5.1 __Introduction__

The language of engineering is mathematics. The theories behind
each engineering specialty are concisely stated in a set of mathematical
procedures. For the engineering specialties of reliability, availability and
maintainability (RAM), the theories are stated in the mathematics of
probability and statistics.

The underlying reason for the use of these concepts is the
inherent uncertainty in predicting a failure. Even given a failure model based
on physical or chemical reactions, the results will not be the time a part
will fail, but rather the time a given percentage of the parts will fail or
the probability that a given part will fail in a specified time. Individual
parts will fail according to their individual strengths, which will vary from
part to part and are practically unknowable. Similarly, the time to repair a
failure will also vary dependent on many factors whose values in individual
cases are practically unknowable.

Since RAM parameters must be defined in probabilistic terms,
probabilistic parameters such as random variables, density functions, and
distribution functions are utilized in the development of RAM theory.

This section describes some of the basic concepts, formulas, and
simple examples of application of RAM theory which are required for better
understanding of the underlying principles and design techniques presented in
later sections. Practicality rather than rigorous theoretical exposition is
emphasized. Many excellent texts are available (see references) for
the reader who is interested in delving into the rigorous theoretical
foundations of these disciplines.