Assignment 1 - CA - Bhimashankar

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Troy University, Troy *

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5545

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Industrial Engineering

Date

Apr 3, 2024

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docx

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3

Uploaded by MajorMusicBadger33

Assignment 1 Name – Bhimashankar Malbhage Student ID – 1684859 1.1 a) What is the yield for the Phoenix chip? Ans -> The formula for Yield= Water yield x 1/ (1 + (Defects per unit area x Die area)) ^N. Assuming wafer yield is 100%. Yield = 1/(1 + (0.04 x 2))14== 1/(1 + (0.08)14==1/1.0814== 1/2.94 == 0.34. 1.1 b) Why does Phoenix have a higher defect rate than BlueDragon? Ans -> Manufacturing size of Phoenix is smaller than manufacturing size of BlueDragon indicating that BlueDragon is equipped with an older facility. With the aging of plants, processes tend to become more refined, thereby reducing the failure rate as for BlueDragon. And Phoenix being new architecure it has a higher defect rate as it is not yet refined. 1.7 a) According to the trend in device scaling historically observed by Moore’s Law, the number of transistors on a chip in 2025 should be how many times the number in 2015? Ans -> Moore's law states that the number of transistors in a dense chip approximately doubles each 2 years. The duration between 2015 and 2025 equals to 10 years. During this period, the transistor count is expected to double five times (10/2), resulting in the number of transistors in 2025 being 32 times greater than the number in 2015 (2^5). 1.7 b) The increase in performance once mirrored this trend. Had performance continued to climb at the same rate as in the 1990s, approximately what performance would chips have over the VAX-11/780 in 2025? Ans -> As per figure, performance in the year 1990 is 52% per year. The duration from 1990 to 2025 is 35 years. Now If performance doubled every year as it mirrored this trend in the 1990s. Performance chips would have over the VAX-11/780 would be 2^35 times.
1.7 c) At the current rate of increase of the mid-2000s, what is a more updated projection of performance in 2025? Ans -> As per the figure, there is a notable decrease in the rate of performance improvement during the mid-2000s in comparison to the 1990s. It would be between 3400 and 3500. 1.10 a) We have a single processor with a failure in time (FIT) of 100. What is the mean time to failure (MTTF) for this system? Ans-> Mean Time To Failure (MTTF) is a maintenance metric that measures how long a product can perform in the field before it fails. And MTFF = 10^9/FIT = 10^9/100 = 10^7. 1.10 b) If it takes one day to get the system running again, what is the availability of the system? Ans-> MTTR = One day = 24 hrs. Availability of the system = MTTF/(MTTF + MTTR) Availability of the system = (10^7)/((10^7) + 24) = 0.9999 = 99%. 1.10 c) Imagine that the government, to cut costs, is going to build a supercomputer out of inexpensive computers rather than expensive, reliable computers. What is the MTTF for a system with 1000 processors? Assume that if one fails, they all fail. Ans-> FIT = No. of processors × FIT per processor = 1000 × 100 = 10^5. And MTTF = 1 / (10^5/10^9) = 10^9/10^5 = 10^4. 1.11 a) If a company has 10,000 computers, each with an MTTF of 35 days, and it experiences catastrophic failure only if 1/3 of the computers fail, what is the MTTF for the system? Ans-> MTFF = no. of failures needed / FIT. The number of failures needed = 1/3 * 10000 = 3333.33. FIT = 1/35 * 10000 = 285.71. So MTFF = 3333.33 / 285.71 = 11.66 days.
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