Negative Log-Gamma Modeling for Reliability Trends in Series Systems

• Activity Number: 334
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Roger Zoh*+ and Alyson Wilson and Scott Vander Wiel and Earl Lawrence
• Companies: Iowa State University and Iowa State University and Los Alamos National Laboratory and Los Alamos National Laboratory
• Keywords: negative log-gamma ; system reliability ; prior distribution ; trend

Abstract

Modeling system reliability over time when binary data are collected both at the system and component level has been the subject of many papers. In a series system, it is often assumed that component reliability is linear in time through some link function. Often little or no prior information exists on the parameters of the linear regression, and in a Bayesian analysis they are modeled using very diffuse priors. This can have unintended consequences for the analysis, specifically in the prediction of system reliability. In this work, we consider negative log-gamma distributions as means of specifying prior information on reliability. We first show how our method can be implemented in modeling the reliability of a series system at a given time and then extend to the case where we are interested in modeling reliability over time.