Bayesian Modification of the Failure Rate Function.

TLDR: In this paper, the authors studied the general shape of the failure rate function H*(z) in terms of H(z/a) and g(a) using Bayesian analysis.

Abstract: : The failure rate function is widely used in such theoretical frameworks as dynamic programming and control theory, reliability and redundancy, queueing and renewal theory; which have been developed for such diverse applications as modeling research and development, priority schemes for time sharing computers, demand for replacement parts, and design of space vehicles. The parameters of the function are often uncertain; furthermore the fact of non-failure up to a point z yields information on the parameters. As Lucas has pointed out, specification of an initial prior distribution g(a) on the parameter vector a leads directly via Bayesian analysis from the original failure rate function h(z/a) to a modified failure rate function H*(z) which may then be used in the analysis as if it were deterministic. Of great interest are results about the general shape of H*(z) (increasing, decreasing, unimodal, convex, etc.) in terms of H(z/a) and g(a). (Author)