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This paper considers fault detection (FD) for large-scale systems with many nearly identical units operating in a shared environment. A special class of hybrid system mathematical models is introduced to describe such multi-unit systems, and a general approach for estimation and change detection is proposed. A novel FD algorithm is developed based on estimating a common Gaussian-mixture (GM) distribution for unit parameters whereby observations are mapped into a common parameter-space and clusters are then identified corresponding to different modes of operation via the expectation-maximization (EM) algorithm. The estimated common distribution incorporates information from all units and is utilized for FD in each individual unit. The proposed algorithm takes into account unit mode switching and parameter drift and can handle sudden, incipient, and preexisting faults. It can be applied to FD in various industrial, chemical, or manufacturing processes, sensor networks, and others. The second part of the paper is focused on the application of the new technique to practical heating, ventilation, and air-conditioning (HVAC) systems. Reliable and timely FD is a significant and still open practical problem in the HVAC industry, and, as such, the first application of this approach is aimed at this industry. It addresses important details of the algorithm's implementation and presents results from an extensive performance study based on both Monte Carlo simulations and real data collected from three operational large HVAC systems. The results demonstrate the capabilities of the new technique in a more realistic setting and provide insights that can facilitate the design and implementation of practical FD for systems of similar type in other industrial applications.