Daytime Project

Age-Based Maintenance


“We consider a system with a finite lifespan and a single critical component that is subject to random failures. An age-based replacement policy is applied to preventively replace the component before its failure. The components used for replacement come from either a weak population or a strong population, referred to as population heterogeneity. Even though the true type of the population is unknown, the decision maker has a belief on the probability of components coming from a weak population. We build a partially observable Markov decision process model that optimizes the age-based replacement decisions with the objective of minimizing the total cost over the lifespan of the system. The resulting optimal policy updates the belief variable in a Bayesian way by using the data obtained throughout the system lifespan. It optimally balances the trade-off between the cost of learning the true population type (via deliberately delaying the preventive replacement time to better learn the population type) and the cost of maintenance activities.” 

“To the best of our knowledge, this model is the first to study optimally balancing the exploration and exploitation in a finite lifespan problem for a critical component under population heterogeneity.” 

This research paper is accepted by a peer-reviewed journal, European Journal of Operational Research.



A tool is developed based on the mathematical model mentioned above and uploaded on Github at 21 September 2021. The model is developed in R. A demonstrator is created by R shiny app and uploaded to


Link to tool:

Link to Demonstrator:



A general discrete time-to-failure distribution is assumed for the optimization model. In numerical experiments, discrete Weibull distribution with scale 10 and 20, shape 5 and 10 parameters is used.


We compare the performance of the optimal policy to two benchmark heuristic policies (namely, the myopic policy and the threshold policy) from the literature. In our numerical experiments, we obtain that the threshold policy is up to 5.8% more costly compared to the optimal policy. The myopic policy is up to 23.6% more costly compared to the optimal policy. We also show that the true component type is learned much faster and more accurately under the optimal policy due to the effective use of exploration.




Contact Information:

İpek Dursun | Eindhoven University of Technology |