Exponentially distributed data are commonly encountered in high‐quality processes. Control charts dedicated to the univariate exponential distribution have been extensively studied by many researchers. In this paper, we investigate a multivariate cumulative sum (MCUSUM) control chart for monitoring Gumbel's bivariate exponential (GBE) data. Some tables are provided to determine the optimal design parameters of the proposed MCUSUM GBE chart. Furthermore, both zero‐state and steady‐state properties of the proposed MCUSUM GBE chart for the raw and the transformed GBE data are compared with the multivariate exponentially weighted moving average (MEWMA) chart and the paired individual cumulative sum (CUSUM) chart. The results show that the proposed MCUSUM GBE chart outperforms the other two types of control charts for most shift domains. In addition, an extension to Gumbel's multivariate exponential (GME) distribution is also investigated. Finally, an illustrative example is provided in order to explain how the proposed MCUSUM GBE chart can be implemented in practice.

中文翻译：

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用于监视Gumbel的双变量指数数据的多元CUSUM控制图

高质量过程中通常会遇到指数分布的数据。许多研究人员已经广泛研究了专门针对单变量指数分布的控制图。在本文中，我们研究了用于监控Gumbel的双变量指数（GBE）数据的多变量累积和（MCUSUM）控制图。提供了一些表来确定建议的MCUSUM GBE图表的最佳设计参数。此外，针对原始和转换后的GBE数据，将建议的MCUSUM GBE图表的零状态和稳态属性与多元指数加权移动平均值（MEWMA）图和成对的个体累积总和（CUSUM）图进行比较。结果表明，对于大多数移位域，拟议的MCUSUM GBE图表优于其他两种类型的控制图。此外，还研究了Gumbel多元指数（GME）分布的扩展。最后，提供了一个说明性示例，以说明如何在实践中实现建议的MCUSUM GBE图。