Question: (10 points) 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

1. What is the value of \(\bar{\bar{x}}\) ?
2. What is the value of \(\bar{R}\) ?
3. What are the UCL( \(\bar{\bar{x}}\) ) and LCL( \(\bar{\bar{x}}\) ) , using 3 \(\sigma \) ? Plot the data.
4. What are the UCL R and LCLR , using 3ó? Plot the data.
5. If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCL x and LCL x ?

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