We present a novel concept of Minimal Set of Analytical Redundancy Relation (ARRs) and an efficient method for its calculation for application to system diagnosis. ARRs are one of the crucial tools for model-based diagnosis as well as for optimizing, analyzing, and validating the system of sensors. However, despite the importance of the ARRs for system diagnosis, it seems that less attention has been paid to their efficient application. In this paper, we first discuss the complexity of model-based diagnosis by using ARRs. We then present the concept of Minimal Set of ARRs which enables a faster system diagnosis by significantly reducing the number of ARRs to be evaluated for diagnosis purpose. We then show that the derivation of minimal set of ARRs can be mapped as a 0-1 Integer Programming problem and present an efficient branch-and-bound algorithm for this derivation. We also present the results of application of our method for generating the minimal set of ARRs, to both synthetic and industrial examples, to show the significant reduction in the computational cost that can be achieved for system diagnosis.
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