Generalized confidence intervals of quantile-based process capability indices for inverse Gaussian distribution

Process capability index (PCI) is widely used to evaluate the process capability in various industries. In this article, generalized confidence intervals (GCIs) of two widely used percentile-based PCIs for the inverse Gaussian (IG) distribution are constructed. Meanwhile, the GCI of the difference between two IG processes' PCIs is also considered. In addition, the performance of the proposed GCI is evaluated and compared with that of the confidence intervals based on the traditional bootstrap method. The simulation results indicate that the GCI outperforms the bootstrap counterparts in terms of the coverage probabilities, and the actual coverage probabilities of the GCI are sufficiently close to the target value. Finally, two real examples are presented to illustrate the implementation of the proposed method.

Automated summary

This article constructs generalized confidence intervals for two commonly used PCIs based on the inverse Gaussian distribution and considers the confidence interval for the difference between two inverse Gaussian processes' PCIs. The simulation results demonstrate that the proposed confidence interval outperforms the traditional bootstrap method in terms of coverage probabilities.