hw5_new_new

# hw5_new_new - IEOR 130 Methods of Manufacturing Improvement...

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1 IEOR 130 - Methods of Manufacturing Improvement Spring, 2009 Prof. Leachman Homework Assignment 5 - Due Tuesday, March 10 1. A product with 400 die per wafer has an average die yield of 60% and a die area of 0.5 cm 2 . The best die yield observed near the center of the wafer map is 82%. (a) In-line inspections have been implemented at the Metal 1, Metal 2 and Poly layers, and the observed defects have been correlated with the wafer maps of die yield to estimate the fraction of observed defects that are fatal. The following results were obtained: Layer Defect density Fraction fatal (defects per cm 2 ) Metal 1 0.32 0.38 Metal 2 0.45 0.50 Poly 0.25 0.40 What amount of fatal defect density is occurring that is not observed by the above three inspections? How much yield loss does that account for? (b) The following systematic yield loss mechanisms have been identified: Mechanism Fraction of wafers Fraction die loss Total yield loss Wafer edge loss 1.00 0.05 0.05 Missing photo patterns (excluding the edge loss) 1.00 0.02 0.02 Particle excursions 0.05 0.40 0.02 How much systematic yield loss is the result of mechanisms yet to be discovered? 2. When the "O" ring in a low-pressure CVD machine fails, the machine down time averages 4.5 hours. If the "O" ring is replaced as part of weekly preventive maintenance procedures, the incremental downtime is only 0.5 hours. Data on the lifetimes of "O" rings in this machine type are as follows. (The notation p t denotes the fraction of the "O" ring population that fails during the t th week of operation.)

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2 t p t 1 .15 2 .20 3 .25 4 .25 5 .15 What policy for "O" ring replacement will maximize machine availability? 3. It is desired to schedule preventive maintenance (PM) procedures for a particular type of wafer processing machine. The expected cost to repair the machine after it goes down while in service is \$200. The expected cost to perform a PM on a machine in working order is \$50. Data on machine failures is as follows: Number of Probability Days of Service of Failure 1 0.08 2 0.12 3 0.16 4 0.24 5 0.18 6 0.12 7 0.10 (a) Determine the frequency at which the PM should be scheduled to minimize the expected costs. (b)
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hw5_new_new - IEOR 130 Methods of Manufacturing Improvement...

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