Parametric bootstrap process capability index control charts for both mean and dispersion

Abstract

Non-normal processes are common in practice. In this paper, we propose a novel approach to defining bootstrap process capability index (PCI) control charts to monitor the performance of in-control skew normal processes. We use a bootstrap method to calculate phase I control limits of the corresponding PCI control charts. The β-risk curves of the associated PCI control charts will be used to assess the performance of the PCI control charts. We use Monte-Carlo simulation to evaluate the performance of the proposed PCI control charts. A numerical example to illustrate the implementation of the proposed control charts.

Keywords:

• Process capability index
• control charts
• statistical quality control
• Bootstrap
• Monte-Carlo simulation
• β-risk
• average run length (ARL)

Acknowledgements

The authors are grateful to the reviewer’s insightful comments on the simulation study that have improved presentation significantly.

ORCID

Jiaqing Xu http://orcid.org/0000-0002-1539-5418

Cheng Peng http://orcid.org/0000-0002-0618-7887

Additional information

Funding

Xu acknowledges the partial support of the Collaborative Strategic Research Program between Ningbo Municipal City and Chinese Academy of Social Science (NZKT201712) and a Program Innovation and Pedagogical Research Fund from Zhejiang Province (KG20160460). Peng thanks to the Center of Data Engineering at Ningbo University of Technology for facilitating this collaborative research while he was on sabbatical leave from the University of Southern Maine in the spring of 2017.