Statistics for Maintenance Modelling: Basic Probability Concepts

# Introduction¤

Reliability is defined to be the probability that a component or system will perform a required function for a given period of time when used under stated operating conditions. In other words, it is the probability of a non-failure over time.

The risk associated with an event (e.g. the failure of a component) is most often defined as the probability of that failure occurring and the impact of that event once it has occurred. For instance the probability of an outage of the size seen in North West America in August 2003 is very small, but the impact of such an event is very large.

Knowing these definitions of reliability and risk, it is clear that in order to study the two quantities we need to understand some ideas and concepts of probability. Indeed, the concepts of probability form the foundation of all decision making. By using the concepts of probability one is able to deal with uncertainty because this uncertainty can be measured. Once the uncertainty has been measured we can use the information to come to decisions.

There are two general approaches to modelling uncertainty by using probability concepts:

1. the more basic method makes use of the idea of sample space and events defined over the sample space. The probabilities of these events and the probabilities of other related events are then formed using 'unions' and 'intersections' of the elementary events.
2. the second method is based on the concept of a random variable and a probability distribution associated with the random variable. A random variable is a variable that takes on certain values in accordance with specified probabilities.