Maximum likelihood estimation of convex arrival rate

Abstract

It is commonly believed that failures of a repairable system follow a time dependent Poisson process with ‘bathtub-shaped’ arrival rate. A natural problem then is maximum likelihood estimation of arrival rate subject to the constraint that it be convex. This paper employs theoretical considerations to reduce that task to a finite dimensional nonlinear programming problem and completes the solution by computer. The resulting estimates are interesting graphical presentations of the reliability characteristics of the system.