In this paper, a novel fault diagnosis scheme for linear process systems using dissipativity theory is developed. Dissipativity (supply rate) of a process is an input/output property, which may not be valid when a fault occurs. For a given process, dissipativity is not a unique property, with different dissipative supply rates reflecting different aspects of its dynamics. In this approach, the dissipativity of a process is "shaped" such that it is fault-sensitive (i.e., no longer valid when faults occur) and fault-selective (i.e., no longer valid when one particular fault occurs). By adopting the storage functions and supply rates in the quadratic difference form (QdF), the dissipativity conditions are represented as quadratic functions of the input/output trajectories of the process, which captures much more detailed dynamical features compared to conventional dissipativity (e.g., QSR-type supply rates). These dissipativity properties are determined offline by solving an optimization problem with linear matrix inequality constraints. The online diagnosis algorithm involves checking of inequalities on input/output trajectories, which is much simpler compared to the diagnosis approaches based on observers or parameter estimation. The proposed approach is illustrated using a case study of fault diagnosis of a heat exchanger. (C) 2017 Elsevier Ltd. All rights reserved.