Analyzing the reliability of autonomous ships has recently attracted attention mainly due to epistemic uncertainty (lack of knowledge) integrated with automatic operations in the maritime sector. The advent of new random failures with unrecognized failure patterns in autonomous ship operations requires a comprehensive reliability assessment specifically aiming at estimating the time in which the ship can be trusted to be left unattended. While the reliability concept is touched upon well through the literature, the operational trustworthiness needs more elaboration to be established for system safety, especially within the maritime sector. Accordingly, in this paper, a probabilistic approach has been established to estimate the trusted operational time of the ship machinery system through different autonomy degrees. The uncertainty associated with ship operation has been quantified using Markov Chain Monte-Carlo simulation from likelihood function in Bayesian inference. To verify the developed framework, a practical example of a machinery plant used in typical short sea merchant ships is taken into account. This study can be exploited by asset managers to estimate the time in which the ship can be left unattended. Keywords: reliability estimation, Bayesian inference, autonomous ship, uncertainty.