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

States that the concept of condition‐based maintenance (CBM) has been widely accepted in practice since it enables maintenance decisions to be made based on the current state of equipment. Existing CBM methods, however, mainly rely on the inspector’s experience to interpret data on the state of equipment, and this interpretation is not always reliable. Aims to present a preventive maintenance policy based on inspections and a proportional hazards modelling approach with time‐dependent covariates to analyse failure‐time data statistically. Presents the structure of the software, currently under develop‐ ment and supported by the CBM Project Consortium.

Optimal replacement policy and the structure of software for condition‐based maintenance

Optimal Bayesian fault prediction scheme for a partially observable system subject to random failure

Autoregressive model-based gear shaft fault diagnosis using the Kolmogorov–Smirnov test

A multivariate Bayesian control chart for monitoring process mean under the assumption that the vector of process observations follows a multivariate normal distribution is considered. Traditional control charts such as Hotelling's T2, EWMA, and CUSUM charts have been applied to control industrial processes characterized by several measurable variables. It is well known that these traditional, non-Bayesian process control techniques are not optimal, but very few results regarding the structure of the Bayesian control policy have been reported in the literature, all dealing with the univariate, finite-horizon case. In this paper, we formulate the multivariate Bayesian process control problem in the optimal stopping framework. The objective is to find a stopping rule under partial observations, minimizing the long-run expected average cost per unit time for a given sample size and sampling interval. Under standard operating and cost assumptions, it is proved that a control limit policy is optimal, and an algorithm is presented to find the optimal control limit and the minimum average cost.

Viliam Makis

Papers

Optimal replacement policy and the structure of software for condition‐based maintenance

Optimal Bayesian fault prediction scheme for a partially observable system subject to random failure

Autoregressive model-based gear shaft fault diagnosis using the Kolmogorov–Smirnov test

Multivariate Bayesian control chart

A note on optimal replacement policy under general repair