Abstract

A profile is a relationship between the response variable(s) and the independent variable(s), which describes the quality of a process or product. The profile can be monitored by a process control chart, which is an important tool in the statistical process control. Using the robust estimators in monitoring profiles in the presence of contamination is so effective, and it improves the efficiency of a control chart in detecting any sustained shift in phase II. In this research, a novel robust control chart is proposed for monitoring multiple linear profiles using two robust estimate methods. In the proposed robust control chart, the parameters of a multiple linear profile are estimated using the M-estimator and the Fast-τ-estimator. Also, the efficiency of the proposed robust control chart is evaluated by means of ARL criterion and compared to the classic control chart in phase II. The results of simulation studies show that the proposed robust control chart performs as well as the classic control chart in the absence of contamination, while in the presence of contamination, it can detect the shifts quicker than the classical one. Moreover, the proposed robust control chart using Fast-τ-estimator and M-estimator performs better in low and high contamination, respectively.

摘要

概况是响应变量和自变量之间的关系，它描述了过程或产品的质量。可以通过过程控制图来监控轮廓，这是统计过程控制中的重要工具。在存在污染的情况下使用稳健的估计器监测剖面非常有效，它提高了控制图在检测第二阶段任何持续变化方面的效率。在这项研究中，提出了一种新颖的鲁棒控制图，用于使用两种鲁棒估计方法监测多个线性轮廓。在所提出的鲁棒控制图中，使用 M 估计器和 Fast-τ 估计器来估计多线性轮廓的参数。还，所提出的鲁棒控制图的效率通过ARL准则评估，并与第二阶段的经典控制图进行比较。仿真研究结果表明，所提出的鲁棒控制图在没有污染的情况下表现与经典控制图一样好，而在存在污染的情况下，它可以比经典控制图更快地检测到偏移。此外，所提出的使用 Fast-τ 估计器和 M 估计器的鲁棒控制图分别在低污染和高污染中表现更好。