Yield-based process capability indices for nonnormal continuous data

Abstract

Process capability indices (PCIs) are widely used to assess whether an in-control process meets manufacturing specifications. In most applications of classical PCIs, the process characteristic is assumed normally distributed. However, the normal distribution has been found inappropriate in various applications. In the literature, the percentile-based PCIs are widely used to deal with the nonnormal process. One problem associated with the percentile-based PCIs is that they do not provide a quantitative interpretation to the process capability. In this study, new PCIs that have a consistent quantification to the process capability for both normal and nonnormal processes are proposed. The proposed PCIs are generalizations of the classical normal PCIs in the sense that they are the same as the classical PCIs when the process characteristic follows a normal distribution, and they offer the same interpretation to the process capability as the classical PCIs when the process characteristic is nonnormal. We then discuss nonparametric and parametric estimation of the proposed PCIs. The nonparametric estimator is based on the kernel density estimation and confidence limits are obtained by the nonparametric bootstrap, while the parametric estimator is based on the maximum likelihood estimation and confidence limits are constructed by the method of generalized pivots. The proposed methodologies are demonstrated using a real example from a manufacturing factory.

Keywords:

• confidence limits
• coverage probability
• kernel estimation
• nonparametric bootstrap

Acknowledgment

We are grateful to the editor and two referees for their insightful comments that have considerably improved the article.

Additional information

Funding

Bing Xing Wang was partially supported by the National Natural Science Foundation of China (grant 11371322, 11671303), the Zhejiang Provincial Natural Science Foundation of China (grant LY18G010003), and First Class Discipline of Zhejiang–A (Zhejiang Gongshang University–Statistics). Zhi-Sheng Ye was partially supported by the National Natural Science Foundation of China (grant 71601138).

Notes on contributors

Piao Chen

Piao Chen received the B.E. degree in industrial engineering from Shanghai Jiao Tong University, China, in 2013, and the Ph.D. degree in industrial systems engineering and management from the National University of Singapore in 2017. He is currently a research scientist in the Institute of High Performance Computing, Singapore. His research interests include data analysis, reliability engineering and statistical inference.

Bing Xing Wang

Bing Xing Wang received the B.S. degree in mathematics from East China Normal University, Shanghai, China in 1985, and the M.S. degree in Statistics from the East China Normal University in 1990. He is currently a Professor with the Department of Statistics, Zhejiang Gongshang University. His research interests include reliability engineering, and quality control.

Zhi-Sheng Ye

Zhi-Sheng Ye received the joint B.E. degree in material science and engineering and economics from Tsinghua University, Beijing, China in 2008, and the Ph.D. degree in industrial and systems engineering from the National University of Singapore in 2012. He is currently an Assistant Professor with the Department of Industrial Systems Engineering and Management, National University of Singapore. His research interests include reliability engineering, complex systems modeling, and industrial statistics.