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664 HW7 Solns

664 HW7 Solns - Statistics 664 Autumn 2010 Homework 7...

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Statistics 664 – Autumn 2010 Homework 7 Solutions 1. Problem 6.7 (just redo part a of 6.2) Here are the x and s charts from Minitab. 19 17 15 13 11 9 7 5 3 1 15.0 12.5 10.0 7.5 5.0 Sample Sample Mean _ _ X= 10.32 UCL= 14.73 LCL= 5.92 19 17 15 13 11 9 7 5 3 1 6.0 4.5 3.0 1.5 0.0 Sample Sample StDev _ S= 2.703 UCL= 6.125 LCL= 0 Xbar-S Chart of Ex6-2V All points are within the control limits for both charts. Thus the process appears to be in control if we assume that the historical values for x and s represent “in control” values. (Note: An acceptable alternative answer is the following. The nominal output voltage is supposed to be 350V. This means that the x i values should fluctuate around 0, i.e., that the center line in our x chart should be 0. The upper and lower control limits would then be LCL = -4.40 and UCL = 4.40. Since all the points are above 5.77, every point would be above the UCL and the process would be declared out of control). 2. Problem 6.8 (just redo part a of 6.3) Here are the x and s charts from Minitab.
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19 17 15 13 11 9 7 5 3 1 40 20 0 -20 Sample Sample Mean _ _ X= 10.9 UCL= 46.91 LCL= -25.11 19 17 15 13 11 9 7 5 3 1 60 45 30 15 0 Sample Sample StDev _ S= 25.23 UCL= 52.71 LCL= 0 Xbar-S Chart of Ex6-3Dia All points in both charts are with the control limits so the process appears to be in control, assuming the historical values represent “in control” values. (Note: An alternative answer is to argue that if the process is in control the mean should be 0. This should be the center line of the x chart. In this case, the control limits would be LCL = –36.01 and UCL = 36.01. All the data lie within these control limits, but after sample 7 all are positive, which would be considered unusual. So one might argue that the process is not in control after sample 7.) 3.
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664 HW7 Solns - Statistics 664 Autumn 2010 Homework 7...

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