Inference for the Process Performance Index of Products on the Basis of Power-Normal Distribution

Jianping Zhu, Hua Xin, Chenlu Zheng and Tzong-Ru Tsai
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Jianping Zhu: School of Management, Xiamen University, Xiamen 361005, China
Hua Xin: School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China
Chenlu Zheng: School of Management, Xiamen University, Xiamen 361005, China
Tzong-Ru Tsai: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan

Mathematics, 2021, vol. 10, issue 1, 1-14

Abstract: The process performance index (PPI) can be a simple metric to connect the conforming rate of products. The properties of the PPI have been well studied for the normal distribution and other widely used lifetime distributions, such as the Weibull, Gamma, and Pareto distributions. Assume that the quality characteristic of product follows power-normal distribution. Statistical inference procedures for the PPI are established. The maximum likelihood estimation method for the model parameters and PPI is investigated and the exact Fisher information matrix is derived. We discuss the drawbacks of using the exact Fisher information matrix to obtain the confidence interval of the model parameters. The parametric bootstrap percentile and bootstrap bias-corrected percentile methods are proposed to obtain approximate confidence intervals for the model parameters and PPI. Monte Carlo simulations are conducted to evaluate the performance of the proposed methods. One example about the flow width of the resist in the hard-bake process is used for illustration.

Keywords: bootstrap methods; maximum likelihood estimation; Monte Carlo simulation; process performance index; power-normal distribution; quality control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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