Bayesian Inference of the Intensity of the Power Law Process

• Activity Number: 150
• Type: Contributed
• Date/Time: Monday, August 12, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical & Engineering Sciences*
• Author(s): Ananda Sen*+
• Affiliation(s): Oakland University
• Keywords: Bayesian inference ; Repairable systems ; Power Law Process ; MCMC

Abstract

In analyzing failure data pertaining to a repairable system, perhaps the most widely used parametric model is a nonhomogeneous Poisson process model with Weibull intensity, more commonly referred to as the Power Law Process (PLP) model. Investigations relating to inference of parameters of the PLP under a frequentist framework abound in the literature. The focus of this talk is to supplement those findings from a Bayesian perspective, which has thus far been explored to a limited extent in this context. Main emphasis is on the inference of the intensity function of the PLP. Both estimation and future prediction are considered under traditional, as well as more complex, censoring schemes. Modern computational tools, such as Markov Chain Monte Carlo, are exploited efficiently to facilitate the numerical evaluation process. Results from the Bayesian inference are contrasted with the corresponding findings from a frequentist analysis, both from a qualitative and a quantitative viewpoint. The developed methodology is implemented in analyzing interval-censored failure data of equipments in a fleet of marine vessels.