*For evaluating risks using Markov graphs*

Markov is used to model a system as a Markov graph. It produces simple models suited to all domains (aeronautics, automobile, rail, oil & gas, etc.) and provides a large amount of information including the availability and Equivalent Lambda of a system over the time. The Markov module uses ALBIZIA, the Markov and BDD computation engine developed by Total that is based on efficient matrix computation algorithms.

**Modeling and computations**

Users can easily create a Markov graph via an intuitive graphical interface in which the different states of the system can be entered and connected via transitions. For each state of the graph, they can indicate whether or not the system is available. For production efficiency studies, users can indicate the efficiency of the system in each state. Finally, when the transition rate between states has been entered, the Markov graph is complete and computations can then be launched.

The Markov module delivers many results:

– The probability of being in a state;

– The sojourn times in each state;

– The availability/reliability of the system;

– The failure rate and Equivalent Lambda of the system over the time.

**Specificities and strenghts**

*Values over the time**:*

Over a given operating period, the probability of a system being in a state at the end of a mission is interesting but knowing its evolution over the time is even more useful.

The opposite figure is a graphical example obtained for a system made up of 3 components. Each curve represents the probability of being in one of the 4 states below (at t=0, a component has failed):

- State1: the 3 components are working;
- State2: 1 component is failed;
- State3: 2 components are failed;
- State3: 3 components are failed.

*Efficiency computations*

GRIF Markov module will calculate a system efficiency. When a state in the graph indicates that the system is available, it is possible to indicate the efficiency of the system in this state. In this way, downgraded states can be taken into account and production availability computations performed.

*Interaction with Boolean modules:*

A Markov graph of this module can be used to describe a component failure for Boolean module (Tree, ETree, BFiab).

*Multi-Phase Markov Chains*

A system does not follow the model throughout its lifetime. It may undergo tests or repairs during which time the system is represented by a different Markov graph.

These different phases in the life of a component can be modelled in the Markov module, which can be used, for example, to display the availability of a system that is periodically tested, taking into account a large number of parameters: duration and efficiency of the test, reconfiguration errors…

**Using data and results**

- Synthesis of input data in the form of tables that makes it easier to control the quality of an entry.
- Possibility of automating calculations (batch run).
- Results stored in the same document and exportable in different formats (csv, XML, Excel, etc.).
- Visualization of results as curves, pie charts or histograms.
- Vector printing of graphic elements and curves in PDF format which maintains optimum quality, even in A3 or A2 format.
- Interaction with the operating system: option to copy/paste curves, systems or results to word processing software, spreadsheets or presentation tools.
- Possible connection to MySQL, Access and Excel databases to recover the values to be used for the settings.