Adaptive control charts for skew-normal distribution

被引:9
|
作者
Chiang, Jyun-You [1 ]
Tsai, Tzong-Ru [2 ]
Su, Nan-Cheng [3 ]
机构
[1] Southwestern Univ Finance & Econ, Sch Stat, Chengdu 610074, Sichuan, Peoples R China
[2] Tamkang Univ, Dept Stat, New Taipei 25137, Taiwan
[3] Natl Taipei Univ, Dept Stat, New Taipei 23741, Taiwan
关键词
adaptive control charts; average run length; cumulative sum charts; exponentially weighted moving average charts; Markov chain approach; VARIABLE SAMPLE-SIZE; AVERAGE CONTROL SCHEMES; ECONOMIC DESIGN; (X)OVER-BAR CHARTS; INTERVALS;
D O I
10.1002/qre.2274
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The standard Shewhart-type X chart, named FSS-X chart, has been widely used to detect the mean shift of process by implementing fixed sample and sampling frequency schemes. The FSS-X chart could be sensitive to the normality assumption and is inefficient to catch small or moderate shifts in the process mean. To monitor nonnormally distributed variables, Li et al [Commun Stat-Theory Meth. 2014; 43(23): 4908-4924] extended the study of Tsai [Int J Reliab Qual Saf Eng. 2007; 14(1): 49-63] to provide a new skew-normal FSS-X (SN FSS-X) chart with exact control limits for the SN distribution. To enhance the sensitivity of the SN FSS-X chart on detecting small or moderate mean shifts in the process, adaptive X charts with variable sampling interval (VSI), variable sample size (VSS), and variable sample size and sampling interval (VSSI) are introduced for the SN distribution in this study. The proposed adaptive control charts include the normality adaptive charts as special cases. Simulation results show that all the proposed SN VSI-X, SN VSS-X, and SN VSSI-X charts outperform the SN FSSX chart on detecting small or moderate shifts in the process mean. The impact of model misspecification on using the proposed adaptive charts and the sample size impact for using the FSS-X chart to monitor the mean of SN data are also discussed. An example about single hue value in polarizer manufacturing process is used to illustrate the applications of the proposed adaptive charts.
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页码:589 / 608
页数:20
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