Residual-based cumulative sum charts to monitor time series of counts via copula-based Markov models

Abstract

Several scientific observations produce data that consist of serially dependent counts that are difficult to accurately analyze due to the absence of normality and the limited literature on dealing with such data. In this article, we propose a cumulative sum chart to monitor serially dependent counts using copula-based Markov models. After reviewing such models, we introduce the randomized quantile residuals obtained from the Markov process. The proposed method is evaluated using a comprehensive simulation study and a real-life example. Results suggested that the method is effective and easily implemented.