IV$.$ Cok $($Process Capability Index$)$ of capable processes are ones with a ratiolindex of $1\mathrm{.}33(4$ sigma$)$ or greater. $(25$ points$)$

You are the process improvement manager and have developed a new machine to cut insoles for the company's top$-$of$-$the$-$line ruming shoes. The company's goal is no more than $3\mathrm{.}4$ defects per million. The insoles cannot be more than $\frac{+}{-}\mathrm{.}001$ of an inch from the thickness specification of $\mathrm{.}250.$ The new process has a mean $=\mathrm{.}250$ inch and a standard deviation $=\mathrm{.}0005$ inch.

a$)$ Should you replace the existing machine which has a Cok of $1\mathrm{.}0?$

b$)$ If the insoles can be $\frac{+}{-}{\mathrm{.}002}^{n2}($instead of ${\mathrm{.}001}^{\text{'}})$ from the required $250,$ what is new the CDts and would you replace the existing machine?

C$)$ What else can be considered to improve the Col?