Background: In a multi-state system, either the entire system or its components will have
more than two states. Different kind of multi-state systems have been investigated, such as multistate
series-parallel systems, multi-state k-out-of-n systems and multi-state linear consecutive-k-outof-
Methods: Performability analysis is concerned with the calculation of probability distribution of
different system performance levels. In this paper, Multi-valued Decision Diagram (MDD) based
approaches are discussed to conduct the performability analysis of multi-state systems.
Results: Examples are provided to illustrate the use of MDD approaches for three types of multistate
systems, e.g. multi-state series-parallel systems, multi-state k-out-of-n systems and multi-state
linear consecutive-k-out-of-n systems.
Conclusion: The empirical results show that the MDD approaches have lower computational complexity
than the traditional methods in model generation and evaluation.