There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

A review on machinery diagnostics and prognostics implementing condition-based maintenance

Remaining useful life estimation - A review on the statistical data driven approaches

A survey of maintenance policies of deteriorating systems

An Optimal Maintenance Policy for a Two-unit Production System Using a Proportional Hazards Model

Improved abnormal formation pressure detection from drilling performance data in a partially observable setting

An inspection model with generally distributed restoration and repair times

In this paper, we investigate the residual life prediction problem for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model with unknown parameters. The parameter estimation procedure based on an EM algorithm is developed and the formulas for the conditional reliability function and the mean residual life are derived, illustrated by a numerical example. Keywords—Partially observable system, hidden Markov model, competing risks, residual life prediction.

Viliam Makis

Papers

An Optimal Maintenance Policy for a Two-unit Production System Using a Proportional Hazards Model

Improved abnormal formation pressure detection from drilling performance data in a partially observable setting

An inspection model with generally distributed restoration and repair times

Residual Life Prediction for a System Subject to Condition Monitoring and Two Failure Modes

A model of age-based replacement with regular services