The Shewhart-type RZ control chart for monitoring the ratio of autocorrelated variables
研究了在X和Y存在自相关和互相关时，用休哈特型RZ控制图监测比值Z=X/Y的性能，通过数值实验分析VAR(1)模型参数对控制图设计的影响，并给出炉工艺实例。
In many industrial manufacturing processes, the quality of products can depend on the relative amount between two quality characteristics X and Y. Often, this calls for the on-line monitoring of the ratio Z=X/Y as a quality characteristic itself by means of a control chart. A large number of control charts monitoring the ratio have been investigated in the literature under the assumption of independent normal observations of the two quality characteristics. In practice, due to the high frequency in sensor data collection, both autocorrelation and cross-correlation between consecutive observations can exist for X and Y and should be modelled to protect against the false alarm rate inflation when implementing a control chart for monitoring the ratio Z=X/Y. In this paper, we tackle this problem by investigating the performance of the Phase II Shewhart-type RZ control chart monitoring the ratio of two normal variables whose relationship is captured by a bivariate time series autoregressive model VAR(1), which can also account for the cross-correlation between the two quality characteristics. With the numerical study, we discuss how the design and the statistical performance of the Shewhart-type RZ control chart change with the VAR(1) model's parameters. We also provide an example to illustrate the use of the Shewhart-type RZ control chart with bivariate time series of observations in a furnace process.