  Especially when facing reliability data with limited information (e.g., a
small number of failures), there are strong motivations for using Bayesian
inference methods. These include the option to use information from
physics-of-failure or previous experience with a failure mode in a particular
material to specify an informative prior distribution. Another advantage is the
ability to make statistical inferences without having to rely on specious (when
the number of failures is small) asymptotic theory needed to justify
non-Bayesian methods. Users of non-Bayesian methods are faced with multiple
methods of constructing uncertainty intervals (Wald, likelihood, and various
bootstrap methods) that can give substantially different answers when there is
little information in the data. For Bayesian inference, there is only one
method of constructing equal-tail credible intervals-but it is necessary to
provide a prior distribution to fully specify the model. Much work has been
done to find default prior distributions that will provide inference methods
with good (and in some cases exact) frequentist coverage properties. This paper
reviews some of this work and provides, evaluates, and illustrates principled
extensions and adaptations of these methods to the practical realities of
reliability data (e.g., non-trivial censoring).
