The effect of measurement errors on the performance of adaptive control charts has rarely been investigated in the univariate case and, as far as we know, it has not been investigated at all in the multivariate case. In this paper, we evaluate the effect of measurement errors on the VSS (Variable Sample Sizes) Hotelling’s T² control chart. To do so, we suggest using six different performance measures: (i) the average and (ii) the standard deviation of the run length, (iii) the average and (iv) the standard deviation of the number of observations to signal, (v) the average and (vi) the standard deviation of the number of switches to signal. These performance measures should be as small as possible when the process is out-of-control to ensure an optimal chart efficiency. We use two models for defining the objective function which includes at least one of these performance measures. We find the optimal values of the sample sizes and the overall performance measures for each model and for different values of the measurement errors variance, the numbers of measurements and the values of the error model’s constants. Finally, we present an illustrative example to show the application of the proposed method.

在单变量情况下很少研究测量误差对自适应控制图性能的影响，据我们所知，在多变量情况下根本没有研究过。在本文中，我们评估了测量误差对Hotelling T ²的VSS（可变样本大小）的影响控制图。为此，我们建议使用六种不同的性能指标：（i）平均值和（ii）行程长度的标准偏差，（iii）平均值和（iv）观测信号的数量的标准偏差，（ v）信号开关数量的平均值和（vi）标准偏差。当流程失控时，这些性能指标应尽可能小，以确保最佳图表效率。我们使用两个模型来定义目标函数，其中至少包括这些绩效指标之一。我们找到每个模型的样本大小和总体性能指标的最佳值，以及不同的测量误差方差，测量次数和误差模型常数的值。最后，