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General

Cosyra is a free software intended for reliability analysis of complex systems. 
The probability of failure modes and events contributing to the systems failure conditions can be modeled by various distribution functions like Exponential, Weibull, Normal, or LogNormal distribution.
The probability of the failure conditions of a system are modeled by Fault Trees, Dependency Diagrams, or State Machines, which can be either continuous or discrete.
Fault Tree and Dependency Diagrams are different graphical representations of a failure condition, where each of the independent, contributing events either exist or not.
Continuous State Machine can be used to model systems, where the contributing events are not independent, e.g. a system with a stand-by channel. The failure probability of such a stand-by channel can increase once it becomes active and therefore depend on the failure of the normal channel.
Discrete State Machines allow to model complex repair sequences. For each state which may represent failures of different components it can be specified after which interval the components or part of the components are repaired. 

The Calculation of Fault Tree and Dependency Diagrams is based on the computation of the orthogonal boolean function of the model. Calculation results represent therefore an exact solution, while most other programs available just calculate upper boundaries or approximations.

Continuous State Machines a calculated as Markov Processes, while discrete State Machines are calculated Markov Chains. The transition matrix of the Markov chain is formulated using the failure probability. After each step, which is performed by multiplying the previous vector of state probabilities with the transition matrix, the repair matrix is checked if any repair interval is exceeded. A repair is represented by transition matrix, which contains a one for the change of state resulting from the repair and zeros for all other positions.