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Fault detection has been recognized in the semiconductor industry as an effective component of advanced process control framework in increasing yield and product quality. Principal component analysis (PCA) has been applied widely to semiconductor manufacturing process monitoring. However, the unique characteristics of semiconductor processes - high dimension of data, nonlinearity in most batch processes, and multimodal batch trajectories due to multiple operating conditions - significantly limit applicability of PCA to semiconductor manufacturing. This paper proposes a manifold learning algorithm, local and nonlocal preserving projection (LNPP), for feature extraction. Different from PCA, which aims to discover the global structure of Euclidean space, LNPP can find a good linear embedding that preserves local and nonlocal information. This may enable LNPP to find meaningful low-dimensional information hidden in high-dimensional observations. The Gaussian mixture model (GMM) is applied to handle process data with nonlinearity or multimodal features. GMM-based Mahalanobis distance is proposed to assess process states, and a Bayesian inference-based method is proposed to provide the process failure probability. A variable replacing-based contribution analysis method is developed to identify the process variables that are responsible for the onset of process fault. The proposed monitoring model is demonstrated through its application to a batch semiconductor etch process.