MGMT 361 HW 4

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Purdue University *

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36100

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Management

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Apr 3, 2024

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MGMT361 Fall 2024 Homework 4 Due Monday 3/18 Section time: 1:30PM . Student Name: Salvador de Leon . Round the answers to 2 decimal places if required. Question 1 (5+5=10 points) A quality control inspector has taken 4 samples with five observations each, measuring the volume of chips per bag. If the average range for the fours samples is 0.2 ounce and the grand mean of the observations is 12.5 ounces, find the control limits for X-bar and R-charts.

Question 2 (2+4+4 =10 points) Breeze Toothpaste Company makes tubes of toothpaste. The toothpaste is produced and then pumped into tubes and capped. The production manager is concerned whether the filling process for the tubes of toothpaste is in statistical control. The process should be centered around 7 ounces per tube. Samples of 5 tubes were taken and each tube was weighed. The weights are given in the table below. Sample Ounces of Toothpaste per tube Tube 1 Tube 2 Tube 3 Tube 4 Tube 5 X-bar R Sample 1 6.89 6.87 7.11 7.21 6.99 7.014 0.34 Sample 2 7.22 6.78 6.76 7.02 7.13 6.982 0.46 Sample 3 6.78 7.34 7.24 6.23 7.12 6.942 1.11 Sample 4 7.02 6.57 7.21 7.23 7.02 7.01 0.66 Sample 5 6.77 6.76 6.87 6.78 7.03 6.842 0.27 Sample 6 7.05 6.89 7.02 6.98 6.78 6.944 0.27 a) Find the sample average and range for each of the six samples. (2pts) X double bar = 6.956 R-bar = 0.518 b) Construct the control limits of the X-bar chart. Is there any out of control sample? (4pts) N = 5, so A2 = 0.577, D3 = 0, D4 = 2.114 UCLx = 6.956 + 0.577(0.518) = 7.26 LCLx = 6.956-0.577(0.518) = 6.66 No out of control samples. c) Construct the control limits of the R-chart. Is there any out of control sample? (4pts) UCLr = 2.114(0.518) = 1.096 LCLr = 0(0.519) = 0 Yes, sample 3 is out of control because 1.11 is greater than the upper control limit.

Question 3: (2+3+3+2=10) A chocolate factory has weighed 4 chocolate truffles coming out of production over 5 working days to obtain the following data, weights are in grams. Mon Tue Wed Thu Fri 10am 30.50 30.30 30.15 30.60 30.15 11am 29.75 31.00 29.50 32.00 30.25 2pm 29.90 30.20 29.75 31.00 30.50 3pm 30.25 30.50 30.00 30.00 29.70 a) Group the data by day into five samples and find the sample average and range for each sample. b) Suppose the process has a mean of 30 and a standard deviation of 0.3. Construct the 3-sigma control limits of the mean chart. Is the process in control? N = 5, so A2 = 0.577 D3 = 0 D4 = 2.114 UCLx = 30 + (0.577*1) = 30.58 LCLx = 30 – (0.577*1) = 29.42 Yes, the process is in control. Mon Tue Wed Thu Fri 10am 30.5 30.3 30.15 30.6 30.15 11am 29.75 31 29.5 32 30.25 2pm 29.9 30.2 29.75 31 30.5 3pm 30.25 30.5 30 30 29.7 x bar 30.1 30.5 29.85 30.9 30.15 R 0.75 0.8 0.65 2 0.8 double x bar 30.3 r bar 1

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c) Suppose we do not know the mean and the standard deviation of the process. Construct the 3-sigma control limits of the mean chart. Is the process mean under control? (Table next page) Using the double X bar and R bar calculated in part a: UCLx = 30.3+0.729(1) = 31.03 LCLx = 30.3 – 0.729(1) = 29.57 The process mean is under control. d) Construct the control limits of the range chart. Is the process range under control? UCLr = 2.114*1 = 2.11 LCLr = 0 * 1 = 0 Yes, the process range is under control.

n 2 3 4 5 6 7 8 9 10 A 2 1.88 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 n 11 12 13 14 15 16 17 18 19 20 A 2 0.285 0.266 0.249 0.235 0.223 0.212 0.203 0.196 0.187 0.180 n 2 3 4 5 6 7 8 9 10 D 3 0 0 0 0 0 0.076 0.136 0.184 0.223 D 4 3.268 2.574 2.282 2.114 2.004 1.924 1.864 1.816 1.777 n 11 12 13 14 15 16 17 18 19 20 D 3 0.256 0.284 0.308 0.329 0.348 0.364 0.379 0.392 0.404 0.414 D 4 1.744 1.716 1.692 1.671 1.652 1.636 1.621 1.608 1.596 1.586

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