No abstract

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 , 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.