Explicit results for wear processes in a Markovian environment

We consider the reliability of a single-unit system whose cumulative damage over time is a continuous wear process {X(t): t≥0} that depends on an external environment process {Z(t): t≥0}. We explicitly derive the failure time distribution and moments in terms of Laplace–Stieltjes transforms by analyzing the Markov addictive process {(X(t),Z(t)): t≥0} and demonstrate its applicability on an example problem.