Prior distributions expressing ignorance about convex increasing failure rates

This paper deals with the specification of probability distributions expressing ignorance concerning annual or otherwise discretized failure or mortality rates, when these rates can safely be assumed to be increasing and convex, but are completely unknown otherwise. Such distributions can be used as noninformative priors for Bayesian analysis of failure data. We demonstrate why a uniform distribution used in earlier work is unsatisfactory, especially from the point of view of insensitivity with respect to the time scale that is chosen for the problem at hand. We suggest alternative distributions based on Dirichlet distributed weights for the extreme points of relevant convex sets, and discuss which consequences a requirement for scale neutrality has for the choice of Dirichlet parameters.