Supplement Chapter $6$S:$1$

Auto pistons at Rust$-$eze's plant in Radiator Springs 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:

a$)$ What is the value of $\stackrel{}{x}?$

b$)$ What is the value of $\frac{?}{\text{b}\text{a}\text{r}}(R)?$

d$)$ What are the UCLR and LCLR$,$ using $3?$ Plot the data.

e$)$ Is the process in control?

f$)$ If the true diameter mean should be $155mm$ and you want this as your center $($nominal$)$

line, what are the new UCLJX and L$.$CIX?