A parametric Markov chain to model age- and state-dependent wear processes

Abstract

Abstract. Many technological systems are subjected, during their operating life, to a gradual wear process which, in the long run, may cause failure. According to the literature, it results that statisticians and engineers have almost always modeled wear processes by independent increments models, which imply that future wear is assumed to depend, at most, on the system's age. In many cases it seems to be more realistic and appropriate to adopt stochastic models which assume that factors other than age affect wear. Indeed, wear models which can (also) account for the dependence on the system's state have been previously proposed in the literature [1,3,11,13]. Many of the abovementioned models present a very complex structure that prevents their application to the kind of data that are usually available. As such, in this paper, a new simple parametric Markov chain wear model is proposed, in which the transition probabilities between process states depend on both the current age and the current wear level of the system. An application based on a real data set referring to the wear process of the cylinder liners of heavy-duty diesel engines for marine propulsion is analysed and discussed.

Degradation modeling–based remaining useful life estimation: A review on approaches for systems with heterogeneity

“…Prognostics of both performance and RUL were achieved in Dong 58 by a combination of HsMM and autoregression (AR) model for time series data. Giorgio et al 59,60 considered the age- and state-dependency of the degradation process in the framework of Markovian degradation model. A very good result was obtained when the proposed models were applied to the degradation process of a marine engine cylinder.…”

“…However, the studies on age- and state-dependent degradation modeling are very limited in the literature, as opposed to a great deal of efforts made to age-dependent degradation models. Most recently, Giorgio et al 59,60 made the first attempt along this direction and presented some Markov chain–based degradation models whose transition probabilities between the process states depend on the current state and the current age of the system under study. It is worth pointing out that their developed models are only suitable to represent strictly monotonic degradation processes.…”

“…However, in many industrial systems, a non-monotonic degradation process, for example, resulting from minor repair or reduced intensity of use, can provide a good description of the system’s degradation signals. Besides, the continuous degradation process is approximated by a Markov chain with discrete degradation states in Giorgio et al 59,60 This approximating process introduces many context-dependent parameters, which might pose difficulty in applications. Together with these discussions, it can be concluded that it is still challenging to develop age- and state-dependent degradation models for continuously degradation systems whose degradation progression might be non-monotonic.…”