Quality improvement has been receiving great attention in industries. In recent years, the finite horizon process is commonly encountered in industries due to flexible manufacturing production. Past research works on finite horizon process monitoring are still limited. Because of this, three run rules Hotelling's T² charts are proposed to monitor a finite horizon process. The performance measures of the proposed charts are derived using the Markov-chain approach. The proposed schemes can serve as a framework for quality engineers who wish to perform process monitoring easily and efficiently. Numerical comparisons between the proposed and existing Shewhart (SH) T² charts have been made. The statistical performance measures were investigated in this article. The findings reveal that the proposed charts outperform the SH T² chart for detecting small and moderate process shifts in a finite horizon process. The illustration of the run rules (RR) T² chart is shown on a real manufacturing dataset in a finite horizon process.

中文翻译：

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一种改进的 Hotelling T2 图，用于基于运行规则方案监控有限范围过程：马尔可夫链方法

质量提升一直受到行业的高度重视。近年来，由于柔性制造生产，有限范围过程在工业中普遍存在。过去关于有限范围过程监测的研究工作仍然有限。因此，提出了三个运行规则 Hotelling 的T ^{2 控制}图来监控有限范围过程。建议图表的性能度量是使用马尔可夫链方法得出的。所提议的方案可以作为希望轻松有效地执行过程监控的质量工程师的框架。提议的和现有的 Shewhart (SH) T ²之间的数值比较图表已经制作完成。本文研究了统计性能指标。研究结果表明，在检测有限范围过程中的小和中等过程变化时，建议的控制图优于 SH T ^{2 控制}图。运行规则 (RR) T ²图的图示显示在有限范围过程中的真实制造数据集上。