# Dynamic Fault Tree Method (Part 3 of 3)

Simulation based methods, especially Monte Carlo simulation based techniques, can solve these problems.
According to the researches, complex systems which may be difficult to solve with analytical methods are simply solved with Monte Carlo simulation approach [3,4,7,12].
The reliability methods, which are based on Monte Carlo simulation approach, because of their ability in modeling the real conditions and stochastic behavior of the system, can eliminate uncertainty in reliability modeling [7].
The utilization of this approach is increasing for the calculation and estimation of reliability of dynamic systems.

DFT Versus SFT
Although, there are many rational reasons to utilize the dynamic methods in industrial field, the usage of these methods is not very common yet.
Perhaps, the main reason for this problem is directly related to the owners.
They do not bother to modernize existing static methods, such as RBD and SFT, which are extensively used in industrial field.
It comes from two main causes [5]; First of all, static approaches are more simplified and aggressively tested.
In addition, dynamic approaches are still too vague to apply to industrial applications.
Also, from a technical point of view, a SFT can be translated in a RBD, but this conversation to a DFT has to be figured out.

A Simple Example of DFT and SFT
Fig. 3 presents a simple example of SFT (the left one) and DFT for a similar system.
Let us consider the failure rate value of 0.01 (1/hrs) for all BEs.
In this example, Top Event (TE) of SFT will occur if all of the BEs occur; that is occurring of A, B and C at a same time, all together, no matter the sequences of them.

Now, Let us consider the DFT of this case.
Also, for this DFT, Top Event (TE) will occur if all of the BEs occur, at a same time, all together, but the way how this configuration is reached, matters.
In this case, due to the presence of the PAND gate, the sequences of events are important.
In this case, to occurrence DFT’s TE, A and B must occur before C.
At the mission time of 1000 hours, unreliability value for SFT and DFT, are 9.99E-16 and 3.33E-16, respectively (numerical analysis was done by “PTC Windchill” software).

References
[1] Bechta Dugan, J., Bavuso, Salvatore J., Boyd, M.A., 1992, “Dynamic Fault-Tree Models For Fault-Tolerant Computer Systems,” IEEE Transactions on Reliability, Vol. 41, pp. 363 – 377.
[2] Xing, L., Amari, S. V., 2008, “Handbook of Performability Engineering,” Fault Tree Analysis, London, Springer London, pp. 595-620.
[3] DurgaRao, K., et al., 2009, “Dynamic Fault Tree Analysis Using Monte Carlo Simulation In Probabilistic Safety Assessment,” Reliability Engineering & System Safety, Vol. 94, pp. 872–883.
[4] Berg, G.V., “Monte Carlo Sampling of Dynamic Fault Trees for Reliability Prediction,”
[5] Manno, G., et al., 2014, “Conception of Repairable Dynamic Fault Trees and resolution by the use of RAATSS, a Matlab toolbox based on the ATS formalism.” Reliability Engineering & System Safety, Vol. 121, pp.
250–262.
[6] Chiacchio, F., et al., 2011, “Dynamic Fault Trees Resolution: A Conscious Trade-Off between Analytical and Simulative Approaches,” Reliability Engineering & System Safety, Vol. 96, pp. 1515–1526.
[7] Faulin Fajardo, J., et al., 2010, “Simulation Methods for Reliability and Availability of Complex Systems,” British Library Cataloguing in Publication Data, pp. 41-64.
[8] Amari, S., Dill, G., Howald, E., 2003, “A New Approach To Solve Dynamic Fault Trees,” Annual Reliability and Maintainability Symposium, IEEE Publisher., pp. 374 – 379.
[9] Rausand, M., Hoyland, A., 2003, “System Reliability Theory: Models, Statistical Methods, and Applications,” 2nd Edition, New York, USA, Wiley-Interscience