There are two ways to measure how capable a manufacturing process is compared to specifications, Cp $($Process Capability Ratio$)$ or Cpk $($Process Capability Index$).$ Capable processes are ones with a ratio$/$index of $1\mathrm{.}33(4$ sigma$)$ or greater.

a$)$ Explain the differences between these process capability indicators and circumstances where they would provide the same answer.

You are the process improvement manager and have been asked to determine the capability for the processes below. In addition, the director of the department wants to understand for those that are not capable what is the percentage improvement in standard deviation required for achieving capability.

Process Mean Standard Deviation Lower Spec Upper Spec

$17\mathrm{.}50\mathrm{.}107\mathrm{.}08\mathrm{.}0$

$24\mathrm{.}50\mathrm{.}124\mathrm{.}34\mathrm{.}9$

$36\mathrm{.}00\mathrm{.}145\mathrm{.}56\mathrm{.}7$