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20 July 2025

参数估计对二项分布 CUSUM 控制图的性能影响分析

鑫越 苏1 薇 杨2 久军 张1
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1 辽宁大学 数学与统计学院, 中国
2 鞍山师范学院 数学院, 中国
ASDS 2025 , 1(5), 97–101; https://doi.org/10.61369/ASDS.2025050020
© 2025 by the Author. Licensee Art and Design, USA. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC BY-NC 4.0) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

传统控制图大都是基于参数已知的假设,当参数未知时需要通过历史数据来进行估计,但估计的误差会对控制图的性能产生一定影响.基于此,本文考虑了参数估计对检测二项分布的CUSUM控制图的性能影响,通过蒙特卡洛模拟方法,得到在不同的历史样本数量条件下的平均运行长度.考查了受控与失控下控制图的性能表现,并通过调整控制线得到给定的平均运行长度。

Keywords
CUSUM控制图
样本量
二项分布
参数估计
References

[1]WalterAShewhart.  Some applications of statistical methods to the analysis of physical and engineering data.  Bell System  Technical Journal, 3(1):43–87, 1924.
 [2]Ewan S Page.  Continuous inspection schemes.  Biometrika, 41(1/2):100–115, 1954.
 [3]Stuart W Roberts.  Control chart tests based on geometric moving averages.  Technomet- rics, 42(1):97–101, 2000.
 [4]James M Lucas. Cumulative sum (cusum) control schemes. Communications in Statistics.
 [5]FF Gan. An optimal design of cusum control charts for binomial counts. Journal of. 
[6]Willis A Jensen, L Allison Jones-Farmer, Charles W Champ, and William H Woodall. Effects of parameter estimation on control chart properties: A literature review.  Quality control and applied statistics, 52(3):245–248, 2007.
 [7]Stelios  Psarakis,  Angeliki  K Vyniou,  and  Philippe  Castagliola.   Some  recent  develop- ments on the effects of parameter estimation on control charts. Quality and Reliability Engineering International, 30(8):1113–1129, 2014.
 [8]Ronald JMM Does, Rob Goedhart, and William H Woodall.  On the design of control charts with guaranteed conditional performance under estimated parameters. Quality and Reliability Engineering International, 36(8):2610–2620, 2020.
 [9] 陶桂洪,宋贽,刘强.基于参数估计的CUSUM质量控制图性能分析[J].大连工业大学学报,2018,37(06):489-496.
 [10]Fan Yi and Peihua Qiu. An adaptive cusum chart for drift detection. Quality and Reliability Engineering International, 38(2):887–894, 2022.

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