• Bottom-up method–This is a very simple and fast method. It first finds the probabilities of all basic events, and then it uses these probabilities to find the probabilities of the lowest level gates. Similarly, it uses the lowest level gate probabilities to find next higher level gate probabilities, continuing this process until the top event probability is calculated. This method cannot be used to find the exact top event probability when repeated events exist because it assumes the independence of all sub-trees of the fault tree.

• Top-down method–This is also a very simple and fast method. It is based on recursion. The top event probability is calculated using the probabilities of the gates or events that are connected to the top event. Similarly, this process continues until the required information for performing this recursion is obtained. This method can not be used to find the exact top event probability when repeated events exist because it assumes the independence of all sub-trees of the fault tree.

• Simulation–This method is conceptually simple and can handle any type of fault tree. However, it takes more time in analysing complex systems to arrive at reasonably accurate results. This method first generates random numbers associated with each event, and then determines whether that event has occurred or not. The status of individual events, that is occurrence and non-occurrence information (also the times if temporal order of events is important), is used to find the status of the top event (occurrence or non-occurrence). This process will be continued for many iterations. Then, the probability of the top event is calculated by finding the ratio of the number of top event occurrences and total number of simulation trials.

• Cut Sets Method–This method is useful for finding the exact results of the top event probability, particularly when repeated events exist. It is also useful to find results with a prescribed accuracy. The cut sets method first finds the minimal cut sets of the fault tree and uses these minimal cut sets to find the top event probability of the fault tree.

• Shannon’s Expansion–Shannon’s expansion method uses conditional probabilities recursively to find the top event probability. Consider a fault tree with events A, B and C. The top event probability can be expressed as: Pr{A} Pr{top|A} + Pr{~A} Pr{top|~A}, where Pr{A} and Pr{~A} are the probability of the occurrence of event A and the probability of non-occurrence of event A respectively. Pr{top|A} is the probability of the top event given that event A has occurred. Similarly, Pr{top|~A} is the probability of the top event given that event A has not occurred. Now, Pr{top|A} and Pr{top|~A} are calculated as a sum of conditional probabilities based on the occurrence of other events. This process is continued until the conditional probabilities are known.

• Disjointing Method. Top-down and bottom-up methods can be applied only for modular fault trees (for example, a fault tree without repeated events). If repeated events exist, then these methods do not produce correct results and should not be used. Alternative methods for when repeated events exist include simulation, the cut set method, Shannon’s expansion method and the disjointing method. Simulation and the cut set method are time-consuming and cannot be applied for large systems. Shannon's expansion method uses conditional probability (total probability concept), continuing the process until all conditional probabilities are known. Thus, it may not be very effective when only a few repeated events are present. To overcome this difficulty, conditional probabilities and modularization concepts are used like in RBDs. A module of a fault tree is a subtree when none of its events are present in other parts of the fault tree. In this method, fault trees are disjointed as in Shannon's expansion method; however, they are conditioned on repeated events. For example, if there is a repeated event in the fault tree (say it is event A), the top event probability can be calculated using Pr{A} Pr{top|A} + Pr{~A} P{top|~A}. Because there is only one repeated event in this example, calculating Pr{top|A} and P{top|~A} do not involve any repeated events as the resultant event does not contain event A. Because the resultant fault tree is a module (contains no repeated event), its probability can be obtained using modular techniques (bottom-up approach). Therefore, the number of computations in this process are far fewer than when Shannon's expansion method is used.

• Binary Decision Diagrams–Binary decision diagrams are based on Shannon’s expansion. The main advantage of binary decision diagrams over Shannon’s expansion is that it eliminates the redundant computation in the process of finding the conditional probabilities. Therefore, it takes much less time to find the top event probability.

• Sequential Analysis Using Stochastic Processes–All of the above analytical methods except simulation are applicable only for combinatorial analysis and can not be used for sequence dependent situations such as the presence of dynamic gates. In such cases, the problem cannot be solved using combinatorial methods. If the events have exponentially distributed failure/occurrence and repair times, then top event probability can be found using Markov models. To perform this, the fault tree must be converted into an equivalent Markov model. For additional information, see Markov Modelling. If the distributions are not exponential, non-homogeneous Markov models or Semi-Markov models are needed. Because all dynamic fault trees cannot be converted to equivalent Markov models or Semi-Markov models, simulation methods may be required.

• Hybrid Approach–It is understandable that no method is suitable for all type of fault trees. Although, simulation can be used for any type of fault tree, it takes lots of time. Therefore, it is better to solve each module (independent sub-tree) of the fault tree separately, using an appropriate method, and then combine the results to find the top event probability.