Math to make money: cost-optimizing maintenance

title:Math to make money: cost-optimizing maintenance
topics:Case studies and Applications, Dependability, security and performance
contact:E.J.J. Ruijters MSc & dr. M.I.A. Stoelinga


RAMS (Reliability, Availability, Maintenance, Safety) requirements are of utmost importance for safety-critical systems like nuclear power plants, power grids, and railroad infrastructure. In some cases, there are even legal requirements to prove that such systems meet a certain level of reliability.

Keeping these systems reliable usually requires maintenance. This, however, introduces a trade-off: more maintenance results in increased reliability but also increased costs for workers, lost profits while the systems is down for maintenance, etc. It is therefore important to find the optimal balance between reliability and cost.

A widely used standard for RAMS analysis is fault tree analysis (FTA), which we have extended to include maintenance and its costs through fault maintenance trees (FMTs). A recent development of FMTs models the gradual degradation of components over time, but this new model needs to be tested in practice. In this project you will check this model using a practical case study, where the aim is to find the lowest-cost maintenance plan that ensures the required reliability.

Your tasks will include:

  • Study a physical system to understand its degradation and maintenance
  • Model this system as a fault maintenance tree
  • Validate the outcome of this model against reality
  • Use the model to find the cost-optimal maintenance plan

As part of this project, you will visit NedTrain who will assist with the case study.


  1. W.E. Vesely, F.F. Goldberg, N.H. Roberts, D.F. Haasl, Fault Tree Handbook, Office of Nuclear Regulatory Research, US Nuclear Regulatory Commision, 1981 (Digital version available here)
  2. E. Ruijters, D. Guck, P. Drolenga, M. Stoelinga, Fault maintenance trees: reliability centered maintenance via statistical model checking. (Digital version available here)