A precision parts manufacturer produces bolts for use in military aircraft. The specifications for bolt length are $ 37.50 \pm 0.25 \mathrm{~cm} $. The company has established an $ \bar{x} $-chart and an $ R $-chart using samples of size five. The centerlines for the $ \bar{x} $ chart and $ R $-chart are set at $ 37.65 \mathrm{~cm} $ and $ 1.03 \mathrm{~cm} $, respectively. What is the value of $ C_{p} $ for this process?

A) 0.188
B) 1.333
C) 0.301
D) 0.166

Question

A precision parts manufacturer produces bolts for use in military aircraft. The specifications for bolt length are

37.50 \pm 0.25 \mathrm{~cm}

. The company has established an

\bar{x}

-chart and an

R

-chart using samples of size five. The centerlines for the

\bar{x}

chart and

R

-chart are set at

37.65 \mathrm{~cm}

and

1.03 \mathrm{~cm}

, respectively. What is the value of

C_{p}

for this process?

A) 0.188
B) 1.333
C) 0.301
D) 0.166

Quizplus · Accepted Answer

The value of $ C_{p} $ is calculated as:$$C_{p} = \frac{USL - LSL}{6\sigma}$$where $ USL $ is the upper specification limit, $ LSL $ is the lower specification limit, and $ \sigma $ is the standard deviation of the process.In this case, $ USL = 37.75 \mathrm{~cm} $, $ LSL = 37.25 \mathrm{~cm} $, and $ \sigma = R/d_{2} = 1.03 \mathrm{~cm} / 2.326 = 0.443 \mathrm{~cm} $. Therefore,$$C_{p} = \frac{37.75 - 37.25}{6(0.443)} = 0.188$$

A Precision Parts Manufacturer Produces Bolts for Use in Military 37.50±0.25 cm 37.50 \pm 0.25 \mathrm{~cm} 37.50±0.25 cm

A Precision Parts Manufacturer Produces Bolts for Use in Military $37.50 \pm 0.25 \mathrm{~cm}$