If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are…

Auto pistons at Yongpin Zhou'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 3s?

d. What are the UCLR and LCLR using 3 s?

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.