Problem $1(20$ points$)$ For a key joint width, the lower specification limit is $0\mathrm{.}8100mm$ and the upper specification limit

is $0\mathrm{.}8600mm.$ The precision machining process used to make the joint has a standard deviation of $0\mathrm{.}0060mm$ and a

mean of $0\mathrm{.}8500mm.$ Round all answers to $4$ decimal places.

a$.$ Find the capability indices $C_p$ and $C_{pk}$ for the process.

b$.$ Find the fallout of the process in ppm

c$.$ The company wants to reduce its defect probability to operate at six$-$sigma quality. How can the engineers

accomplish this by adjusting the centering and variability of the process?Problem $1(20$ points$)$ For a key joint width, the lower specification limit is $0\mathrm{.}8100mm$ and the upper specification limit

is $0\mathrm{.}8600mm.$ The precision machining process used to make the joint has a standard deviation of $0\mathrm{.}0060mm$ and a

mean of $0\mathrm{.}8500mm.$ Round all answers to $4$ decimal places.

a$.$ Find the capability indices $C_p$ and $C_{pk}$ for the process.

b$.$ Find the fallout of the process in ppm

c$.$ The company wants to reduce its defect probability to operate at six$-$sigma quality. How can the engineers

accomplish this by adjusting the centering and variability of the process?