Scenario: A manufacturer of automobile glass employs a constant quality control

Question

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 14: Using the data contained in the scenario calculate the Lower Control Limit for an X-bar chart that reflect a 99.7% confidence level.

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

Explanation / Answer

Lower Control Limit = 2.3487

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