Determine the capability index before $({}_0=0\mathrm{.}038)$ and after $({}_0=0\mathrm{.}030)$ improve$-$

ment for the chapter example problem using specifications of $6\mathrm{.}40+-0\mathrm{.}15mm.$

A new process is started, and the sum of the sample standard deviations for $25$

subgroups of size $4$ is $750.$ If the specifications are $700+-80,$ what is the process

capability index? What action would you recommend?

What is the $C_{pk}$ value after improvement for Problem $18$ when the process center

is $6\mathrm{.}40?$ When the process center is $6\mathrm{.}30?$ Explain.

What is the $C_{pk}$ value for the information in Problem $19$ when the process average

is $700,740,780,$ and $820?$ Explain.