A common scenario in engineering is that of a system which operates throughout several sequential and distinct periods of time, during which the modes and consequences of failure differ from one another. This type of operation is known as a phased mission, and for the mission to be a success the system must successfully operate throughout all of the phases. Examples include a rocket launch and an aeroplane flight. Component or sub-system failures may occur at any time during the mission, yet not affect the system performance until the phase in which their condition is critical. This may mean that the transition from one phase to the next is a critical event that leads to phase and mission failure, with the root cause being a component failure in a previous phase. A series of phased missions with no maintenance may be considered as a Maintenance Free Operating Period (MFOP). This paper describes the use of a Petri net to model the reliability of the MFOP and phased missions scenario. The model uses a form of Monte-Carlo simulation to obtain its results, and due to the modelling power of Petri Nets, can consider complexities such as multi-mission periods, component failure rate interdependencies, and mission abandonment. The model operates three different types of Petri Net which interact to provide the overall system reliability modelling.