Auto pistons at JE Piston’s plant in Melbourne are produced in a foreign process, and the diameter is a critical factor that must be controlled. From a sample size of 1000 pistons produced each day, the mean and the range of this diameter has been at follows
| Q17. | Day | Mean mm | Range mm |
| 1 | 156 | 4.2 | |
| 2 | 153 | 4.6 | |
| 3 | 152 | 4.1 | |
| 4 | 155 | 5 | |
| 5 | 157 | 4.5 |
a. what is the value of X =?
b. what is the value of R =?
c. what is the UCLx and LCLx using 3 standard deviation?
d. what is the UCLR and the LCLR using 3 standard deviation?
e. Is it true the diametere mean should be 154m, and you want this as your center (nominal) line, what are the new UCLx and LCLx?
