Problem $4-8$ NEW Gauge Inc.$-$ R&R

A gauge repeatability and reproducibility study at NEW Gauge, Inc., collected the data for three operators, two trials, and eight parts, s found below. Analyze these data. The part specification is $1\mathrm{.}5\backslash$pm $0\mathrm{.}1$ inches. $($Use the R&R template on the next worksheet tab$).$

OPERATOR $1$ OPERATOR $2$ OPERATOR $3$

Part$/$Trial $12$ Part$/$Trial $12$ Part$/$Trial $12$

$11\mathrm{.}5111\mathrm{.}51811\mathrm{.}5221\mathrm{.}49111\mathrm{.}4731\mathrm{.}502$

$21\mathrm{.}5011\mathrm{.}48021\mathrm{.}5101\mathrm{.}49521\mathrm{.}4881\mathrm{.}500$

$31\mathrm{.}4991\mathrm{.}48031\mathrm{.}4731\mathrm{.}54331\mathrm{.}5131\mathrm{.}453$

$41\mathrm{.}5101\mathrm{.}49141\mathrm{.}5251\mathrm{.}48941\mathrm{.}4791\mathrm{.}505$

$51\mathrm{.}4961\mathrm{.}48751\mathrm{.}5311\mathrm{.}45951\mathrm{.}4491\mathrm{.}521$

$61\mathrm{.}4751\mathrm{.}49361\mathrm{.}4951\mathrm{.}49261\mathrm{.}4941\mathrm{.}475$

$71\mathrm{.}5081\mathrm{.}48671\mathrm{.}4751\mathrm{.}47471\mathrm{.}4841\mathrm{.}455$

$81\mathrm{.}4861\mathrm{.}51981\mathrm{.}5261\mathrm{.}50881\mathrm{.}4941\mathrm{.}516$Problem $4-8$

NEW Gauge, Inc.

Gauge Repeatability and Reproducibility

This spreadsheet is designed for up to three operators, three trials, and ten parts. Enter data ONLY in yellow shaded cells.

Number of operators Upper specification limit Average range #DIV$/0!$

Number of trials Lower specification limit Range of operator averages #DIV$/0!$

Number of parts Range of part averages #DIV$/0!<---$ Note: This formula was modified to account for only $8$ parts being measured.

Data Operator $1$ Operator $2$ Operator $3$

Trial Trial Trial Part

Part # $123$ Average Range $123$ Average Range $123$ Average Range Average

$1$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$

$2$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$

$3$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$

$4$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$

$5$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$

$6$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$

$7$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$

$8$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$

$9$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$

$10$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$

Average #DIV$/0!$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$ #DIV$/0!$

$\%$ of Total Variation $\%$ of Tolerance Variance Ratios

Repeatability $($Equipment Variation$)-$ EV #N$/$A EV #N$/$A EV #N$/$A EV #N$/$A

Reproducibility $($Appraiser Variation$)-$ AV #DIV$/0!$ AV #DIV$/0!$ AV #DIV$/0!$ AV #DIV$/0!$

Repeatability and Reproducibility $-$ R&R #N$/$A R&R #N$/$A R&R #N$/$A R&R #N$/$A

Part Variation $-$ PV #DIV$/0!$ PV #DIV$/0!$ PV #DIV$/0!$ PV #DIV$/0!$

Total Variation $-$ TV #N$/$A

Upper control limit for individual ranges #DIV$/0!$

Note: any ranges beyond this limit may be the result

of assignable causes. Identify and correct. Discard

values and recompute statistics.

Do not modify these tables

Trials$/$Operators D$4$ K$1$ K$2$

$23\mathrm{.}274\mathrm{.}563\mathrm{.}65$

$32\mathrm{.}583\mathrm{.}052\mathrm{.}7$

Parts K$3$

$23\mathrm{.}65$

$32\mathrm{.}7$

$42\mathrm{.}3$

$52\mathrm{.}08$

$61\mathrm{.}93$

$71\mathrm{.}82$

$81\mathrm{.}74$

$91\mathrm{.}67$

$101\mathrm{.}62$