reject mu = 12.012, given that the values are the average volume of a sample of 100 items analyzed?
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