Calculate Standard Deviation For Shaft Diameter Variation Assignment

1. A company is considering the purchase of a machine to turn a shaft. A machine is

borrowed for testing purposes, and it is found that 5.48% of the shafts have diameters

greater than 5.032 mm when the machine is set at average 5.00 mm.

(a) Give a graphical representation of the normal distribution probability in this case

and calculate the standard deviation to which the machine is operating.

(b) Assume that the company has managed to achieve and maintain process variation

(based on ±3σ) in a range of 0.12 mm and wishes to produce these shafts to a

design dimension between 4.94 mm and 5.05 mm, and any shafts outside this

range would be rejected. If the machine produces 1 million shafts per month, and

each shafts rejected costs the firm 1p, find the monthly cost of rejects.

purchase. If this machine is known to operate with a standard deviation of 0.016

mm, determine which machine should be purchased?

(d) Assuming the company has purchased the second machine and it is set exactly as

the first one (at 5.00)