Question

In: Operations Management

Q6. A quality analyst took the following samples as a pilot study to construct the mean...

Q6. A quality analyst took the following samples as a pilot study to construct the mean and range charts. The data below shows the weight in ounces. Construct the mean and range charts showing all control (action) –upper and lower limits, and warning upper and lower limits.

Sample Number

Item1

Item2

Item3

Item4

Sample 1

11.9

12.5

12.4

12.7

Sample 2

12.5

12.5

12.4

12.8

Sample 3

12.2

12.8

12.7

12

Sample 4

12.3

12.4

12.8

12.4

Sample 5

12.1

12.8

12.4

11.9

Sample 6

12.6

12.4

12.1

12.3

The following day, the analyst took another 6 samples to check if the process under control or not. Theses samples are as follows:

Sample Number

Item1

Item2

Item3

Item4

Sample 1

11.9

11.5

12.4

12.3

Sample 2

12.5

11.5

13.4

11.8

Sample 3

12.2

11.8

11.7

12

Sample 4

14.3

11.4

11.8

13.4

Sample 5

15.1

11.8

12.4

10.9

Sample 6

11.6

10.4

10.1

15.3

Is the process under control? Why? What actions should you take?

Factors for calculating control limits for control charts

For MEANS

Sample size (n)

Constant (dn)

Factors for warning limits 1.96/dn√n

Factors for action limits 3.09√n

2

1.128

1.23

1.94

3

1.693

0.67

1.05

4

2.059

0.48

0.75

5

2.326

0.38

0.59

6

2.334

0.32

0.50

7

2.704

0.27

0.43

8

2.847

0.24

0.38

9

2.970

0.22

0.35

10

3.078

0.20

0.32

Factors for calculating control limits for control charts

For RANGES

Sample size

Upper warning limit

Lower warning limit

Upper action limit

Lower action limit

2

2.81

0.04

4.12

0.00

3

2.17

0.18

2.98

0.04

4

1.93

0.29

2.57

0.10

5

1.81

0.37

2.34

0.16

6

1.72

0.42

2.21

0.21

7

1.66

0.46

2.11

0.26

8

1.62

0.50

2.04

0.29

9

1.58

0.52

1.99

0.32

10

1.56

0.54

1.94

0.35

Solutions

Expert Solution

Sample No. Item1 Item2 Item3 Item4 Sample Mean Sample Range
Sample 1 11.90 12.50 12.40 12.70 12.38 0.80
Sample 2 12.50 12.50 12.40 12.80 12.55 0.40
Sample 3 12.20 12.80 12.70 12.00 12.43 0.80
Sample 4 12.30 12.40 12.80 12.40 12.48 0.50
Sample 5 12.10 12.80 12.40 11.90 12.30 0.90
Sample 6 12.60 12.40 12.10 12.30 12.35 0.50
Avg. 12.4125 0.6500
Mean chart Range chart
Sample size 4 4
Action limits factor 0.75
UCL 12.900 1.671
LCL 11.925 0.065
CL 12.413 0.650
Warning limits factor 0.48
UAL 12.725 1.255
LAL 12.101 0.189

Using the above [LCL, UCL] and [LAL, UAL] ranges, plot the second set of samples as follows:

Sample Number Item1 Item2 Item3 Item4 Sample Mean Sample Range
Sample 1 11.90 11.50 12.40 12.30 12.03 0.90
Sample 2 12.50 11.50 13.40 11.80 12.30 1.90
Sample 3 12.20 11.80 11.70 12.00 11.93 0.50
Sample 4 14.30 11.40 11.80 13.40 12.73 2.90
Sample 5 15.10 11.80 12.40 10.90 12.55 4.20
Sample 6 11.60 10.40 10.10 15.30 11.85 5.20

The process is out of control both in mean and range charts.


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