Time-Dependent Probabilistic Calculations

This chapter explains how time-dependent probabilistic calculations can be performed with Boolean models when the components of the modelled systems remain independent all over the considered period of time. It describes the RBD and the FT-driven Markov processes which prove to be very effective for such calculations and which combine the logic provided by the Boolean models with small Markov graphs used to calculate the time-dependent input probabilities (for blocks or primary events). This allows to compute all the parameters involved when dealing with safety and dependability studies: instantaneous and average availabilities/unavailabilities, failure frequencies/rates/densities and reliabilities/unreliabilities. Both repaired and non-repaired items are considered and for repaired items, it is explained why only availability/unavailability calculations can be done straightforwardly and why the others need to use the Birnbaum importance factor (described in Chap. 24 ). This chapter also analyses why reliability/unreliability calculations introduce systemic dependencies which make the calculations difficult and why, in the general case, only approximations based on the use of the Vesely failure rate (conditional failure intensity) are available. Compared to exact calculations performed using Markov graphs, the approximations are pretty good.