Bivariate Gamma wear processes for track geometry modelling, with application to intervention scheduling

Abstract

This paper discusses the intervention scheduling of a railway track, based on the observation of two dependent randomly increasing deterioration indicators. These two indicators are modeled through a bivariate Gamma process constructed by trivariate reduction. Empirical and maximum likelihood estimators are given for the process parameters and tested on simulated data. An EM algorithm is used to compute the maximum likelihood estimators. A bivariate Gamma process is then tted to real data of railway track deterioration. Intervention scheduling is de ned, ensuring that the railway track remains of good quality with a high probability. The results are compared to those based on both indicators taken separately, and also on one single indicator. The policy based on the joint information is proved to be safer than the other ones, which shows the potential of the bivariate model.

Reliability Modeling of Infrastructure Load-Sharing Systems With Workload Adjustment

“…We assume components only suffer degradation failures. This assumption is commonly used for systems or products when the wear/degradation dominates failure, e.g., the contact image sensor of fax machines [14], the railway tracks [15], and the print head of color printers [16], to name a few. In the industry problem we consider in Section 6, the component subject to failure is the RGFs in a water utility.…”

“…Then γ −1 i for the ith system follows a Gamma distribution with shape parametervt max +κ and scale parameter (U i (t max ) +φ) −1 . We can compute the estimates of γ for the 15 Based on these results, we can insert the parameter estimates into the model and compute the expected cost. We assume that the operational cost for each component is C O = 0.05 per year, the price of a component is C r = 1 and the fixed replacement…”

Stochastic framework for partially degradation systems with continuous component degradation‐rate‐interactions

“…[25,21,32,33]). Reliability models based on multivariate Gamma processes can be found in [28,41,19,6]. Although Gamma processes provide mathematically tractable forms of the probability distribution of component failure times, such model can only be used to characterize degradation signals that are monotonically increasing, which may not be realistic in many engineering applications.…”

Lifetime Distribution and Associated Inference of Systems with Multiple Degradation Measurements Based on Gamma Processes

“…its joint distribution can be approximated by multivariate normal distribution according to (6) and (7), and follows gamma distribution with shape parameter k v t ∆ and scale parameter . Thus, the log-likelihood function based on measurements on the K degradation paths is given by:…”

“…Li et al [5] discussed a reliability model of a series system with dependent component degradation processes. Mercier et al [6] discussed a track geometry model based on the observation of two dependent randomly increasing deterioration indicators through a bivariate gamma process constructed by trivariate reduction, and then give the intervention scheduling of a railway track. Pan and Balakrishnan [8] proposed a bivariate constant-stress accelerated degradation test model based on Wiener processes and Copulas.…”