Structural approaches have shown to be useful for analyzing and designing diagnosis systems for industrial systems. In simulation and estimation literature, related theories about differential index have been developed and, also there, structural methods have been successfully applied for simulating large-scale differential algebraic models. A main contribution of this paper is to connect those theories and thus making the tools from simulation and estimation literature available for model based diagnosis design. A key step in the unification is an extension of the notion of differential index of exactly determined systems of equations to overdetermined systems of equations. A second main contribution is how differential-index can be used in diagnosability analysis and also in the design stage where an exponentially sized search space is significantly reduced. This allows focusing on residual generators where basic design techniques, such as standard state-observation techniques and sequential residual generation are directly applicable. The developed theory has a direct industrial relevance, which is illustrated with discussions on an automotive engine example. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.