 Reliability HotWire Issue 63, May 2006 Hot Topics Modeling Event Trees in RENO Event trees are excellent tools for assisting analysts in assessing risks (or any type of event) and the probabilities of different possible outcomes. Event trees rely on an effective structured framework within which the different events can be laid out and the possible outcomes of the sequence of events can be investigated. Event trees are widely used in many fields such as finance, economics, reliability, risk assessment and numerous other probabilistic types of analysis. They help in creating a holistic picture of the risks and rewards associated with each possible course of action. They very are popular due to their simplicity. This article introduces event trees and presents an approach for modeling them using RENO.   The Structure of Decision Trees: Event trees use an inductive approach that follows a forward logic representation. Usually, event trees flow from the left to the right. Beginning on the left, the first thing to happen is typically an initiating event followed by other events. It is sometimes useful to think of the events as occurring in a time sequence. Branches emanating from the events correspond to the different subsequent events that could happen. The tree branches out until the final consequences (outcomes) are reached. The quantification of event trees is used to predict the frequency of each outcome.   Example: Assume a complex fuel system is susceptible to leaks: If a leak occurs, then the leak can be classified either as: o Atomizing Leak o Minor Leak o Major Leak Assume uniform probabilities for each type of leak to be 10%, 50% and 40% respectively. For each type of leak assume the following:   Atomizing Leak o An atomizing leak is undetectable. o It is a risk issue if it fails to ventilate and it ignites. Assume a 10% chance of ignition. Minor Leak o A minor leak is detectable. There is an 80% chance of detecting it. o It is a risk issue if it fails to ventilate and it ignites. Assume a 20% chance of ignition. Major Leak A major leak is detectable. There is an 80% chance of detecting it. It is a risk issue if it fails to ventilate and it ignites. Assume a 20% chance of ignition. The goal is to compute the probabilities of each outcome.   The following is the event tree that models the problem. Figure 1: Event tree for the fuel system gas leak In the above figure, the circles correspond to what is commonly referred to in event trees as chance nodes, from which multiple arrows can branch out. Note that each chance node must have branches that correspond to a set of outcomes that are mutually exclusive ( i.e. only one of the outcomes can happen) and collectively exhaustive (i.e. no other possibilities exist, one of the specified outcomes has to occur). The probabilities at each chance node must add up to 1. The probability of reaching a certain outcome is obtained by multiplying the probabilities of the sequences leading to it. For example, the probability that a Gas Leak is of a Minor type and is Detected is P(Minor) P(Detected) = 0.5 0.8 = 0.4. In general, the probability that a certain sequence of events (Pi1, Pi2, ..Pin) will occur and lead to Outcomei is computed as follows: Reno Solution: The main Constructs used to create the diagram shown in Figure 1 in RENO are Standard Blocks (to represent the events and consequences) and Summing Gates (to represent the chance nodes). These Constructs can be added to the diagram by selecting Add Block and then the type of block from the Flowchart menu. The connections are made using the Join Blocks option in the Flowchart menu. The properties of the initiating event, Gas Leak?, is set as follows. The probability of reaching any event in the diagram can be computed by using the IN keyword, which evaluates to the value of the Constructs preceding the current Construct (i.e. the value that is passed into the current Construct). For example, the Ignition block in the bottom right corner of the diagram has the following properties. In the above figure, the IN keyword  is multiplied by the 0.10, which is the probability of ignition. In any block in this example, the IN keyword represents the product of all the probabilities of each event in the sequence of events that leads to that particular block, so in the above figure, IN = 0.4 0.2 = 0.08 and the probability that an ignition will happen is P = 0.08 0.10 = 0.008. Once properties of all of the Standard Blocks are entered in the same manner, the diagram can be analyzed. Select Simulate from the Tools menu or click the Simulate button in the Control Panel and use 1 as the number of simulations (since the values of the probabilities are fixed and do not follow any distribution). The simulation settings required for this example are shown next. Click the Simulate button in the Simulation Console. The event tree is now analyzed. The values of probabilities of reaching all the outcomes are displayed in the diagram on top of the blocks. (If the values are not displayed in your diagram, you can select Show Block Values from the Flowchart menu to display them.)  Copyright 2006 ReliaSoft Corporation, ALL RIGHTS RESERVED