A Note on Bayesian Modification of the Failure Rate Function

The widely used failure rate often has uncertain parameters, and the fact of non-failure yields information on these parameters. As Lucas [4] pointed out, specification of a prior distribution, g(a), on the parameter vector, a, leads via Bayesian analysis from a conditional failure rate, h(z-a), to a modified rate, h*(z). Of interest are results about the shape of h*(z) in terms of h(z \ a) and g(a). A key result of the article is: