Uses of a new asymmetric loss-based process capability index in the electronic industries

Abstract

This article suggests a novel process capability index (PCI) termed as ${\mathcal{S}}_{pk}^{″}$, which is based on an asymmetric loss function (linear exponential) for a normal process and offers a specific method of incorporating the loss in capability analysis. Next, we estimate the suggested PCI using the moment estimation approach when the process follows a normal distribution, and we compare the effectiveness of the investigated estimation methods in terms of their mean squared errors through simulation analysis. Additionally, the confidence intervals for the index ${\mathcal{S}}_{pk}^{″}$ are constructed using the generalized confidence interval (GCI) and parametric bootstrap confidence interval (BCI) approach. Using Monte Carlo simulation, the performance of the GCI and BCI is compared in terms of average width, associated coverage probabilities, and relative coverage. Finally, three real data sets from the electronic industries are re-analyzed to show the usefulness of the suggested index, MOM estimation, GCI and BCI.

Keywords:

• Loss function
• point and interval estimation
• process capability index

Acknowledgments

The author thank the Editor and the Reviewer for their very careful reading and constructive comments which helped me to improve the earlier version of this article. This work was supported by the Dept. of Statistics under the School of Mathematics, Statistics and Computational Sciences of Central University of Rajasthan.

Author’s contributions

The author read and agreed to the published version of the manuscript.

Data Availability Statement

All data analyzed during this study are included in this published articles: Chen and Tong (2003) and Peng (2010). The link of the data sets used in this study are included within the article, and data sets are also provided in the article.

Disclosure Statement

The author declare that he has no conflict of interest.

Additional information

Funding

This research received no external or internal funding.