A probabilistic multivariate fault diagnosis technique is proposed for industrial processes. The joint probability density function containing essential features of normal operation is constructed considering dependency among the process variables. The dependence structures are modelled using Gaussian copula. The Gaussian copula uses rank correlation coefficients to capture the nonlinear relationships between process variables. For real-time monitoring, the probability of each online data samples is computed under the joint probability density function. Those samples having probabilities violating a predetermined control limit are classified to be faulty. For fault diagnosis, the reference dependence structures of the process variables are first determined from normal process data. These reference structures are then compared with those obtained from the faulty data samples. This assists in identifying the root-cause variable(s). The proposed technique is tested on two case studies: a nonlinear numerical example and an industrial case. The performance of the proposed technique is observed to be superior to the conventional statistical methods, such as PCA and MICA. (C) 2015 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.