Modern and evolving technologies have revolutionized the fields of inspection and quality control. In high-quality production processes where events occur infrequently, it is essential to effectively monitor the time between events (TBE). This article introduces a new cumulative sum (CUSUM) monitoring scheme designed for discrete TBE data modeled using the Poisson distribution. The study extends the Gumbel bivariate exponential (GBE) model to a Gumbel bivariate Poisson (GBPO) model. The run length characteristics of the proposed MCUSUM (GBPO) chart are evaluated through Monte Carlo simulations and compared with existing control charts. Results indicate that the proposed chart outperforms current alternatives. Both real and simulated datasets are used to demonstrate the implementation and performance of the proposed method. Additionally, a brief comparison is provided between the proposed chart and those based on other members of the Archimedean copula family.
Talib et al. (Sat,) studied this question.