Proceedings of the

The 33rd European Safety and Reliability Conference (ESREL 2023)
3 – 8 September 2023, Southampton, UK

A Phase-Type Maintenance Model Considering Condition-Based Inspections and Delays Before the Repairs

Tianqi Suna, Jørn Vatnb, Yixin Zhaoc and Yiliu Liud

Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology (NTNU), Norway.


Markov models are widely used in maintenance modelling and system performance analysis due to their computational efficiency and analytical traceability. However, these models are usually restricted by the use of exponential distributions, which are the base of the Markov modelling. Phase-type distributions provide a tool to approximate an adequate distribution, such as Weibull, log-normal and so on, by means of Markov processes.

Our earlier work proposes a phase-type maintenance model considering both condition-based inspections and delays before the repairs, where extra matrices are defined in the modelling of repair delays to keep track of the probability masses to repair. The model provides quite good estimations but is complex and requires good knowledge in its implementation.

This paper aims to get rid of the extra matrices and investigate the modelling of the repair delays with phase-type distributions. An illustration case of road bridges is presented to demonstrate the modelling process and the results.

Keywords: Maintenance modelling, Phase-type distribution, Condition-based inspections, Delays before repairs.

Download PDF