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Unformatted text preview: 1 IEOR130 Midterm Examination Spring, 2009 Prof. Leachman Open notes. Work all problems. Each problem is worth 20 points. 1. At a particular manufacturing step, the important parameter for process control is the deposition thickness. This is measured at five points on a single wafer from each manufacturing lot passing through the step. The mean of this parameter is 380 and the standard deviation is 54. (a) Assuming the estimates of the process mean and standard deviation are valid (i.e., the process was in statistical control during the time data was collected to compute them), specify upper and lower control limits for X-bar and R charts. In X-bar chart: UCL = n 3 + = 380 + 3(54)/2.236 = 452.45, LCL = n 3 = 380 3(54)/2.236 = 307.55 In R-chart: R-bar = d 2 ( ) = 2.326(54) = 125.6 LCL = d 3 * R-bar = 0, UCL = d 4 * R-bar = 2.11(125.6) = 265.02 (b) Suppose the process mean suddenly shifts by 27. What is the probability that there will be Type II errors occurring for both of the next two manufacturing lots? Prob of Type II error in first lot given the mean shifts by is + = = ) ( X E n k X P + = = ) ( X E n k X...
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This note was uploaded on 03/16/2010 for the course ORMS 130 taught by Professor Leachman during the Spring '10 term at Berkeley.
- Spring '10