The following 30 measurements on flash length were taken from the friction welding process when engineers were controlling the process variables at average values of 1.3mm, 38Hz, 75MPa, and 1.3mm for amplitude, frequency, pressure, and burn-off respectively. These process variables followed normal distributions and the standard deviation was 0.2mm, 3Hz, 9MPa, and 0.1mm for the distributions of amplitude, frequency, pressure, and burn-off respectively.

11.18

11.85

11.76

11.79

11.3

9.11

6.35

12.34

9.73

11.59

11.08

11.34

10.88

10.38

9.96

11.05

10.5

12.03

11.28

11.88

11.51

11.31

11.71

12.35

12.33

11.61

9.87

12.54

9.28

12.1

Ideally, flash length should be T = 12 mm, but an acceptable range for this length is given by USL = 14 mm and LSL = 10 mm.

.What is the value for the Process Capability Index, C_P (answer to 2 decimal places)?

.What percentage of the specification band P is used up by the process (answer to 2 decimal places)?

.What is the value for the Process Capability Index, C_P,k (answer to 2 decimal places)?

.Assuming that flash-length measurements taken from the process have a normal distribution, what percentage number of manufactured welds are below the lower specification limit (answer to 2 decimal places)?

.Assuming that flash-length measurements taken from the process have a normal distribution, what is the annual scrap cost assuming the process operates at maximum capacity for the year (answer to nearest whole number)?

.Suppose that the mean could be placed on target as a result of changing some of the operating conditions at the forge. What then would be the percentage number of manufactured welds (based on the normal distribution) that fell outside the specification limits (answer to 2 decimal places)?