Statistical Quality Control-Control Charts (ISS (Statistical Services) Statistics Paper IV): Questions 21 - 22 of 31

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Question number: 21

» Statistical Quality Control » Control Charts » Variable

Essay Question▾

Describe in Detail

a) The number of customer complaints are recorded at a television manufacturing company. Complaints have been recorded over the past 20 weeks. Construct 3-σ control limits for the c-chart.

Construct 3 sigma control limit for c-chart

What is the 3 sigma control limit for c-chart

Week

No. of complaints

Week

No. of complaints

1

0

11

4

2

3

12

3

3

4

13

1

4

1

14

1

5

0

15

1

6

0

16

0

7

3

17

2

8

1

18

1

9

1

19

2

10

0

20

2

b) A machine is manufacturing mica discs. samples of size 5 are drawn every hour and their thickness in units are recorded as follows. From this data construct 3-σ control limits for chart.

Construct 3 sigma control limit for x bar-chart

What is the 3 sigma control limit for x bar-chart

Sample No.

Observstions

1

8

9

15

4

11

2

7

10

7

6

8

3

11

12

10

9

10

4

12

8

6

9

12

5

11

10

6

14

11

6

7

7

10

4

11

7

10

7

4

10

10

8

8

11

11

7

7

9

8

11

8

14

12

10

12

9

12

17

11

11

7

7

9

17

13

12

9

9

4

4

11

13

10

12

12

12

12

14

8

11

9

6

8

15

10

13

9

4

9

16

9

11

8

5

11

Explanation

a) Average number of defects per sample is

=1.5+ =1.5 + 3 (1.22) =5.174

= →0

Since number of defects cannot be negative, can be considered as zero. (rounded up to zero)

b) Second question:

Construct 3 sigma control limit for x bar-chart total, mean and range

What is the 3 sigma control limit for x bar-chart

Sample No.

Observations

Total

Sample Mean

Sample Range

1

8

9

15

4

11

47

9.4

11

2

7

10

7

6

8

38

7.6

4

3

11

12

10

9

10

52

10.4

3

4

12

8

6

9

12

47

9.4

6

5

11

10

6

14

11

52

10.4

8

6

7

7

10

4

11

39

7.8

7

7

10

7

4

10

10

41

8.2

6

8

8

11

11

7

7

44

8.8

4

9

8

11

8

14

12

53

10.6

6

10

12

9

12

17

11

61

12.2

8

11

7

7

9

17

13

53

10.6

10

12

9

9

4

4

11

37

7.4

7

13

10

12

12

12

12

58

11.6

2

14

8

11

9

6

8

42

8.4

5

15

10

13

9

4

9

45

9

9

16

9

11

8

5

11

44

8.8

6

Total

150.6

102

… (126 more words) …

Question number: 22

» Statistical Quality Control » Control Charts » Variable

Essay Question▾

Describe in Detail

When should R-Chart be Analyzed? Six samples which contain 20 observations per sample have been collected and the sample means and sample ranges are computed as shown below. Test whether the sample means are within control limits of ?

Test mean samples and check if they are in control limits of R Chart

Test mean samples and check if they are in control limits of R Chart

Sample

Mean

Range

1

3.06

0.42

2

3.15

0.5

3

3.11

0.41

4

3.13

0.46

5

3.06

0.46

6

3.09

0.45

Explanation

  • Range chart should be analyzed before the mean chart since variability of the process must be in control before the mean chart can be analyzed.

  • If the R chart indicates that the dispersion of the quality by the process is out of control, generally it is better not to construct chart, until the quality dispersion is brought under control

… (66 more words) …

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