For evaluating system architectures using **Fault Tree**

(reliability/safety analysis)

Tree is used to model a system as a fault tree based on Boolean logic, which produces simple models suited to all domains (aeronautics, automobile, rail, oil & gas, etc.). The Tree module uses ALBIZIA, the BDD (Binary Decision Diagram) computation engine developed by TotalEnergies. ALBIZIA offers the advantage of running **accurate analytical computations** and rapidly providing extensive information on the system under study.

**Modeling and computations**

Users can easily create fault trees via an intuitive graphical interface, and enter gates (AND, OR, K/N, NOT, XOR, NAND, NOR, IF-THEN-ELSE) and events according to the logic of the system studied and many probability laws (Exponential, Weibull, Gamma-Lambda-Mu, Periodic-Test…).

When the tree is built, it is easy to distinguish the groups of components subject to common cause failures.

ALBIZIA provides many results:

- Unavailability: Q(t), U(t) or PFD(t), Availability : A(t), Reliability: R(t), Unreliability: F(t);
- Frequency: W(t), UFI(t) or PFH(t);
- Equivalent failure rate: λeq(t), λv(t) or CFI(t);
- Many importance factors (Birnbaum MIF, Critical CIF, Vesely, DIF…);
- Minimal cut-sets;
- Reliability allocation.

For all computations, instantaneous, integral or mean values over a given mission

period can be obtained.

**Specificities and strengths**

*Computing the time spent in the SIL zones :*

In addition to the computations mentioned above, ALBIZIA is the only engine able to compute how long the PFD(t), PFH(t) or EqLambda(t) of a system spends in an interval during its mission period.

*The figure opposite shows a mean availability of 8.44E-3, which corresponds to a SIL2. However, it also indicates the percentage of time the system spent in each SIL over its 30-year mission. In this case, 39.77% of its time was spent in SIL1.*

*User-friendliness :*

Besides the graphical tree structure common to all modules, the Tree module has also a logic tree structure for browsing through the tree according to the system logic.

Groups/sub-trees are simple to create and with the automatic layout function, users can neatly organize their tree just by pressing on F7.

GRIF evolves every year, taking remarks from users into consideration to make the program more user-friendly and computerize repetitive tasks

*Factoring in uncertainties**:*

To be as close as possible to real conditions, parameter-related uncertainties can be factored in. It is possible, for example, to indicate that a failure rate follows a Uniform, Normal or Log-normal law. A Monte-Carlo simulation is performed in addition to the BDD computation in order to obtain mean values. Finally, a quintile computation is run to provide a dispersion interval on each result.

**Data exploitation 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 import the values to be used for the settings.

**Boolean Package**

The Tree module is part of the **GRIF-Workshop Boolean package**. All fault trees performed using this module can be used in Bool module which combines the features of all modules of the package. It will be possible, in a same document, to make calculations using Event Trees (Etree), Fault Trees (Tree), Reliability Block Diagrams (BFiab) and Safety Instrumented Systems (SIL).