Q$2.$ The following data are based on a month of samples, each with $n=6,$ taken from a process

that produces O$-$rings. The measurements are the last three digits. For example, $\stackrel{}{x}=297$ is

actually $1\mathrm{.}4297cm$ and $R=16$ is actually $0\mathrm{.}0016cm.$

$\frac{?}{\text{b}\text{a}\text{r}}(R)=25\mathrm{.}727$

a$)$ Set up the $\stackrel{}{x}$ and $R$ charts.

b$)$ If out of control condition exists, assume that assignable causes can be found. Revise

the control limits if necessary.

c$)$ If the specifications are $(1\mathrm{.}424,1\mathrm{.}428),$ find the percentage of nonconforming $O-$rings.

d$)$ If the process average suddenly shifts to $1\mathrm{.}4284cm,$ what would happen to the

percentage nonconforming?

Answer $(\%25)$: