In recent years, several techniques based on control charts have been developed for the simultaneous monitoring of the time interval T and the amplitude X of events, known as time‐between‐events‐and‐amplitude (TBEA) charts. However, the vast majority of the existing works have some limitations. First, they usually focus on statistics based on the ratio $\frac{X}{T}$, and second, they only investigate a reduced number of potential distributions, that is, the exponential distribution for T and the normal distribution for X. Moreover, until now, very few research papers have considered the potential dependence between T and X. In this paper, we investigate three different statistics, denoted as Z₁, Z₂, and Z₃, for monitoring TBEA data in the case of three potential distributions (gamma, normal, and Weibull), for both T and X, using copulas as a mechanism to model the dependence. An illustrative example considering times between machine breakdowns and associated maintenance illustrates the use of TBEA control charts.

中文翻译：

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评估Shewhart事件之间的时间和幅度控制图的相关数据

近年来，已经开发了几种基于控制图的技术，用于同时监视事件的时间间隔T和事件的幅度X，称为事件之间的时间和幅度（TBEA）图。但是，现有的绝大多数作品都有一定的局限性。首先，他们通常关注基于比率的统计数据$\frac{X}{Ť}$其次，他们仅研究数量减少的电位分布，即T的指数分布和X的正态分布。此外，到目前为止，很少有研究论文考虑过T和X之间的潜在依赖性。在本文中，我们研究了三种不同的统计量，分别表示为Z ₁，Z ₂和Z ₃，用于在T和X的三个潜在分布（伽玛，正态和威布尔）情况下监视TBEA数据。，使用copulas作为一种模型来建立依赖性。考虑机器故障和相关维护之间时间的说明性示例说明了TBEA控制图的使用。