This work is an attempt to establish a probabilistic framework for the assessment and design of observer-based fault detection systems. The fundament of our study is randomized algorithms methods which are successfully applied to deal with uncertainty issues in robust control. For our purpose, probabilistic parameter models for faults and model uncertainties are first introduced. The main focus of our work is on the development of randomized algorithms for the assessment of false alarm rate, fault detection rate and mean time to detection as well as for the design of observer-based fault detection systems. To illustrate the potential applications of the proposed algorithms and methods, benchmark study on a real three-tank system is included. (C) 2019 Elsevier Ltd. All rights reserved.