Basic Statistical Definitions

Random Variables

In general, most problems in reliability engineering deal with quantitative measures, such as the time-to-failure of a component, or whether the component fails or does not fail. In judging a component to be defective or non-defective, only two outcomes are possible. We can then denote a random variable X as representative of these possible outcomes (i.e. defective or non-defective). In this case, X is a random variable that can only take on these values.

In the case of times-to-failure, our random variable X can take on the time-to-failure (or time to an event of interest) of the product or component and can be in a range from 0 to infinity (since we do not know the exact time a priori).

In the first case, where the random variable can take on only two discrete values (let's say defective = 0 and non-defective = 1), the variable is said to be a discrete random variable. In the second case, our product can be found failed at any time after time 0, i.e. at 12.4 hours or at 100.12 hours and so forth, thus X can take on any value in this range. In this case, our random variable X is said to be a continuous random variable. In this reference, we will deal almost exclusively with continuous random variables.

This section includes the following subsections: