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 1,197.50 mm and an upper specification unit (USL) of 1,202.50 mm. A simple random sample of 320 finished ball bearings, which were produced by an approximately normally distributed process, has the sample average of 1,199.70 mm and the sample standard deviation of 0.90 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) Draw a diagram of two scales, one for specifications, and the other for variations.
(b) Give an equation for the process capability index Cp, calculate and interpret it.
(c) Give an equation for the upper one‐sided index Cpu, calculate and interpret it.(d) Give an equation for the lower one‐sided index Cpl, calculate and interpret it.
(e) Give an equation for the process capability index Cpk, calculate and interpret it.
(f) Among the above 4 indexes, which one is the most closely watched? Explain your answer.
(g) If you are the buyer of those ball bearings, what would you say to the manufacturer?