Abstract

Performance of any control scheme in Phase II depends directly on the quality of estimators utilized in Phase I. In practice, outliers could be present in the data which would impact the performance of estimators adversely. This study deals with robust parameter estimation and monitoring linear profiles in the presence of outliers and compares the results with the least squares (LS) estimators. For this purpose, M-estimators are used as robust estimators and empirical distributions for related statistics are determined using Mont Carlo simulation to calculate control limits for two $T^2$ control charts and for codding independent variable method. Using a numerical example, profile parameters are estimated by ordinary least squares and M-estimators and the resulting statistics are monitored by two $T^2$ control schemes. Phase II control charts are determined based on the two types of estimators and compared for different out of control profiles. Empirical distributions did not follow their exact distributions obtained by least squares method. Simulation results confirm that M-estimators lead to better estimates in comparison to LS estimators and also improves classification performance. Robust estimators also lead to improvement in ARL performance in comparison to LS estimators.

摘要

阶段 II 中任何控制方案的性能直接取决于阶段 I 中使用的估计器的质量。在实践中，数据中可能存在异常值，这将对估计器的性能产生不利影响。本研究处理存在异常值的稳健参数估计和监测线性曲线，并将结果与​​最小二乘 (LS) 估计量进行比较。为此，M 估计量用作稳健的估计量，相关统计量的经验分布使用蒙特卡罗模拟来计算两个控制限${吨}^2$控制图和用于编码自变量的方法。使用数值示例，轮廓参数由普通最小二乘和 M 估计器估计，所得统计数据由两个${吨}^2$控制方案。第二阶段控制图是根据两种类型的估计量确定的，并针对不同的失控曲线进行比较。经验分布不遵循通过最小二乘法获得的精确分布。仿真结果证实，与 LS 估计器相比，M 估计器可以产生更好的估计，并且还提高了分类性能。与 LS 估计器相比，稳健的估计器还可以提高 ARL 的性能。