Bayesian reliability applications of a combined lifecycle failure distribution

Abstract

This research seeks to better understand how to update sectional time-to-failure (TTF) distributions, such as the Sandia National Laboratories' developed CoMBined Lifecycle (CMBL) distribution, when new operational TTF data become available. With a bathtub-shaped hazard function, the CMBL probability density function provides an application-friendly method for characterizing a component's failure or lifecycle distribution. Its five parameters are chosen specifically to make it relatively easy to elicit the probability of failure distribution from subject matter experts and limited data. Once a characterization of the component?s lifecycle in terms of failure probability is established, a methodology for how to update that characterization based on the availability of new operational failure data is required. The updating process presented here uses a Bayesian changepoint methodology to return updated CMBL distribution parameters based on new operational TTF data modelled as a Poisson process. In this methodology, the changepoints are determined first, and when combined with the counts of the TTF data, provide enough information to estimate the remaining CMBL distribution parameters. The method developed in this effort for updating the CMBL distribution and other TTF distributions should prove valuable in optimizing large scale system-of-systems supply/repair chain models.