Auto pistons at Rust-eze's plant in Radiator Springs are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:
DAYMEAN (mm)RANGE (mm)
1166.44.5
2162.34.7
3163.74.3
4164.94.9
5166.84.3
a) What is the value of ?x?
b) What is the value of¯R ?
c) What are the UCLx and LCLx, using 3σ? Plot the data.
d) What are the UCLR and LCLR, using 3σ? Plot the data.
e) If the true diameter mean should be 167 mm and you want this as your center (nominal) line, what are the new UCLx and LCLx?