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In this paper we focus on the analytical modeling for the dependability evaluation of phased-mission systems. Because of their dynamic behavior, systems showing a phased behavior offer challenges in modeling. We propose the modeling and evaluation of phased-mission systems dependability through the Deterministic and Stochastic Petri Nets (DSPN). The DSPN approach to the phasedmission systems offers many advantages, concerning both the modeling and the solution. The DSPN model of the mission can be a very concise one, and it can be efficiently solved for the dependability evaluation purposes. The solution procedure is supported by the existence of an analytical solution for the transient probabilities of the marking process underlying the DSPN model. This analytical solution can be fully automated. We show how the DSPN models capabilities are able to deal with various peculiar features of phasedmission systems, including those systems where the next phase to be performed can be chosen at the time the preceding phase ends.

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In this paper, a new algorithm based on Binary Decision Diagram (BDD) for the analysis of a system with multistate components is proposed. Each state of a multistate component is represented by a Boolean variable, and a multistate system is represented by a series of multistate fault trees. A Boolean algebra with restrictions on variables is used to address the dependence among these Boolean variables that collectively represent the same component and a new BDD operation is proposed to realize this Boolean algebra. Due to the nature of the BDD, the sum of disjoint products (SDP) can be implicitly represented, which avoids huge storage and high computational complexity for large multistate systems. Some applications are given to illustrate the use of our new algorithm.