University of Kansas Variation Reduction and Statistics Questions

I’m working on a mechanical engineering multi-part question and need an explanation and answer to help me learn.

1. Using the following sample data, calculate the mean, mode, median, min., max, standard deviation, and range

1.116

1.123

1.133

1.117

1.124

1.119

1.129

1.121

1.128

1.122

1.122

1.125

1.121

1.136

1.127

1.125

1.124

1.122

1.125

1.123

1.118

1.123

1.122

1.122

1.119

Note: Excel Spread sheet also has function in finding these values; mean (average), mode, median, min, max, standard deviation (stdev), and range
Top menu, click “Formulas”, then “Insert Function” (on your far left), then you will see a box. Select a category, “Statistical” from a drop-down menu.

2. If the average wait time is 12 minutes with a standard deviation of 3 minutes, determine the percentage of patrons who wait less than 15 minutes for their main course to be brought to their tables.

3. The thickness of a part is to have an upper specification of 0.925 and a lower specification of 0.870 mm. the average of the process is currently 0.917 with a standard deviation of 0.005. determine the percentage of product above 0.93 mm.

4. The data below are X-bar and R values for 25 samples of size n = 4 taken from a process filling bags of fertilizer. The measurements are made on the fill weight of the bags in pounds.  

Sub group number

X-bar

Range

1

50.3

0.73

2

49.6

0.75

3

50.8

0.79

4

50.9

0.74

5

49.8

0.72

6

50.5

0.73

7

50.2

0.71

8

49.9

0.70

9

50.0

0.65

10

50.1

0.67

11

50.2

0.65

12

50.5

0.67

13

50.4

0.68

14

50.8

0.70

15

50.0

0.65

16

49.9

0.66

17

50.4

0.67

18

50.5

0.68

19

50.7

0.70

20

50.2

0.65

21

49.9

0.60

22

50.1

0.64

23

49.5

0.60

24

50.0

0.62

25

50.3

0.60

Set up the X-bar and R charts on this process. Interpret the charts. Does the process seem to be in control? If necessary, assume assignable causes and revise the trial control limits. If the average fill of the bags is to be 50.0 pounds, how does this process compare?

5. A hospital is using X-bar and R charts to record the time it takes to process patient account information. A sample of five application is taken each day. The first four weeks’ (20 days’) data give the following values:

X-bar-bar = 16 min  R-bar = 7 min

If the upper and lower specifications are 21 minutes and 13 minutes, respectively, calculate 6? , Cp, and Cpk interpret the indices.

6. For the data in question 4, calculate ? , Cp, and Cpk interpret the indices. The specification limits are 50 ± 0.5.

7. Determine the failure rate ? for the following: You have tested circuit boards for failures during a 500-hour continues use test. Four of the 25 boards failed. The first board failed in 80 hours, the second failed in 150 hours, the third failed in 350 hours, the fourth in 465 hours. The other boards completed the 500-hour test satisfactorily. What is the mean life of the product?

8. A power station has installed 10 new generators to provide electricity for a local metropolitan area. In the past year (8,760), two of those generators have failed, one at 2,460 hours and one at 5,962 hours. It took five days, working 24 hours a day, to repair each generator. Using one year as the teest period, what is the mean time between failures for these generators? Given the repair information, what is the availability of all 10 generators?

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