Q$2$: $(15$ pts$)$

A typical gauge R&R experiment is shown in the table. A gauge is used to measure a critical dimension on a

part. The data was collected by the same inspector with five different test units. Each part was measured twice

in order to evaluate the gauge capability. Use the data to answer the following questions.

$($a$)$ Estimate the repeatability of the gauge, ${}_{\text{r}\text{e}\text{p}\text{e}\text{a}\text{t}\text{i}\text{b}\text{i}\text{l}\text{i}\text{t}\text{y}}^2={}_{\text{g}\text{a}\text{u}\text{g}\text{e}}^2.(5$ pts$)$

Sigma$-$guage $=(R\frac{-}{b}ar\frac{?}{d2})=(\frac{1\mathrm{.}2}{1\mathrm{.}128})=1\mathrm{.}0638$

$($b$)$ If the product specifications are at $LSL=5$ and USL$=60,$ Calculate the $\frac{P}{T}$ ratio using $k=6(3$ pts$).$ Will

you recommend the gauge system, why? $(2$ pts$)$

$\frac{P}{T}$ ratio $=6^{**}\frac{1\mathrm{.}0638}{55}=0\mathrm{.}1161$

$\frac{P}{T}$ ratio $>0\mathrm{.}1,$

$($c$)$ It is known that ${}_{\text{T}\text{o}\text{t}\text{a}\text{l}}^2=10.$ Suppose that the total variance comes only from ${}_{\text{P}\text{a}\text{r}\text{t}}^2$ and ${}_{\text{G}\text{a}\text{u}\text{g}\text{e}}^2.$

Calculate the discrimination ratio $($DR$)$ where $DR=\frac{1+{}_P}{1-{}_P}$ and ${}_P=\frac{{}_{\text{P}\text{a}\text{r}\text{t}}^2}{{}_{\text{T}\text{o}\text{t}\text{a}\text{l}}^2}.(5$ pts$)$

${}_{\text{P}\text{a}\text{r}\text{t}}^2=10-{1\mathrm{.}0638}^{{?}^{{?}^{?}}}2=8\mathrm{.}8683$

${}_P=\frac{8\mathrm{.}8683}{10}=0\mathrm{.}88683$

$DR=\frac{1+0\mathrm{.}88683}{1-0\mathrm{.}88683}=16\mathrm{.}67253$

APPENDIX VI

Factors for Constructing Variables Control Charts