HW7 - ) (b) Fill in the blank in the table based on your...

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Page 1 of 3 Problem 1: Textbook 9.4 (Hint for b: use MR chart to estimate sigma. Compare whether the estimated sigma is close to the assumed sigma). Problem 2: Textbook 9.6
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Page 2 of 3 Problem 3: The following data present individual observations on a certain process. The mean value of the molecular weight is 28, and process standard deviation is known to be 2. A CUSUM chart is built as shown in the following table. Obs, i x i C i + N + C i - N - 1 26.40 0 0 1.1 1 2 25.30 0 0 3.3 2 3 31.80 3.3 1 0 0 4 27.10 1.9 2 0.4 1 5 28.50 ?? 3 0 0 6 20.20 0 0 7.3 1 7 19.30 0 0 ?? 2 8 22.70 0 0 20.3 3 9 20.40 0 0 27.4 4 10 19.50 0 0 35.4 5 11 21.70 0 0 41.2 6 12 24 0 0 44.7 7 (a) Based on the data in the CUSUM chart, what is the slack value K? (You cannot assume k=1/2. You should find K base on the data in the table using the CUSUM statistic formula. You need to show your steps
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Unformatted text preview: ) (b) Fill in the blank in the table based on your obtained K in (a).( Show your steps) (c) Based on this tabular CUSUM, please conclude whether the process has a mean shift using h=5, If the process has a mean shift, please indicate at which sample this process was last in control, and estimate the magnitude of this mean shift. Page 3 of 3 Problem 4: Textbook 9.19 (Table 9E.2, miu=8.02, sigma=0.05) Problem 5: extra credit point: for normally distributed data ) , ( ~ 2 N X i t X is the sample average at time t with the sample size n Define EWMA monitoring statistic as Please prove Var (Z t ) = 2 n 2 ( ) 1 (1 ) 2t You are required to write out each step assumption. 1 ) 1 ( ) 1 ( t j t t j j t X Z...
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This note was uploaded on 03/16/2012 for the course IEOR 466 taught by Professor Richard during the Spring '12 term at Columbia.

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HW7 - ) (b) Fill in the blank in the table based on your...

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