Evaluating failure time probabilities for a Markovian wear process

We present simplified analytical results for the numerical evaluation of failure time probabilities for a single-unit system whose cumulative wear over time depends on its external environment. The failure time distribution is derived as a one-dimensional Laplace–Stieltjes transform with respect to the temporal variable using a direct solution approach and by inverting an existing two-dimensional result with respect to the spatial failure threshold variable. Two numerical examples demonstrate that accurate cumulative probability values can be obtained in a straightforward manner using standard computing environments.Scope and purposeReliability models that incorporate the effect of a stochastic and dynamic environment on a unit's lifetime have attracted a moderate amount of attention in the past decade. However, evaluating failure time probabilities using such models is nontrivial in all but a few cases. Kharoufeh 1] provided a closed-form lifetime distribution for a continuous Markovian wear process as a two-dimensional Laplace transform. The main purpose of this paper is to reduce the lifetime distribution to a one-dimensional Laplace transform in order to facilitate simpler numerical implementation.