The test and evaluation of
complex systems often centers on reliability—the probability that
a component, subsystem, or system perform successfully for a given
period of time under specified conditions. Efforts to reduce test
and evaluation costs at many facilities have resulted in fewer
tests, which places greater emphasis on the need to use all
available pertinent information. Bayesian statistical methods
provide the analyst with a powerful tool for incorporating such
information in situations such as this as well as numerous other
settings.

Bayesian methods are
characterized by probabilistic models rather than confidence
intervals that are used in classical statistics. For example, the
failure rate q could be expressed as

P(a < q
< b) = 0.95

in a Bayesian analysis,
where a and b represent two quantiles from the probability
distribution for q . In contrast,
classical statistics provides an interval (c, d) with the
accompanying statement that there is 95% confidence that the true,
but unknown, failure rate q , is
contained in the interval. In reality, the interval (c, d) either
contains the true value of q or it does
not contain it and there is no probabilistic interpretation for the
interval.