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 3sigma
control charts. The Xbar 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 Xbar 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 outofspec?
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 Xbar 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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 Spring '07
 Leachman

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