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

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  • Jianping Zhu

    (School of Management, Xiamen University, Xiamen 361005, China
    Data Mining Research Center, 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
    Data Mining Research Center, Xiamen University, Xiamen 361005, China)

  • Tzong-Ru Tsai

    (Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan)

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.

Suggested Citation

  • Jianping Zhu & Hua Xin & Chenlu Zheng & Tzong-Ru Tsai, 2021. "Inference for the Process Performance Index of Products on the Basis of Power-Normal Distribution," Mathematics, MDPI, vol. 10(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:35-:d:709271
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    References listed on IDEAS

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    1. Hsiu-Mei Lee & Jong-Wuu Wu & Chia-Ling Lei & Wen-Liang Hung, 2011. "Implementing lifetime performance index of products with two-parameter exponential distribution," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(8), pages 1305-1321.
    2. Wu, Shu-Fei & Lin, Ying-Po, 2016. "Computational testing algorithmic procedure of assessment for lifetime performance index of products with one-parameter exponential distribution under progressive type I interval censoring," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 79-90.
    3. Lee, Wen-Chuan & Wu, Jong-Wuu & Hong, Ching-Wen, 2009. "Assessing the lifetime performance index of products from progressively type II right censored data using Burr XII model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2167-2179.
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    Cited by:

    1. Heba F. Nagy & Amer Ibrahim Al-Omari & Amal S. Hassan & Ghadah A. Alomani, 2022. "Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data," Mathematics, MDPI, vol. 10(21), pages 1-19, November.

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