Problem $5(15$ points$)$ A production process is monitored with the c$-$chart shown below. Total number of defects from

$15$ inspection units equaled to $68.$ Assuming that assignable causes of out$-$of$-$control points are found, recalculate the

UCL, LCL and CL of the chart. After recalculating the control limits$,$ clearly state if there are any units that fall outside

the control limits$.$ Use $3-$sigma control limits$.$

hat$(c)=\frac{68}{16}=4\mathrm{.}533$

recaculate

hat$(C)=\frac{42}{13}=3\mathrm{.}2301$

UCL$=$hat$(C)+3\sqrt[\phantom{2}]{h}at(C)=3\mathrm{.}2301+3\sqrt[\phantom{2}]{3\mathrm{.}2301}=8\mathrm{.}6218$

$CL=$hat$(C)=3\mathrm{.}2301$

$LCL=$hat$(C)-3\sqrt[\phantom{2}]{h}at(3)=3\mathrm{.}231-3\sqrt[\phantom{2}]{3\mathrm{.}231}=-2\mathrm{.}161$~~$0$

There are no units autside