Example $1$

A process has a $$ of $132\mathrm{.}8$ mm and a process standard deviation $$ of $0\mathrm{.}2$ mm$.$ The customer has a target

of $133$ mm$,$ with a tolerance of $\backslash$pm $1$ mm$.$ The average range is $0\mathrm{.}02$ mm and the standard deviation of the

ranges is $0\mathrm{.}005$ mm$.$

a$.$ Please calculate the UTL and LTL

b$.$ Please calculate $$ and $$ using the theoretical method

c$.$ Please calculate $$ and $$ using the theoreti