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:
[tex]cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu-LSL}{3\sigma})[/tex]
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:
[tex]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[/tex]
cpk = 0.03
