This paper is concentrated on two new distributed data-driven optimal fault detection approaches in large-scale systems using a group of sensor blocks, each of which accesses part of the process variables. Towards this end, an optimal fault detection problem is first formulated and solved, which lays a foundation for further distributed studies. Based on it, the first distributed data-driven optimal fault detection scheme, consisting of offline distributed learning and online distributed detection, is developed using the average consensus algorithm. To further reduce communication and computation efforts, the second average consensus based fault detection is investigated. Considering that the iteration computations for average consensus algorithm can lead to fault detection delay, a variation of the average consensus based fault detection scheme is proposed with iterative estimation of the covariance matrices of random variables and implementation of the distributed test statistic during the consensus iteration. A numerical example and a case study on the PRONTO heterogeneous benchmark dataset are used to demonstrate the proposed approaches. (C) 2020 Elsevier Ltd. All rights reserved.