1. Suppose that a window manufacturer is monitoring the process used to make its windows. Every...

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1. Suppose that a window manufacturer is monitoring the process used to make its windows. Every 15 minutes, the manufacturer measures the width of 5 windows. Over the course of two and a half hours, the following 12 samples (each of size 5) are taken. All measurements are in meters. Sample x1 x2 1 1.11 2 1.21 1.28 1.06 3 1.31 1.04 1.19 4 1.21 1.12 1.11 5 1.22 1.15 1.29 6 0.96 1.00 1.09 1.03 7 1.03 1.15 1.20 1.15 8 1.12 0.99 1.02 1.28 x3 x4 X5 R 1.03 1.33 1.30 1.12 1.18 0.30 1.30 1.04 1.18 0.26 1.07 0.99 1.12 0.32 0.98 1.23 1.13 0.26 1.05 1.18 1.18 0.24 1.14 1.04 0.18 1.21 1.15 0.18 0.28 T 1.18 1.12 9 1.30 1.11 1.27 1.05 1.00 1.15 0.31 10 1.04 1.26 1.04 1.09 1.05 1.10 0.22 11 1.05 1.23 1.10 1.18 1.14. 1.14 0.18 12 1.27 1.20 1.33 1.01 0.97 1.16 0.36 a. Calculate the upper and lower control limits for the x-chart and the R-chart associated with this data. See below for the table of the D2, D3, and D4 values. Sample Size D2 D3 D4 2 1.128 0 3.268 3 1.693 0 2.574 4 2.059 0 2.282 5 2.326 0 2.115 6 2.534 0 2.004 7 2.704 .0761 1.924 b. Plot the x-chart and the R-chart. Determine whether or not the process is in control. If it is not in control, state what looks wrong on the control chart and what could possibly be causing this. 2. Detroit Central Hospital is trying to improve its image by providing a positive experience to its patients and their relatives. Part of the program involves providing meals that are both tasty and healthy. A questionnaire accompanies each meal served, asking the patient whether s/he is satisfied or unsatisfied with the meal. A 300-patient sample of the survey results over the past 8 days yielded the following data (see next page). Day Sample Size No. of Unsatisfied Patients 1 300 268 2 300 146 3 300 95 4 300 193 5 300 99 6 300 198 7 300 286 8 300 244 Construct a p-chart that plots the percentage of patients unsatisfied with their meals. Set the control limits to include 95.45% of the random variation in meal satisfaction. Is this process in control or out of control? Justify carefully your answer. Sample x1 x2 x3 x4 x5 x-bar R 123456782222 1.11 1.03 1.33 1.30 1.12 1.18 0.30 1.21 1.28 1.06 1.30 1.04 1.18 0.26 1.31 1.04 1.19 1.07 0.99 1.12 0.32 1.21 1.12 1.11 0.98 1.23 1.13 0.26 1.22 1.15 1.29 1.05 1.18 1.18 0.24 0.96 1.00 1.09 1.03 1.14 1.04 0.18 1.03 1.15 1.20 1.15 1.21 1.15 0.18 1.12 0.99 1.02 1.28 1.18 1.12 0.28 1.30 1.11 1.27 1.05 1.00 1.15 0.31 10 1.04 1.26 1.04 1.09 1.05 1.10 0.22 1.05 1.23 1.10 1.18 1.14 1.14 0.18 1.27 1.20 1.33 1.01 0.97 1.16 0.36 Number Sample Day Unsatisfied Size 1 268 300 2345 2 146 300 3 95 300 4 193 300 5 99 300 6 198 300 7 286 300 8 244 300 1. Suppose that a window manufacturer is monitoring the process used to make its windows. Every 15 minutes, the manufacturer measures the width of 5 windows. Over the course of two and a half hours, the following 12 samples (each of size 5) are taken. All measurements are in meters. Sample x1 x2 1 1.11 2 1.21 1.28 1.06 3 1.31 1.04 1.19 4 1.21 1.12 1.11 5 1.22 1.15 1.29 6 0.96 1.00 1.09 1.03 7 1.03 1.15 1.20 1.15 8 1.12 0.99 1.02 1.28 x3 x4 X5 R 1.03 1.33 1.30 1.12 1.18 0.30 1.30 1.04 1.18 0.26 1.07 0.99 1.12 0.32 0.98 1.23 1.13 0.26 1.05 1.18 1.18 0.24 1.14 1.04 0.18 1.21 1.15 0.18 0.28 T 1.18 1.12 9 1.30 1.11 1.27 1.05 1.00 1.15 0.31 10 1.04 1.26 1.04 1.09 1.05 1.10 0.22 11 1.05 1.23 1.10 1.18 1.14. 1.14 0.18 12 1.27 1.20 1.33 1.01 0.97 1.16 0.36 a. Calculate the upper and lower control limits for the x-chart and the R-chart associated with this data. See below for the table of the D2, D3, and D4 values. Sample Size D2 D3 D4 2 1.128 0 3.268 3 1.693 0 2.574 4 2.059 0 2.282 5 2.326 0 2.115 6 2.534 0 2.004 7 2.704 .0761 1.924 b. Plot the x-chart and the R-chart. Determine whether or not the process is in control. If it is not in control, state what looks wrong on the control chart and what could possibly be causing this. 2. Detroit Central Hospital is trying to improve its image by providing a positive experience to its patients and their relatives. Part of the program involves providing meals that are both tasty and healthy. A questionnaire accompanies each meal served, asking the patient whether s/he is satisfied or unsatisfied with the meal. A 300-patient sample of the survey results over the past 8 days yielded the following data (see next page). Day Sample Size No. of Unsatisfied Patients 1 300 268 2 300 146 3 300 95 4 300 193 5 300 99 6 300 198 7 300 286 8 300 244 Construct a p-chart that plots the percentage of patients unsatisfied with their meals. Set the control limits to include 95.45% of the random variation in meal satisfaction. Is this process in control or out of control? Justify carefully your answer. Sample x1 x2 x3 x4 x5 x-bar R 123456782222 1.11 1.03 1.33 1.30 1.12 1.18 0.30 1.21 1.28 1.06 1.30 1.04 1.18 0.26 1.31 1.04 1.19 1.07 0.99 1.12 0.32 1.21 1.12 1.11 0.98 1.23 1.13 0.26 1.22 1.15 1.29 1.05 1.18 1.18 0.24 0.96 1.00 1.09 1.03 1.14 1.04 0.18 1.03 1.15 1.20 1.15 1.21 1.15 0.18 1.12 0.99 1.02 1.28 1.18 1.12 0.28 1.30 1.11 1.27 1.05 1.00 1.15 0.31 10 1.04 1.26 1.04 1.09 1.05 1.10 0.22 1.05 1.23 1.10 1.18 1.14 1.14 0.18 1.27 1.20 1.33 1.01 0.97 1.16 0.36 Number Sample Day Unsatisfied Size 1 268 300 2345 2 146 300 3 95 300 4 193 300 5 99 300 6 198 300 7 286 300 8 244 300