Estimation and statistical process control are performed under copula-based time-series models. Available are statistical methods in Long and Emura (2014 JCSA), Emura et al. (2017 Commun Stat-Simul) <DOI:10.1080/03610918.2015.1073303>, Huang and Emura (2021 Commun Stat-Simul) <DOI:10.1080/03610918.2019.1602647>, Lin et al. (2021 Comm Stat-Simul) <DOI:10.1080/03610918.2019.1652318>, Sun et al. (2020 JSS Series in Statistics)<DOI:10.1007/978-981-15-4998-4>, and Huang and Emura (2021, in revision).