A ball bearing design for wheel assemblies used in giant mining
dump trucks requires the inner diameter to have a lower
specification unit (LSL) of 1014.50 mm and an upper specification
unit (USL) of 1017.50 mm. A simple random sample of 240 finished
ball bearings, which were produced by an approximately normally
distributed process, has the sample average of 1015.70 mm and the
sample standard deviation of 0.48 mm. A too small inner diameter is
especially not good because the ball bearing cannot be fitted into
a regular axle. You would need to use 3 decimals in the following
calculations.

(a)[2] Draw a diagram of two scales, one for specification, and
the other for production.
(b)[2] Give an equation for the process capability index Cp,
calculate and interpret it.
(c)[1] Give an equation for the upper one-sided index Cpu,
calculate and interpret it.
(d)[1] Give an equation for the lower one-sided index Cpl,
calculate and interpret it.
(e)[1] Give an equation for the process capability index Cpk,
calculate and interpret it.
(f)[2] Among the above 4 indexes, which one is the most closely
watched? Explain your answer. (g)[1] If you are the buyer of those
240 ball bearings, what would you say to the manufacturer?