5.5 __Bayesian Statistics in
Reliability Analysis__

Bayesian statistics have been increasingly used in reliability
analysis. The advantage to the use of Bayesian statistics is that it allows
prior information (e.g., predictions, test results, engineering judgment) to
be combined with more recent information, such as test or field data, in order
to arrive at a prediction/assessment of reliability based upon a combination
of all available data. It also permits the reliability prediction/assessment
to be continually updated as more and more test data are accumulated.
The Bayesian approach is intuitively appealing to design engineers because it
permits them to use engineering judgment, based upon prior experience with
similar equipment designs, to arrive at an initial estimate of the reliability
of a new design. It is particularly useful for assessing the reliability of
new systems where only limited field data exists. For example, it can be
argued that the result of a reliability test is not only information available
on a product, but that information which is available prior to the start of
the test, from component and subassembly tests, previous tests on the product,
and even intuition based upon experience. Why should this information not be
used to supplement the formal test result? Bayes’ Theorem can be used to
combine these results.

Thus, the basic difference between Bayesian and non-Bayesian
(classical) approaches is that the former uses both current and prior data,
whereas the latter uses current data only.

One of the main disadvantages to the use of the Bayesian
approach is that one must be extremely careful in choosing the prior
probabilities based upon part experience or judgment. If these are
capriciously or arbitrarily chosen for Bayesian analysis, the end results of
Bayesian analysis may be inaccurate and misleading. Thus, the key to the
successful use of the Bayesian method resides in the appropriate choice of
prior probability distributions. An objective prior such as existing test data
is much better than a subjective prior based on opinion.