Modeling of increasing age- and state-dependent degradation processes: a new closed form Markovian solution

A new continuous Markovian model for increasing degradation processes is presented, in which the increments of degradation over disjoint time intervals s are non-independent, but depend both on the current age and on the current state of the unit under study. Unlike other increasing Markovian processes with non-stationary and non-independent increments recently proposed in the literature, the proposed process is mathematically tractable and does not introduce undesirable approximations due to time and/or state discretization. Indeed, for such a new process, the conditional distribution of the degradation growth over a generic time interval, given the current state and age of the unit, can be formulated in closed form. The main properties of the proposed process are discussed and maximum likelihood estimators of the model parameters are developed. Finally, an application relative to a real set of degradation data is used to illustrate the estimation procedure and the capability of the proposed process in a real applicative context.