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

In this paper, we examine a replacement problem for a system subject to stochastic deterioration. Upon failure the system must be replaced by a new one and a failure cost is incurred. If the systemis replaced before failure a smaller cost is incurred. The failure of the system depends both on its age and also on values of a diagnostic stochastic process observable at discrete points of time. Cox’s proportional hazards model is used to describe the failure rate of the system. We consider the problem of specifying a replacement rule which minimizes the long-run expected average cost per unit time. The form of the optimal replacement policy is found and an algorithm based on a recursive computational procedure is presented which can be used to obtain the optimal policy and the optimal expected average cost.

Optimal Replacement In The Proportional Hazards Model

The focus of the paper is the optimization of condition-based maintenance decisions within the contexts of physical asset management. In particular, the analysis of a preventive replacement policy of the control-limit type for a deteriorating system subject to inspections at discrete points of time is presented. Cox’s PHM with a Weibull baseline hazard function and time dependent stochastic covariates is used to describe the failure rate of the system. The methods of estimating model parameters and the calculation of the optimal policy are given. The structure of the decision-making software EXAKT is presented. Experience with collecting, preprocessing and using real oil and vibration data is reported.

A Control-Limit Policy And Software For Condition-Based Maintenance Optimization

This paper describes a case study in which the Weibull proportional-hazards model is used to determine the optimal replacement policy for a critical item which is subject to vibration monitoring. Such an approach has been used to date in the context of monitoring through oil debris analysis, and this approach is extended in this paper to the vibration monitoring context. The Weibull proportional-hazards model is reviewed along with the software EXAKT used for optimization. In particular the case considers condition-based maintenance for circulating pumps in a coal wash plant that is part of the SASOL petrochemical company. The condition-based maintenance policy recommended in this study is based on histories collected over a period of 2 years, and is compared with current practice. The policy is validated using data that arose from subsequent operation of the plant.

https://link.springer.com/content/pdf/10.1057%2Fpalgrave.jors.2601261.pdf

Viliam Makis

Papers

Optimal Replacement In The Proportional Hazards Model

A Control-Limit Policy And Software For Condition-Based Maintenance Optimization

Optimal component replacement decisions using vibration monitoring and the proportional-hazards model

A wavelet approach to fault diagnosis of a gearbox under varying load conditions

Condition monitoring and classification of rotating machinery using wavelets and hidden Markov models