A continuous-state Markov model for age- and state-dependent degradation processes

In order to approximate the unknown transition probability densities of a state-dependent, possibly inhomogeneous, Markov degradation model, a continuous-state discrete-time Markov model is proposed, which is based on the use of the Pearson’s family of distributions for approximating the true transition density. Unlike the alternative approach based on Markov chain approximation, the proposed one has the decisive advantage of dramatically reducing the computing time of the estimation procedure, thus allowing a age- and state-dependent model to be potentially applied also in more complex experimental frameworks, e.g., in presence of random effects. Hence, the proposed model is used to analyse, on the basis of real data from the literature, two different degradation phenomena, namely: the wear of some cutting tools and the crack growth of metallic specimens.

► We propose a continuous-state discrete-time Markov model degradation processes.
► Time and age are both assumed to affect degradation growth.
► We approximate the true transition density through Pearson family of distributions.
► The moments of the true transition density are approximated via the delta method.
► The presence of random effects can also be assumed.