  Prediction of events such as part replacement and failure events plays a
critical role in reliability engineering. Event stream data are commonly
observed in manufacturing and teleservice systems. Designing predictive models
for individual units based on such event streams is challenging and an
under-explored problem. In this work, we propose a non-parametric prognostic
framework for individualized event prediction based on the inhomogeneous
Poisson processes with a multivariate Gaussian convolution process (MGCP) prior
on the intensity functions. The MGCP prior on the intensity functions of the
inhomogeneous Poisson processes maps data from similar historical units to the
current unit under study which facilitates sharing of information and allows
for analysis of flexible event patterns. To facilitate inference, we derive a
variational inference scheme for learning and estimation of parameters in the
resulting MGCP modulated Poisson process model. Experimental results are shown
on both synthetic data as well as real-world data for fleet based event
prediction.
