Prognostics is the ability to predict the remaining useful life of a specific system, or component, and represents a key enabler of any effective condition-based-maintenance strategy. Among methods for performing prognostics such as regression and artificial neural networks, particle filters are emerging as a technique with considerable potential. Particle filters employ both a state dynamic model and a measurement model, which are used together to predict the evolution of the state probability distribution function. The approach has similarities to Kalman filtering, however, particle filters make no assumptions that the state dynamic model be linear or that Gaussian noise assumptions must hold true. The technique is applied in predicting the degradation of thermal processing units used in the treatment of waste gases from semiconductor processing chambers. The performance of the technique demonstrates the potential of particle filters as a robust method for accurately predicting system failure. In addition to the use of particle filters, Gaussian Mixture Models (GMM) are employed to extract signals associated with the different operating modes from a multi-modal signal generated by the operating characteristics of the thermal processing unit.