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HP1_S04_ChE_252 - 3 D evelop a CUSUM chart for the...

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Department of Chemical Engineering University of California, Santa Barbara Ch.E. 252 Due: April 7, 2004 Home Problem 1 1. An analyzer measures the pH of a process stream every 15 minutes. During normal process operation, the mean and standard deviation for the pH measurement are x = 5.75 and s = 0.05, respectively. When the process is operating normally, what is the probability that a pH measurement will exceed 5.9? 2. In a computer control system, the high and low warning limits for a critical temperature measurement are set at the “2-sigma limits”, ˆ 2 T T σ ± , where T is the the nominal temperature and ˆ T σ is the estimated standard deviation. If the process operation is normal and the temperature is measured every minute, how many “false alarms” (that is, measurements that exceed the warning limits) would you expect to occur during an eight
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Unformatted text preview: 3. D evelop a CUSUM chart for the thickness data of Example 21.2 of the SEM textbook using Κ =0 and H =4 ˆ x . If the grand mean of the available data is used as the target T , how many chart violations occur? Repeat for an EWMA chart and a value of λ =0.25. 3. In a manufacturing process, the impurity level of the product is measured on a daily basis. When the process is operating normally, the impurity level is approximately normally distributed with a mean value of 0.800 % and a standard deviation of 0.021 %. The laboratory measurements for a period of eight consecutive days are shown below. From an SPC perspective, is there strong evidence to believe that the mean value of the impurity has shifted? Justify your answer. Day Impurity (%) 1 0.812 2 0.791 3 0.841 4 0.814 5 0.799 6 0.833 7 0.815 8 0.807 2...
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