On the performance of different capability indices under normal and non-normal distributions

Abstract

In this article, we have examined the performance of some useful capability indices using normal and non-normal distributions. The confidence intervals are calculated and mean coverage rates are observed for different capability indices. The effects of symmetry and kurtosis of parent distributions are examined on the mean coverage rates of different capability indices. Moreover, we have investigated the robustness (of confidence interval) using the median and percentile-based indices. We have considered the well-known distributions including normal, gamma, t, Weibull, and chi-squared. For these process scenarios, we have observed that some indices resist disturbance only in symmetry of the parent distribution, some resist the disturbance in symmetry and kurtosis of the distribution, and some indices don’t resist against either type of disturbance.

Keywords:

• Capability indices
• confidence intervals
• coverage rates
• kurtosis
• normality
• non-normality
• skewness

Acknowledgments

The authors are thankful to the anonymous reviewer for the constructive comments that helped in improving the last version of the paper. The author Muhammad Riaz is also indebted to King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, for providing excellent research facilities and environment.