Problem $4(20$ pts$)$:

Twenty samples of size $50$ are chosen from a plastic$-$injection molding machine producing small containers. The number of nonconforming containers for each sample is shown in table below.

QUALITY MANAGEMIENI

$4\mathrm{.}1.$ Develop a p$-$chart using $3-$sigma limits$.$ Setup the p$-$chart and plot the observations to determine if the process was out of control at any point.

$4\mathrm{.}2.$ Use pattern tests to further determine if the process is in control.