A system and method for maintaining health of a fleet of assets implementing an asset maintenance framework for collective anomaly detection that provides for a more accurate maintenance planning solution for the fleet or assets that may be prioritized. Based on a Bayesian multi-task multi-modal sparse mixture of sparse Gaussian graphical models (MTL-MM GGM), the methods combine the variational Bayes framework with (1) Laplace prior-based sparse structure learning and (2) an 0-based sparse mixture weight selection approach. Dual sparsity is guaranteed over both variable-variable dependency and mixture components to efficiently learn multi-modal distributions that are observed in various applications. A generated model represents the fleet-level CbM model as a combination between two model components: 1) S sets of sparse mixture weights representing individuality of the assets in the fleet; and 2) One set of sparse GGMs that are shared with the S assets to represent commonality across the S assets.