Structural reliability models suffer from some drawbacks mainly related to the assumptions necessary to apply them. We propose a model which intends to overcome some of these limitations appearing in previous published works. We discuss on an approach that can make more realistic the usual Markovian assumptions when considering the structural modeling of the execution process. Moreover, we define a failure process allowing to model different and general situations and we give analytic results and algorithmic methods to perform the corresponding quantitative evaluations. We show that our model and the obtained results include as particular cases some previous proposed models. We also discuss about some interesting asymptotic properties of the model.