AND and OR Gate Probability Calculations

AND and OR Gate Probability Calculations

In system modeling and fault tree analysis (FTA) we use a set of similar calculations based on Boolean logic, the AND and OR gate probability calculations. Within FTA, the AND and OR gates are just two of many possible ways to model a system. Within system modeling, often reliability block diagrams (RBD) we model parallel and series elements of a system.

In order to do these basic calculations, we need to consider a few assumptions then proceed to the math.

First the Assumptions

A key assumption for AND & OR gates as well as series or parallel system modeling is the individual components, or failure mechanisms are independent. This implies that a change in the probability of one event does not change the probability of other events.

For example, if one component begins to fail it may heat up to near its maximum rating, thus increasing the probability of that component failing. If that increase in temperature also increases the chance of nearby components to fail or other failure mechanisms within the component to accelerate toward failure, then the items are not independent.

The way I think of this if each component in a system behaves on its own, reacting to loads…