Missing data commonly exists in industry processes, primarily due to sensor failures, signal transmission issues. Effective key performance indicator (KPI)-related fault detection for processes with missing data is essential for improving product quality and yield. This paper proposes a novel framework to monitor KPI-related faults, which consists of data imputation and fault detection. During the data imputation process, a novel location embedding generative adversarial imputation network (LEGAIN) is proposed. The LEGAIN transforms the distance between each pair of observation points into a position-aware weight matrix, which captures the location information to facilitate accurate data imputation. LEGAIN introduces a symmetric window mask strategy to enhance its ability in capturing local dynamic characteristics. During the fault detection process, the deep feature correlation analysis (DFCA) is proposed. The DFCA introduces a dual-branch variational autoencoder (VAE) to separately extract nonlinear features from process variables and KPIs. The spatial-temporal correlation between these two sets of features is analyzed and considered as a part of the loss function. Generalized singular value decomposition is applied to effectively distinguish KPI-related subspace and KPI-unrelated subspace. Corresponding theory analysis is provided. Experiment results demonstrate the superiority of the proposed method.