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中国科学院大学学报 ›› 2024, Vol. 41 ›› Issue (6): 728-735.DOI: 10.7523/j.ucas.2023.001

• 数学与物理学 • 上一篇    

逆瑞利分布和对数逻辑分布下过程能力指数的区间估计

牟唯嫣1, 贾晓芳1, 熊世峰2   

  1. 1. 北京建筑大学理学院, 北京 100044;
    2. 中国科学院数学与系统科学研究院, 北京 100190
  • 收稿日期:2022-04-26 修回日期:2023-01-09 发布日期:2023-03-15
  • 通讯作者: 熊世峰,E-mail:xiong@amss.ac.cn
  • 基金资助:
    国家自然科学基金(12171462,11871033,11871294)和北京建筑大学研究生创新项目(PG2021018)资助

Interval estimation for the process capability index under the inverse Rayleigh and log-logistic distributions

MU Weiyan1, JIA Xiaofang1, XIONG Shifeng2   

  1. 1. College of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China;
    2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2022-04-26 Revised:2023-01-09 Published:2023-03-15

摘要: 讨论在逆瑞利分布和对数逻辑分布下一个重要的过程能力指数CNpk的统计推断问题。构造CNpk的广义枢轴量,然后提出其广义置信区间。数值结果表明,所提出的区间估计在覆盖率和区间长度方面比bootstrap方法具有更好的性能。

关键词: 广义枢轴量, 广义置信区间, 过程能力指数, 逆瑞利分布, 对数逻辑分布

Abstract: In this paper, we discuss the statistical inferential problem on an important process capability index CNpk under the inverse Rayleigh and log-logistic distributions. We construct the generalized pivotal quantities for CNpk, and subsequently the generalized confidence intervals proposed. Numerical results show that the proposed interval estimation performs better than the bootstrap method in terms of coverage rate and interval width.

Key words: generalized pivot quantity, generalized confidence interval, process capability indices, inverse Rayleigh distribution, log-logistic distribution

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