General Mathematics Colloquium
Speaker: Stella Kapodistria (Eindhoven University of Technology)
Decision making under uncertainty
In the area of maintenance of highly valued equipment, it is paramount to investigate when to preventively replace the equipment given a cost structure. In this talk, we investigate two directions of maintenance: age based and condition based.
In the context of age based maintenance, failure data is modelled so as to compute the lifetime distribution of equipment and based on a cost structure (average cost criterium - long run rate of cost - or discounted cost criterium) one can obtain the optimal maintenance policy, using notions from renewal theory and Markov decision processes (MDPs). In practice, failure data exhibit “overdispersion" and cannot realistically be modelled using the simplistic framework of a single distribution. To this end, we propose to model the remaining lifetime of an equipment using a fluid model under a Markov modulated environment. We show how to derive the optimal maintenance policy. This is joint work with Martijn Gösgens and Sándor Kolumbán, TU/e.
In the context of condition based maintenance, the condition (e.g., pressure, vibration, etc.) can be accurately modelled using some known stochastic process, such as a compound Poisson process, geometric Brownian motion, etc. and based on a cost structure (discounted cost criterium) one can obtain the optimal maintenance policy. In practice, “overdispersion” is again exhibited and, to this purpose, we propose the use of a Bayesian structure for the underlying stochastic process, which is used to model the condition. This is joint work with Colin Drent, TU/e. Furthermore, we establish connections between supervised learning and Bayesian MDPs. This is joint work with Paulo Serra, TU/e.
Finally, we propose a joint formulation of age and condition based maintenance, as highly used equipment has the tendency to suffer mostly from wear/degradation captured by the condition model, while lightly used equipment mainly suffers from ageing captured by the lifetime distribution. This is joint work with Marko Boon, TU/e.
Location: KdVI meeting room, Science Park 107, room F3.20
Science Park 107
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