STATISTICAL PROCESS CONTROL

THE  QUESTIONS REFER TO STATISTICAL PROCESS CONTROL

Scenario: A manufacturer of automobile glass employs a constant quality control technique where the thickness of glass is checked periodically by taking a sample of 5 units and measuring the thickness. The results of one shift’s quality control inspections are shown in the table below.

Sample

Thickness

Sample

Thickness

1

4, 3, 4, 2, 4

11

1, 6, 4, 4, 2

2

5, 3, 5, 4, 2

12

3, 3, 4, 5, 4

3

3, 3, 3, 3, 4

13

3, 8, 3, 8, 6

4

4, 5, 5, 4, 5

14

3, 2, 5, 4, 2

5

2, 8, 7, 2, 2

15

3, 3, 3, 2, 1

6

4, 5, 2, 5, 4

16

4, 4, 4, 5, 3

7

3, 5, 4, 4, 5

17

5, 3, 4, 4, 3

8

2, 4, 4, 4, 3

18

4, 4, 5, 3, 3

9

5, 4, 3, 2, 5

19

6, 4, 3, 3, 3

10

4, 4, 4, 4, 4

20

4, 4, 3, 5, 4

Question 21: Using the data contained in the scenario calculate the Upper Control Limit for an X-bar chart that reflect a 99.7% confidence level. (2.5 points)

Question 22: Using the data contained in the scenario calculate the Lower Control Limit for an X-bar chart that reflect a 99.7% confidence level. (2.5 points)

Question 23: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for an X-bar chart, which samples are out of control? (5 points)

Question 24: Using the data contained in the scenario calculate the Upper Control Limit for an R chart that reflect 99.7% level of confidence. (2.5 points)

Question 25: Using the data contained in the scenario calculate the Lower Control Limit for an R chart that reflect 99.7% level of confidence. (2.5 points)

Question 26: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for an R chart, which samples are out of control? (5 points)

Scenario: A canning company packages canned soup for a major soup manufacturer for distribution to regional wholesalers.  The company processes 5,000 cans of soup each day using an automated packaging machine that is programmed to fill each can with 74.0 ± 0.1 ounces net weight of soup.  The company's quality assurance process consists of randomly selecting five cans from the production line each hour and carefully weighing them. Sample observations for a 24-hour production run are reflected in the table below. 

Hour

Sample 1

Sample 2

Sample 3

Sample 4

Sample 5

1

74.030

74.002

74.019

73.992

74.008

2

73.995

73.992

74.001

74.011

74.004

3

73.988

74.024

74.021

74.005

74.002

4

74.002

73.996

73.993

74.015

74.009

5

73.992

74.007

74.015

73.989

74.014

6

74.009

73.994

73.997

73.985

73.993

7

73.995

74.006

73.994

74.000

74.005

8

73.985

74.003

73.993

74.015

73.988

9

74.008

73.995

74.009

74.005

74.004

10

73.998

74.000

73.990

74.007

73.995

11

73.994

73.998

73.994

73.995

73.990

12

74.004

74.000

74.007

74.000

73.996

13

73.983

74.002

73.998

73.997

74.012

14

74.006

73.967

73.994

74.000

73.984

15

74.012

74.014

73.998

73.999

72.866

16

74.000

73.984

74.005

72.652

73.996

17

73.994

74.012

73.071

74.005

74.007

18

74.006

72.356

74.018

74.003

74.000

19

74.785

74.002

74.003

74.005

73.997

20

74.000

74.010

74.013

74.020

74.003

21

73.982

74.001

74.015

74.005

73.996

22

74.004

73.999

73.990

74.006

74.009

23

74.010

73.989

73.990

74.009

74.014

24

74.015

74.008

73.993

74.000

74.010

25

73.982

73.984

73.995

74.017

74.013

Question 27: Using the data contained in the scenario calculate the Upper Control Limit for an X-bar chart that reflect a 99.7% confidence level. (5 points)

Question 28: Using the data contained in the scenario calculate the Lower Control Limits for an X-bar chart that reflect a 99.7% confidence level. (5 points)

Question 29: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for an X-bar chart, which samples are out of control? (5 points)

Question 30: Using the data contained in the scenario calculate the Upper Control Limit for an R chart that reflect 99.7% level of confidence. (5 points)

Question 31: Using the data contained in the scenario calculate the Lower Control Limit for an R chart that reflect 99.7% level of confidence. (5 points)

Question 32: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for an R chart, which samples are out of control? (5 points)