In a study to isolate both gauge repeatability and gauge reproducibility, two operators use the same gauge to measure $10$ parts three times each. The data are shown in Table $8$E$.8.$

$($a$)$ Estimate gauge repeatability and reproducibility.

$($b$)$ Estimate the standard deviation of measurement error.

$($c$)$ If the specifications are at $50+-10,$ what can you say about gauge capability?

TABLE $8$ E$.8$

Measurement Data For Exercise $8\mathrm{.}26$

$\backslash$table$[[$Part$,\backslash$table$[[$Operator $1],[$Number$]],,\backslash$table$[[$Operator $2],[$Measurements$]]],[1,2,3,,1,2,3$