Accurate fault prognosis is of vital importance for condition-based maintenance. As to complex mechanical systems, multiple sensors are often used to collect condition signals and the observation process may rather be non-Gaussian and non-stationary. Traditional hidden semi-Markov models cannot provide adequate representation for multivariate non-Gaussian and non-stationary time series. The innovation of this article is to extend classical hidden semi-Markov models by modeling the observation as a linear mixture of non-Gaussian multi-sensor signals. The proposed model is called as a multi-sensor mixtured hidden semi-Markov model. Under this new framework, modified parameter re-estimation algorithms are derived in detail based on the complete-data expectation maximization algorithm. In the end the proposed prognostic methodology is validated on a practical bearing application. The experimental results show that the proposed method is indeed promising to obtain better prognostic performance than classical hidden semi-Markov models.