mont4e_sm_ch16_mind - Mind Expanding Exercises 16-81 If the...

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Mind Expanding Exercises 16-81 a) According to Table 16-10, if there is no shift, ARL=500. If the shift in mean is 1 X σ , ARL=17.5. b) According to Table 16-10, if there is no shift, ARL=500. If the shift in mean is 2 X , ARL=3.63. 16-82 a) I-MR chart for Refining percentage Observation Individual Value 63 56 49 42 35 28 21 14 7 1 30 20 10 _ X=15.65 UC L=25.26 LC L=6.04 Moving Range 63 56 49 42 35 28 21 14 7 1 15 10 5 0 __ MR=3.61 UC L=11.81 LC L=0 1 1 1 1 1 I-MR Chart of refine I-MR chart for Dist& Marketing percentage 63 56 49 42 35 28 21 14 7 1 25 20 15 10 5 _ X=12.45 UC L=23.34 LC L=1.56 63 56 49 42 35 28 21 14 7 1 16 12 8 4 0 __ MR=4.09 UC L=13.38 LC L=0 1 1 I-MR Chart of distribution 16-58
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b) I-MR chart for crude oil percentage of retail price. It appears there have been a couple of shifts in the process around observations 16 and 56. Observation Individual Value 63 56 49 42 35 28 21 14 7 1 55 50 45 40 35 _ X=44.63 UC L=50.45 LC L=38.82 Moving Range 63 56 49 42 35 28 21 14 7 1 8 6 4 2 0 __ MR=2.185 UC L=7.139 LC L=0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I-MR Chart of crude c) 63 56 49 42 35 28 21 14 7 1 60 40 20 _ X=25.41 UC L=41.85 LC L=8.97 63 56 49 42 35 28 21 14 7 1 24 18 12 6 0 __ MR=6.18 UC L=20.20 LC L=0 1 1 1 1 1 1 1 1 I-MR Chart of refine_v 16-59
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Observation Individual Value 63 56 49 42 35 28 21 14 7 1 40 30 20 10 0 _ X=19.56 UC L=37.02 LC L=2.09 Moving Range 63 56 49 42 35 28 21 14 7 1 24 18 12 6 0 __ MR=6.57 UC L=21.46 LC L=0 1 1 1 I-MR Chart of distribution_v 16-83 Let p denote the probability that a point plots outside of the control limits when the mean has shifted from μ 0 to μ = μ 0 + 1.5 σ . Then: () 5 . 0 ) 0 6 ( 4 when 5 . 1 3 5 . 1 3 3 / 5 . 1 / 3 / 5 . 1 5 . 1 | 3 3 5 . 1 | 1 0 0 0 0 = < < = = + < < = + < < = + = + < < = + = < < = Z P n n Z n P n n X n P n X n P UCL X LCL P p σ μ σμ Therefore, the probability the shift is undetected for three consecutive samples is (1 - p ) 3 = 0.5 3 =0. 125.
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This note was uploaded on 10/12/2009 for the course IND E 315 taught by Professor Kailashkapur during the Spring '09 term at University of Washington.

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mont4e_sm_ch16_mind - Mind Expanding Exercises 16-81 If the...

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