Quantification of Simultaneous-AND Gates in Temporal Fault Trees

Fault Tree Analysis has been a cornerstone of safety-critical systems for many years. It has seen various extensions to enable it to analyse dynamic behaviours exhibited by modern systems with redundant components. However, none of these extended FTA approaches provide much support for modelling situations where events have to be "nearly simultaneous", i.e., where events must occur within a certain interval to cause a failure. Although one such extension, Pandora, is unique in providing a "Simultaneous-AND" gate, it does not allow such intervals to be represented. In this work, we extend the Simultaneous-AND gate to include a parameterized interval - referred to as pSAND - such that the output event occurs if the input events occur within a defined period of time. This work then derives an expression for the exact quantification of pSAND for exponentially distributed events and provides an approximation using Monte Carlo simulation which can be used for other distributions