Auto pistons at Wemming Chung's plant in Shanghai 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:
|
DAY
|
MEAN (MM)
|
RANGE (MM)
|
|
1
|
156.9
|
4.2
|
|
2
|
153.2
|
4.6
|
|
3
|
153.6
|
4.1
|
|
4
|
155.5
|
5.0
|
|
5
|
156.6
|
4.5
|
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 155 mm and you want this as your center (nominal) line, what are the new UCLx^- and LCLx^-?