We present XEM, an eXplainable-by-design Ensemble method for Multivariate time series classification. XEM relies on a new hybrid ensemble method that combines an explicit boosting-bagging approach to handle the bias-variance trade-off faced by machine learning models and an implicit divide-and-conquer approach to individualize classifier errors on different parts of the training data. Our evaluation shows that XEM outperforms the state-of-the-art MTS classifiers on the public UEA datasets. Furthermore, XEM provides faithful explainability-by-design and manifests robust performance when faced with challenges arising from continuous data collection (different MTS length, missing data and noise).