Problem $1(24$ Points$)$ An auto parts supplier has a target of Cp $=1\mathrm{.}00.$ The manufacturing process average $=105$ mils. Product specification limits are $100\backslash$pm $15$ mils. $5$ samples are taken daily. $(14$ Points$)$ a$)$ Determine the following with the current process. UCLX $=|$ LCLX $=$ XpoubleBar $=105$ Cp $=1\mathrm{.}00$ RBar $=$ UCLR $=100$ Spec. Nominal Spec. Limits $=15$ LCLR $=|$ Sample Size $=$ PPM Reject Rate $=$ Cpk $=(6$ Points$)$ b$)$ The company wants a target of Cp $=$ Determine the values for the two methods of achieving the target: $1\mathrm{.}33$ Method $1$: Make the process average $=100$ And reduce the production variability: Method $2$: mils, and o $=$ With current process average of: $105$ USL $=$ Increase specification to: mils, mils, LSL c$)$ To change the Cpk to: $105$ given current process average $=1\mathrm{.}33$ and the process standard deviation, o$,=+$ SL $($Spec$.$ Tol.$)=|$ Determine: Cp $=$