Recent advancements in computing, telecommunications, and metrology have propelled data-driven decision making across the industries. Industrial health management in particular has been increasingly reliant on Machine Learning techniques for data-driven prognosis as modern assets are exhaustively monitored by their embedded sensors. Data-driven prognosis constitute the bedrock for the emerging highly-flexible predictive maintenance policies. The original equipment owners and customers also mutually enjoy its cost benefits via servitisation for example, where the customers pay for asset uptimes rather than ownerships. Such business offerings are possible only due to the recent advent of distributed control systems and real-time prognosis. However, the diversity in asset operating conditions results in non-ergodicity which is often a challenge while modelling the asset fleet data. A fleet-wide model trained by pooling the data from all the assets is associated with a high bias, whereas the independent assets- specific models are associated with high variance for the assets with sparse data. Thankfully there exist similarities due to age, upkeep, manufacturing processes, etc. across the assets that enable learning possibilities within the asset fleet, via collaborative prognosis. This thesis proposes, and demonstrates, that statistical hierarchical modelling is a sys- tematic technique for collaborative prognosis and also for anomaly detection in the asset condition data. Hierarchical models presented herewith extend the independent models by formulating distributions at multiple levels, such that the parameters of the lower level assets- specific models are commonly sampled from the corresponding higher level distributions. This encourages learning for the assets with sparse data as they inherit prior information about the operations from the other similar assets comprising the fleet. It is concluded that, for prognosis and anomaly detection, the hierarchical models out- perform the independent and the fleet-wide models in terms of accuracy and variance for the assets with sparse data. Hierarchical models model the asset fleets in their natural order and also enable manual intervention for modelling the asset similarities via the higher level distributions. As data is accumulated along the asset operations, both hierarchical and in- dependent models converge similarly. The conclusions are also supported by a case study presented for an industrial fleet of long-haulage trucks.