1. A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that the process standard deviation is two ounces. Each day last week, he randomly selected four packages and weighed each. The data from that activity appears below.

Weight

Day Package 1 Package 2 Package 3 Package 4

Monday 23 22 23 24

Tuesday 23 21 19 21

Wednesday 20 19 20 21

Thursday 18 19 20 19

Friday 18 20 22 20

(a)Calculate all sample means and the mean of all sample means.

(b)Calculate upper and lower control limits that allow for natural variations.

(c)Is this process in control?

2.Cartons of Plaster of Paris are supposed to weigh exactly 32 oz. Inspectors want to develop process control charts. They take ten samples of six boxes each and weigh them. Based on the following data, compute the lower and upper control limits and determine whether the process is in control.

Sample Mean Range

1 33.8 1.1

2 34.6 0.3

3 34.7 0.4

4 34.1 0.7

5 34.2 0.3

6 34.3 0.4

7 33.9 0.5

8 34.1 0.8

9 34.2 0.4

10 34.4 0.3

3.The width of a bronze bar is intended to be one-eighth of an inch (0.125 inches). Inspection samples contain five bars each. The average range of these samples is 0.01 inches. What are the upper and lower control limits for the X-bar and R-chart for this process, using 3-sigma limits?

4.A part that connects two levels should have a distance between the two holes of 4". It has been determined that X-bar and R-charts should be set up to determine if the process is in statistical control. The following ten samples of size four were collected. Calculate the control limits, plot the control charts, and determine if the process is in control.

Mean Range

Sample 1 4.01 0.04

Sample 2 3.98 0.06

Sample 3 4.00 0.02

Sample 4 3.99 0.05

Sample 5 4.03 0.06

Sample 6 3.97 0.02

Sample 7 4.02 0.02

Sample 8 3.99 0.04

Sample 9 3.98 0.05

Sample 10 4.01 0.06

Weight

Day Package 1 Package 2 Package 3 Package 4

Monday 23 22 23 24

Tuesday 23 21 19 21

Wednesday 20 19 20 21

Thursday 18 19 20 19

Friday 18 20 22 20

(a)Calculate all sample means and the mean of all sample means.

(b)Calculate upper and lower control limits that allow for natural variations.

(c)Is this process in control?

2.Cartons of Plaster of Paris are supposed to weigh exactly 32 oz. Inspectors want to develop process control charts. They take ten samples of six boxes each and weigh them. Based on the following data, compute the lower and upper control limits and determine whether the process is in control.

Sample Mean Range

1 33.8 1.1

2 34.6 0.3

3 34.7 0.4

4 34.1 0.7

5 34.2 0.3

6 34.3 0.4

7 33.9 0.5

8 34.1 0.8

9 34.2 0.4

10 34.4 0.3

3.The width of a bronze bar is intended to be one-eighth of an inch (0.125 inches). Inspection samples contain five bars each. The average range of these samples is 0.01 inches. What are the upper and lower control limits for the X-bar and R-chart for this process, using 3-sigma limits?

4.A part that connects two levels should have a distance between the two holes of 4". It has been determined that X-bar and R-charts should be set up to determine if the process is in statistical control. The following ten samples of size four were collected. Calculate the control limits, plot the control charts, and determine if the process is in control.

Mean Range

Sample 1 4.01 0.04

Sample 2 3.98 0.06

Sample 3 4.00 0.02

Sample 4 3.99 0.05

Sample 5 4.03 0.06

Sample 6 3.97 0.02

Sample 7 4.02 0.02

Sample 8 3.99 0.04

Sample 9 3.98 0.05

Sample 10 4.01 0.06

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