A Two$-$Replication$/$Two Operator$/5$ Part Gage Capability Study was conducted for a bushing outside diameter with a total engineering tolerance equal to $\mathrm{.}020$ of an inch. The following are the recorded measurements:

$\backslash$table$[[$Part$,$Jim$-$Rep $1,$Jim$-$Rep $2,$Jane$-$Rep $1,$Jane$-$Rep $2],[1,0\mathrm{.}491,0\mathrm{.}490,0\mathrm{.}488,0\mathrm{.}489],[2,0\mathrm{.}495,0\mathrm{.}494,0\mathrm{.}492,0\mathrm{.}491],[3,0\mathrm{.}510,0\mathrm{.}510,0\mathrm{.}506,0\mathrm{.}506],[4,0\mathrm{.}501,0\mathrm{.}500,0\mathrm{.}498,0\mathrm{.}497],[5,0\mathrm{.}504,0\mathrm{.}505,0\mathrm{.}503,0\mathrm{.}502]]$

What is the Gage R&R as a percent of engineering tolerance and as a percent to study variation? Show all work. Use either Minitab or appropriate M$/$S Excel template and paste below to substantiate your answers.

Worth $3$ points: Gage Capability $(\%$ to Tolerance$)$: $\_\_\_\_\_\_\_$

Worth $2$ points: Gage Capability $(\%$ to Study Variation$)$: $\_\_\_\_\_\_\_\_$

Per the Gage Study in Problem $6,$ what would you recommend as the next course of action?

a$)$ Buy a new and more expensive gage with better resolution since NDC

b$)$ Ignore it as long as the gage calibration sticker is in date.

c$)$ Get Design Engineering to increase the total tolerance of the part feature.

d$)$ Investigate the measurement methods the two inspectors used and work to reduce the bias between them.