ABSTRACT Due to advances in technology, sampling procedures and short lag times between successive sampling, autocorrelation among the measured data has become common in most applications. Neglecting autocorrelation leads to a poor false alarm performance. In the current paper, the effect of the autocorrelation on the performance of a variable-parameters multivariate single control chart is investigated in the case of the simultaneous monitoring of the mean and variability. At first, formulas for the sample mean and variability of a multivariate autoregressive-moving average process are derived. Then, a variable-parameters single control chart is developed for the simultaneous monitoring of the mean vector and the covariance matrix of an autocorrelated multivariate normal process. Next, the performance of the proposed control chart is evaluated by using eight performance measures based on a dedicated Markov chain model. Finally, by presenting an illustrative example, the application of the proposed scheme is demonstrated in practice.

中文翻译：

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用于同时监测自相关多元正态过程的均值和变异性的自适应可变参数方案

摘要 由于技术进步、采样程序和连续采样之间的短滞后时间，测量数据之间的自相关在大多数应用中变得普遍。忽略自相关会导致较差的误报性能。在当前的论文中，在同时监测均值和变异性的情况下，研究了自相关对可变参数多元单一控制图性能的影响。首先，推导出多元自回归移动平均过程的样本均值和变异性的公式。然后，开发了一个可变参数单一控制图，用于同时监测自相关多元正态过程的均值向量和协方差矩阵。下一个，通过使用基于专用马尔可夫链模型的八种性能度量来评估所提出的控制图的性能。最后，通过给出一个说明性的例子，在实践中证明了所提出方案的应用。