Abstract
Fault tree analysis (FTA) strives to reveal all possible sources of critical failures. It starts from the most critical event (“top event”) and looks at its reasons, and continues in this way backwards to the initial events leading finally to the failure. So-called fault tree, plotted using the symbols of Boolean algebra can then be used for the construction of a reliability block diagram, which serves for finding the critical way and probability of failure. The principle of Markov analysis is explained as well.
Keywords
- Failure
- fault tree
- fault tree analysis
- FTA
- top event
- reliability block diagram
- probability of failure
- Boolean algebra
The failure modes and effects analysis (FMEA), explained in the previous chapter, strives for finding all possible sources of future failures. It starts with failures of single elements, with mistakes of personnel, etc., and looks for their consequences for the structure or process. It is very efficient but has two drawbacks. First, it reveals perhaps all sources of many possible failures, but only few of them are really serious and have fatal consequences, such as the collapse of the structure. Moreover, complex objects can fail in various ways. Second, FMEA is a rather qualitative analysis and does not give information on the probabilities of failure.
For these reasons,
A simple example with electric lighting in a room with two lamps is shown in Fig. 2. The top event is “there is darkness in the room”. This can happen if none of the two lamps lights, and four possible reasons exist for this (either both the lamps have failed, there is no voltage in the network, the switch is off or failed, or the fuse has burnt).
A single fault tree is used to analyze one and only one top event (or undesired event). FTA involves five principal steps:
Definition of the undesired event to be studied. A system engineer with a deep knowledge of the system can best help to define the undesired events.
Obtaining an understanding of the system. Analysts and system designers can help here.
Construction of the fault tree.
Evaluation of the fault tree.
Control of all identified hazards, with the effort to reduce the probability of their occurrence.
In contrast to FMEA, fault tree analysis is able to consider also events caused by external reasons.
Fault tree analysis is often used in the aviation industry, as well as chemical, petrochemical, nuclear power, and other high-hazard industries.
A fault tree can be converted into a
A reliability block diagram RBD may be drawn using switches instead of blocks, where a closed switch represents a working component and an open switch represents a failed component. If a path may be found through the network of switches from the beginning to the end, the system is still working. The system can also be solved using the rules of Boolean algebra. Series paths can be replaced by AND gates and parallel paths with OR gates, etc.
In complex systems consisting of many blocks, various blocks can fail simultaneously. If connections exist between certain elements, the failure of one or even more blocks does not necessarily mean the failure of the whole system. Reliability in such systems is studied by the
Another approach to reliability analysis of complex systems uses the so-called Markov chains or
More details to fault tree analysis and reliability block diagram can be found in the literature [1 - 3]. These methods have also been incorporated into reliability standards, e.g. IEC 61025, and commercial computer programs for FTA are also available. More about cut set and tie sets can be found in [2, 3], more about Markov analysis is in [3 - 5].
References
- 1.
Bentley J P. Introduction to Reliability and Quality Engineering. Harlow, England: Addison-Wesley; 1999. 202 p. - 2.
Ireson W G, Coombs C F Jr, Moss R Y. Handbook of reliability engineering and management. 2nd ed. New York: McGraw-Hill; 1996. 816 p. - 3.
O´Connor Patrick D T. Practical Reliability Engineering. 4th ed. Chichester: John Wiley & Sons; 2002. 513 p. - 4.
Freedman D. Markov Chains, Berlin: Springer; 1983. 382 p. - 5.
Bednařík J et al. Reliability techniques in electronic practice (In Czech: Technika spolehlivosti v elektronické praxi). Praha: SNTL; 1990. 336 p.