IEOR 130
Methods of Manufacturing Improvement
Spring, 2009
Prof. Leachman
Second homework assignment  due Thursday Feb. 19.
1. A control chart is being set up to track the resistivity after the ion implantation process step.
Five sample measurements are made from one wafer per lot. The average of the measurements
and the range of the measurements are computed. One hundred observations from 20 wafers
have been collected. The average mean is 97.5, and the average range of the wafer measurements
is 5.21.
(a) Assuming the process was stable during processing of the 20 wafers, determine threesigma
control limits for R and Xbar charts.
(b) Suppose the mean of the resistivity shifts to 100.0. What is the probability that the Xbar
chart will make a Type 2 error in the next lot?
(c) What is the probability the Xbar chart will make Type 2 errors in the next five lots? (A
Type2 error means the process is out of control but the control chart does not detect this.)
2. A process is monitored using an Xbar chart with UCL = 13.8 and LCL = 8.2. The process
standard deviation is estimated to be 6.6. If the Xbar chart is based on threesigma limits,
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 Spring '10
 Leachman
 Mean, Control Chart, Process capability, UCL

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