A textile manufacturer wants to set up a control chart for irregularities per 10

Question

A textile manufacturer wants to set up a control chart for irregularities per 100 square yards of carpet. The following data were collected from a sample of twenty 100-square-yard pieces of carpet:

Sample :           1 2   3 4   5 6 7   8 9    10

Irregularities : 11 8 9 12 4 16 5 8 17 10

Sample :         11 12 13 14 15 16 17 18 19 20

Irregulaties:     11   5    7   12 13   8 19   11  9   10

a) Using these data, set up a c-chart with z= 3.

b) Suppose that the next five samples had 15, 18, 12, 22, and 21 irregularities. What do you conclude?

Explanation / Answer

Ans:

Using the above data, set up the appropriate control chart using 3-sigma limits and determine if the process is in control. Also plot the chart

We see that all the Irregularities are between the UCL & LCL. So Process is in control.

Results

Total units sampled

20

Total Defects

205

Defect rate, l

10.25

Standard deviation

3.201562

z value

         3.00

Upper Control Limit

19.85469

Center Line

10.25

Lower Control Limit

0.645314

B.Computer upgrades have a nominal time of 80 minutes. Samples of five observations each have been taken, and the results are as listed below. Using the factors A2, D3 and D4, determine upper and lower control limits for mean and range charts, and decide if the process is in control. Draw the X-bar chart and R-chart also in order to illustrate your conclusions

Details are shown below & in attached excel.

As all Observations are within UCL & LCL and within Range, Process is in Control

Sample #

1

2

3

4

5

6

79.20

80.50

79.60

78.90

80.50

79.70

78.80

78.70

79.60

79.40

79.60

80.60

80.00

81.00

80.40

79.70

80.40

80.50

78.40

80.40

80.30

79.40

80.80

80.00

81.00

80.10

80.80

80.60

78.80

81.10

Data

Mean

Range

Sample 1

       79.48

            2.60

Sample 2

       80.14

            2.30

Sample 3

       80.14

            1.20

Sample 4

       79.60

            1.70

Sample 5

       80.02

            2.00

Sample 6

       80.38

            1.40

Average

       79.96

            1.87

Results

Xbar

Range

x-bar value

79.96

R bar

1.866667

Upper control limit

81.03707

3.948

Center line

79.96

1.866667

Lower control limit

78.88293

0

Results

Total units sampled

20

Total Defects

205

Defect rate, l

10.25

Standard deviation

3.201562

z value

         3.00

Upper Control Limit

19.85469

Center Line

10.25

Lower Control Limit

0.645314

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