Adaptive control charts for skew‐normal distribution
Adaptive control charts for skew‐normal distribution
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DOI：
10.1002/qre.2274
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发表时间：
2018-06
影响因子：
2.3
通讯作者：
Jyun-You Chiang;Tzong-Ru Tsai;Nan-Cheng Su
中科院分区：
文献类型：
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作者：
Jyun-You Chiang;Tzong-Ru Tsai;Nan-Cheng Su
标准休哈特X图，称为FSS-X图，已被广泛用于通过实施固定样本和采样频率方案来检测过程的平均漂移。FSS-X图表可能对正态分布假设很敏感，在捕捉过程平均值中的小或中等变化时效率较低。为了监控非正态分布的变量，Li等人[Commun Stat-Theology Meth.2014；43(23)：4908-4924]扩展了对蔡英文的研究[Int J Reliab Qual Saf Eng.2007；14(1)：49-63]为SN分布提供具有精确控制限制的新的偏态正态FSS-X(SN FSS-X)图。为了提高SN FSS-X图对检测过程中微小或中等均值漂移的灵敏度，本研究引入了具有可变采样间隔(VSI)、可变样本量(VSS)和可变样本量和采样间隔(VSSI)的自适应X图来进行SN分布。所提出的自适应控制图包括正态自适应图作为特例。仿真结果表明，所有提出的SN VSI-X、SN VSS-X和SN VSSI-X图表在检测过程均值的小或中等偏移方面都优于SN FSS-X图表。文中还讨论了模型错误对使用所提出的自适应图表的影响，以及使用FSS-X图表监测SN数据平均值的样本量影响。以偏光片制造过程中的单色值为例，说明了所提出的自适应图表的应用。
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 FSS‐ X¯ 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.