5.2 __Reliability Theory__

Because, as was mentioned previously, reliability is defined in
terms of probability, probabilistic parameters such as random variables,
density functions, and distribution functions are utilized in the development
of reliability theory. Reliability studies are concerned with both discrete
and continuous random variables. An example of a discrete variable is the
number of failures in a given interval of time. Examples of continuous random
variables are the time from part installation to failure and the time between
successive equipment failures.

The distinction between discrete and continuous variables (or
functions) depends upon how the problem is treated and not necessarily on the
basic physical or chemical processes involved. For example, in analyzing “one shot” systems such as
missiles, one usually utilizes discrete functions such as the number of
successes in “n” launches. However, whether or not a missile is successfully
launched could be a function of its age, including time in storage, and could,
therefore, be treated as a continuous
function.