The combined effect of two real-world-occurring phenomena: ‘measurement errors’ and ‘autocorrelation between observations’ has rarely been investigated. In this paper, it will be investigated for the first time on ‘adaptive’ and/or ’simultaneous monitoring’ charts and also for the first time by using the multivariate linearly covariate measurement errors and VARMA (vector mixed autoregressive and moving average) autocorrelation models, and Markov chains-based performance measures. In addition, this paper for the first time proposes a skip-sampling strategy in an ARMA/VARMA model for alleviating the autocorrelation effect. To do so, we add the above-mentioned measurement errors and autocorrelation models to a recently developed adaptive max-type chart. Then, we develop a Markov chain model to compute the performance measures. After that, extensive numerical analyses will be performed to investigate their combined effect as well as some methods to alleviate their negative effects. Finally, an illustrative example involving a real industrial case will be presented.