Complex industrial processes often have multiple operating modes and present time-varying behavior. The data in one mode may follow specific Gaussian or non-Gaussian distributions. In this paper, a numerically efficient moving window local outlier probability algorithm is proposed. Its key feature is the capability to handle complex data distributions and incursive operating condition changes including slow dynamic variations and instant mode shifts. First, a two-step adaption approach is introduced and some designed updating rules are applied to keep the monitoring model up-to-date. Then, a semi-supervised monitoring strategy is developed with an updating switch rule to deal with mode changes. Based on local probability models, the algorithm has a superior ability in detecting faulty conditions and fast adapting to slow variations and new operating modes. Finally, the utility of the proposed method is demonstrated with a numerical example and a non-isothermal continuous stirred tank reactor. Complex industrial processes often have multiple operating modes and present time-varying behavior. The data in one mode may follow specific Gaussian or non-Gaussian distributions. In this paper, a numerically efficient moving window local outlier probability algorithm is proposed. the capability to handle complex data distributions and incursive operating condition changes including slow dynamic variations and instant mode shifts; first two-step adapter approach is introduced and some designed updating rules are applied to keep the monitoring model up-to-date. Then , based on local probability models, the algorithm has a superior ability in detecting faulty conditions and fast adapting to slow variations and new operating modes. Finally, the utility of the proposed method is demonstrated with a numerical example and a non-isothermal continuous stirred tank r eactor.