Q$1$: $(15$ pts$)$ The table presents the number of nonconformities observed in $5$ successive samples of $10$ printed

circuit boards. Note that, for reasons of convenience, the inspection unit is defined as $10$ boards. Set up a $c$

chart for these data.

$($a$)$ Find the $3-$sigma control limits $c$ chart. $(5$ pts$)$

$($b$)$ What is the probability of making type$-$I error $($i$.$e$.,Pr\{D!in[LCL,$UCL$]\},$ where D is the number of

nonconformities$)$ for this control chart in $($a$)?(5$ pts$)$

$($c$)$ Find the ARLo. $($Not $370$ in this case$)(5$ pts$)$

Table for

$P(xx)={\displaystyle \underset{r=0}{\overset{1}{}}}*\frac{e^{-}}{r!}$