A Parametric Markov Chain to Model Age- and State-Dependent Wear Processes

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.