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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^-?
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