Question

A precision parts manufacturer produces bolts for use in military aircraft. The specifications for bolt length are 37.50 plus/minus 0.25 cm. The company has established an x-bar chart and an R-chart using samples of size five. The center lines for the x-bar chart and R-chart are set at 37.35 cm and 1.05 cm, respectively. What is the value of Cpk for this process?

Answer 1

Answer:

Please see the attached Picture for the complete answer.

Explanation:

Answer 2

Answer:

cpk = 0.03

Explanation:

Cpk is a process capability index used to measure the production capability of a process. Cpk does not use the assumption that the process mean is centered between the specification limits. Assuption of the Cpk is based that the measurements are normally distributed. The formula of cpk is given as:

$cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu-LSL}{3\sigma})$

Where:

USL = upper bound, LSL = lower bound, μ = mean, σ = standard deviation

Given that:

The center lines for the x-bar chart and R-chart are set at 37.35 cm and 1.05 cm, Therefore, μ = 37.35 cm and σ = 1.05 cm

The specifications for bolt length are 37.50 ± 0.25 cm

USL = 37.5 + 0.25 = 37.75 cm

LSL  = 37.5 - 0.25 = 37.25 cm

Substituting:

$cpk=min(\frac{37.75-37.35}{3*1.05}, \frac{37.35-37. 5}{3*1.05})= min(0.13,0.03)=0.03$

cpk = 0.03