Question

A company making tires for bikes is concerned about the exact width of its cyclocross tires. The company has a lower specification limit of 22.8 mm and an upper specifica- tion limit of 23.2 mm. The standard deviation is 0.15 mm and the mean is 23 mm. What is the process capability index for the process?

Answer 1

\(\hat{C}_{p k}=\min \left[\frac{U S L-\hat{\mu}}{3 \hat{\sigma}}, \frac{\hat{\mu}-L S L}{3 \hat{\sigma}}\right]\)

where Cpk is the process capability index for the process, USL (23.2) and LSL(22.8) are upper and lower specification limits of the process, \(\mu\) is mean (23), \(\hat{\sigma}\) is the standard deviation(0.15). So by applying the formula, we get

Cpk = minimum of \(\left[(23.2-23) /\left(3^{*} 0.15\right),(23-22.8) /\left(3^{*} 0.15\right)\right]\)

\(=0.444\)