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Advanced multivariate cumulative sum control charts based on principal component method with application
Quality and Reliability Engineering International ( IF 2.3 ) Pub Date : 2021-04-22 , DOI: 10.1002/qre.2889
Muhammad Riaz 1 , Babar Zaman 2 , Rashid Mehmood 2 , Nasir Abbas 1 , Mu'azu Abujiya 3
Affiliation  

Existing multivariate cumulative sum (MCUSUM) control charts involve entire associated variables of a process to monitor variations in the mean vector. In this study, we have offered MCUSUM control charts with principal component method (PCM). The proposed MCUSUM control charts with PCM capture the whole process variations using fewer latent variables (principal components) while preserving as much data variability as possible. To show the significance of proposed MCUSUM control charts with PCM, various performance measures are considered including average run length, extra quadratic loss, relative average run length, and performance comparison index. Furthermore, performance measures are calculated through advanced Monte Carlo simulation method to explore the behavior of proposed MCUSUM control charts and to conduct comparative analysis with existing models. Results revealed that proposed MCUSUM control charts with PCM are efficient to detect variations timely by involving smaller number of principal components instead of considering entire associated variables. Also, proposed MCUSUM control charts have the ability to accommodate the features of existing control charts, which are illustrated as the special cases. Besides, to highlight the implementation mechanism and advantages of proposed MCUSUM control charts with PCM, a real-life example from wind turbine process is included.

中文翻译:

基于主成分法的高级多元累积和控制图及其应用

现有的多变量累积总和 (MCUSUM) 控制图涉及过程的整个相关变量,以监控平均向量的变化。在这项研究中,我们提供了主成分法 (PCM) 的 MCUSUM 控制图。建议的 MCUSUM 控制图与 PCM 使用较少的潜在变量(主成分)捕获整个过程的变化,同时保留尽可能多的数据可变性。为了显示提出的带有 PCM 的 MCUSUM 控制图的重要性,考虑了各种性能度量,包括平均运行长度、额外二次损失、相对平均运行长度和性能比较指数。此外,性能指标是通过先进的蒙特卡罗模拟方法计算的,以探索提议的 MCUSUM 控制图的行为,并与现有模型进行比较分析。结果表明,提出的带有 PCM 的 MCUSUM 控制图通过涉及较少数量的主成分而不是考虑整个相关变量,可以有效地及时检测变化。此外,提议的 MCUSUM 控制图能够适应现有控制图的特征,这些特征被说明为特殊情况。此外,为了突出使用 PCM 提出的 MCUSUM 控制图的实现机制和优势,还包括一个来自风力涡轮机过程的真实示例。结果表明,提出的带有 PCM 的 MCUSUM 控制图通过涉及较少数量的主成分而不是考虑整个相关变量,可以有效地及时检测变化。此外,提议的 MCUSUM 控制图能够适应现有控制图的特征,这些特征被说明为特殊情况。此外,为了突出使用 PCM 提出的 MCUSUM 控制图的实现机制和优势,还包括一个来自风力涡轮机过程的真实示例。结果表明,提出的带有 PCM 的 MCUSUM 控制图通过涉及较少数量的主成分而不是考虑整个相关变量,可以有效地及时检测变化。此外,提议的 MCUSUM 控制图能够适应现有控制图的特征,这些特征被说明为特殊情况。此外,为了突出使用 PCM 提出的 MCUSUM 控制图的实现机制和优势,还包括一个来自风力涡轮机过程的真实示例。
更新日期:2021-04-22
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