Robust confidence intervals for the process capability index C_pk with bootstrap improvement

The process capability index (PCI), C-pk, one of the widely used tools for assessing the capability of a manufacturing process, expresses the deviation of the process mean from the midpoint of the specification limits. The C-pk is known to perform well under the general assumption that the experimental data are normally distributed without contamination. Under this assumption, the sample mean and sample standard deviation are used for the estimation of the PCI. However, the sample mean and sample standard deviation are quite sensitive to data contamination and this will result in underperformance of C-pk. Therefore, in this article, we propose alternatives to the conventional method by replacing the sample mean and sample standard deviation with robust location and scale estimators. We also propose a method for constructing a robust PCI C-pk confidence interval which lends itself to robust statistical hypothesis testing. The robust hypothesis testing methods based on this confidence interval are shown to be quite efficient when the data are normally distributed yet also outperform the conventional method when data contamination exists.