Degradation Modelling using a Phase Type Distribution (PHD)

Laskowska, Ewa; Vatn, Jørn

doi:10.3850/978-981-14-8593-0_4492-cd

Cited by 2 publications

(4 citation statements)

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“…The model has been re-run with these extra states under the assumption τ 2aE = 0.5, and the result shows that the total failure probability is reduced from 2.5% to 2.2%. This is in accordance with Laskowska and Vatn (2020) where more deterministic behaviour typically gives better per-formance under a given maintenance strategy. Introducing more states will give even more exact results at a cost of a more complicated model.…”

Section: Phase Type Modellingsupporting

confidence: 88%

“…The more states we use, the better could the approximation be. See e.g., Laskowska and Vatn (2020) for a description of the approach in a similar setting as used here.…”

Section: Phase Type Modellingmentioning

confidence: 99%

“…Since fatigue is the dominating failure mechanism, it is not very realistic to claim exponentially distributed sojourn times for each state. In other work, see e.g., Laskowska and Vatn (2020) and Vatn (2020) phase type models for the sojourn time is proposed where virtual sub-states are introduced for each of the main states. In order to keep the model simple, we stick to the assumption that sojourn are exponentially distributed in our basis model, and then we investigate the impact of non-exponential transitions.…”

Section: Introductionmentioning

confidence: 99%

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Optimizing Ultrasonic Inspection Regimes of Railway Rails

Vatn

2023

Proceeding of the 33rd European Safety and Reliability Conference

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Ultrasonic inspection of railway rails is considered as an important safety barrier. Fatigue cracks develop due to the cyclic loads of the passing trains, and the objective is to detect the cracks before they develop to rail breakages. It is crucial to understand the speed of crack propagation to define the inspection regime. Trains equipped with ultrasonic instruments can run at a speed of approximately 50 km/h. As the train runs suspects are identified with their position along the track. The ultrasonic scans are investigated and critical suspects are recorded for manual follow up. The manual inspection uses a hand-held trolley also with ultrasonic instruments for a more precise classification. In Norway a classification regime consisting of the categories 2b, 2a, 1 and 0 are used. The main strategy is to monitor 2a and 2b defects, whereas 1 defects have to be fixed within a month, and 0 defects have to be fixed immediately. The inspection-and follow-up regime is now under revision. Markov modelling is the basis for this study. There are several challenges with the Markov model. First of all, since we assume that fatigue is the main failure mechanism, it is not realistic to assume that transition times follow the exponential distribution. Secondly, times between running the inspection car are almost deterministic which requires a special treatment when solving the Chapman-Kolmogorov differential equations. Finally, the follow-up activities are also deterministic, and phasetype models may be used to handle transitions representing the results of the follow-up activities. In this paper we investigate how we can simplify the modelling without compromising the results too much. Statistics from the Norwegian rail network is used for estimating the transition rates.

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Section: Phase Type Modellingsupporting

confidence: 88%

“…The more states we use, the better could the approximation be. See e.g., Laskowska and Vatn (2020) for a description of the approach in a similar setting as used here.…”

Section: Phase Type Modellingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimizing Ultrasonic Inspection Regimes of Railway Rails

Vatn

2023

Proceeding of the 33rd European Safety and Reliability Conference

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“…In the merging, the transition rates to the absorbing state, i.e. the next macro state, are split according to the initial probability vector of the next states to ensure a good fitting (see proof in Laskowska and Vatn (2020)). Suppose there is a Markov chain with n macro states, where the sojourn times at state j ∈ {1, 2, ...n − 1} are approximated with PH distributions of m j phases.…”

Section: Ph Expansion Of Multi-state Markov Modelsmentioning

confidence: 99%

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

Sun,

Vatn,

Zhao

et al. 2023

Proceeding of the 33rd European Safety and Reliability Conference

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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.

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Degradation Modelling using a Phase Type Distribution (PHD)

Cited by 2 publications

References 0 publications

Optimizing Ultrasonic Inspection Regimes of Railway Rails

Optimizing Ultrasonic Inspection Regimes of Railway Rails

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

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