hw5_sol - IEOR 165: Engineering Statistics, Quality Control...

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IEOR 165: Engineering Statistics, Quality Control and Forecasting, Summer 2009 Homework 5 Solution Chapter 13 Question 1 Control limits are 35 ± 9 / 5 which give LCL=30.98, UCL=39.03. Subgroup 3 falls outside these limits. Question 2 Suppose the mean jumps to 16.2. The probability that the next subgroup falls outside is approx- imately P { X > 14 + 6 / 5 } = P ( Z > 3 - 2 . 2 5 2 ) = 1 - Φ( . 54) = . 2946 . On average, it will take a geometric distributed number of subgroups with mean 1/.2946=3.39 to detect a shift. The result is the same when the mean falls by 2.2. Question 4 (a) X = 357 . 2 / 25 = 14 . 288, ¯ S = 4 . 88 / 25 = . 1952. Control limits are 14 . 288 ± 3 × . 1952 / ( 5 c (5)) which give LCL=14.01, UCL=14.57. (b) The estimate of σ is .1952/ c (5)=.2077. Hence with μ = 14 . 288, σ = . 2077, P { 13 . 85 < X < 14 . 75 } = P ± 13 . 85 - 14 . 288 . 2077 X - 14 . 288 . 2077 14 . 75 - 14 . 288 . 2077 ² = Φ(2 . 224) - Φ( - 2 . 109) = . 969 .
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This note was uploaded on 07/22/2009 for the course IEOR 165 taught by Professor Shanthikumar during the Summer '08 term at University of California, Berkeley.

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hw5_sol - IEOR 165: Engineering Statistics, Quality Control...

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