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# hw3 - IEOR 130 Spring 2007 Prof Leachman Homework#3 due...

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1 IEOR 130 Spring, 2007, Prof. Leachman Homework #3 due Thursday Feb. 15 1. Control charts are in use to track the critical dimensions after etching. Five sample measurements are made from one wafer per lot. The average of the measurements and the range of the measurements are computed and are tracked in standard 3-sigma control charts. The X-bar chart is observed to display upper spec limit = 105.0, upper control limit = 95.4, lower control limit = 79.0, and lower spec limit = 65.0. (Any dice above the upper specification limit or below the lower specification limit are defective and will be scrapped.) (a) What is the process capability index, and what is the process performance index? (b) What are the upper and lower control limits of the range chart? (c) Suppose the mean of the critical dimension shifts to 92.0. What is the probability that the X-bar chart will make a Type 2 error in each of the next five lots? (A “Type 2” error means the process is out of control but the control chart does not detect it.) (d) During the time that the mean shift is not detected, what fraction of die output will be defective because the etch dimension is out-of-spec? 2. The upper specification limit for a critical process parameter is 320.0. At present, the scrap rate due to exceeding the USL is 1.2 percent. There is no lower specification limit. Assume the process parameter has a normal distribution. (a) What is the value of the process performance index? (b) In an X-bar chart for this parameter with sample size of four, the upper control limit is 240.0. What are the mean and standard deviation of the process parameter?

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