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首页> 外文期刊>AStA Advances in statistical analysis >Comparison of joint control schemes for multivariate normal i.i.d. output
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Comparison of joint control schemes for multivariate normal i.i.d. output

机译：多元正态i.d.联合控制方案的比较输出

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摘要

The performance of a product frequently relies on more than one quality characteristic. In such a setting, joint control schemes are used to determine whether or not we are in the presence of unfavorable disruptions in the location () and spread (sigma) of a vector of quality characteristics. A common joint scheme for multivariate output comprises two charts: one for based on a weighted Mahalanobis distance between the vector of sample means and the target mean vector; another one for sigma depending on the ratio between the determinants of the sample covariance matrix and the target covariance matrix. Since we are well aware that there are plenty of quality control practitioners who are still reluctant to use sophisticated control statistics, this paper tackles Shewhart-type charts for and sigma based on three pairs of control statistics depending on the nominal mean vector and covariance matrix, 0 and sigma 0. We either capitalize on existing results or derive the joint probability density functions of these pairs of control statistics in order to assess the ability of the associated joint schemes to detect shifts in or sigma for various out-of-control scenarios. A comparison study relying on extensive numerical and simulation results leads to the conclusion that none of the three joints schemes for and sigma is uniformly better than the others. However, those results also suggest that the joint scheme with the control statistics n (X) over bar- mu(0)) (inverted perpendicular) Sigma(-1)(0) ((X) over bar - mu(0)) and det ((n - 1) S) /det (Sigma(0)) has the best overall average run length performance.
机译：产品的性能通常取决于多个质量特征。在这种情况下，联合控制方案用于确定我们是否在质量特征向量的位置（）和散布（sigma）中存在不利的干扰。一种用于多变量输出的常见联合方案包括两个图表：一个用于基于样本均值向量与目标均值向量之间的加权Mahalanobis距离。 σ取决于样本协方差矩阵与目标协方差矩阵的行列式之比。由于我们知道很多质量控制从业人员仍然不愿意使用复杂的控制统计数据，因此本文根据名义平均矢量和协方差矩阵的三对控制统计数据处理了Shewhart型图表和sigma， 0和sigma0。我们要么利用现有结果，要么导出这些控制统计对的联合概率密度函数，以评估相关联的联合方案检测各种失控场景中的σ或σ的能力。依靠大量数值和模拟结果进行的比较研究得出的结论是，σ和σ的三个关节方案均没有一个总体上优于其他方案。但是，这些结果还表明，联合方案的控制统计为bar-mu（0）上的n（X））（垂直倒置）Sigma（-1）（0）（bar- mu（0）上的（X）） det（（n-1）S）/ det（Sigma（0））具有最佳的总体平均游程性能。

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