An age- and state-dependent Markov model for degradation processes

Many technological units are subjected during their operating life to a gradual deterioration process that progressively degrades their characteristics until a failure occurs. Statisticians and engineers have almost always modeled degradation phenomena using independent increments processes, which imply that the degradation growth depends, at most, on the unit age. Only a few models have been proposed in which the degradation growth is assumed to depend on the current unit state. In many cases, however, both the current age and the current state of a unit can affect the degradation process. As such, this article proposes a degradation model in which the transition probabilities between unit states depend on both the current age and the current degradation level. Two applications based on real data sets are analyzed and discussed.