This paper presents an analytical approach for the evaluation of multi-user safety critical systems presenting a failure delayed behavior pattern. As a consequence of a failure event, the performance of these systems worsens progressively due to the internal fault tolerance mechanisms or the complacency of the users regarding the temporary unavailability of the services. A distinctive feature of the approach is the ability to handle stochastic models containing multiple processes with generalized distributions. The approach is based on the determination of analytical expressions to measure reliability, for instance, frequency and probability of failure states, which may be evaluated using general purpose mathematical tools. The paper first reviews other well-established techniques employed in the assessment of non-Markovian systems, particularly those based on stochastic Petri nets. The rationale of the new approach and its fundamental algorithms are presented together with a set of illustrative examples which highlight the strengths of the approach, as well as its limitations. Copyright © 2012 John Wiley & Sons, Ltd.