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ABSTRACTA self-starting process mean monitoring scheme is needed in applications with short production runs or processes subject to degradation. The major challenge in implementing a self-starting monitoring scheme is that there exists little or no historical in-control data to accurately estimate in-control process parameters. In this paper, we propose a new Bayesian self-starting monitoring scheme to detect on-line whether a process mean has exceeded a pre-determined critical threshold. We assume the process is subject to various types of random drift and random jumps prior to exceeding a critical threshold. In comparison with existing self-starting Bayesian schemes in the literature, our model is more flexible in capturing various types of trends and requires less knowledge of process parameters. In addition, the proposed monitoring scheme is much more computationally efficient, rendering it much more applicable for numerous practical situations where model parameter information is limited and timely detection of a critical event is crucial. Numerical studies based on simulated signals and several real data sets are used to evaluate the performance of the proposed method and compare with existing methods in the literature. The proposed method is shown to be less sensitive to parameter misspecification, more flexible in capturing various trends in the data, and much more computationally efficient.