  Probabilistic model-based diagnosis computes the posterior probabilities of
failure of components from the prior probabilities of component failure and
observations of system behavior. One problem with this method is that such
priors are almost never directly available. One of the reasons is that the
prior probability estimates include an implicit notion of a time interval over
which they are specified -- for example, if the probability of failure of a
component is 0.05, is this over the period of a day or is this over a week? A
second problem facing probabilistic model-based diagnosis is the modeling of
persistence. Say we have an observation about a system at time t_1 and then
another observation at a later time t_2. To compute posterior probabilities
that take into account both the observations, we need some model of how the
state of the system changes from time t_1 to t_2. In this paper, we address
these problems using techniques from Reliability theory. We show how to compute
the failure prior of a component from an empirical measure of its reliability
-- the Mean Time Between Failure (MTBF). We also develop a scheme to model
persistence when handling multiple time tagged observations.
