Specifying prior distributions in reliability applications

Oregon Convention Center 

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---but
it is necessary to provide a prior distribution to fully specify the model.
This presentation 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).

Bayesian inference

default prior

Reliability

few failures

noninformative prior

reference prior 

Section on Bayesian Statistical Science