Partition-Based Priors and Multiple Event Censoring: An Analysis of Rosen’s Fibrous Composite Experiment

Abstract

Multiple event censoring occurs when the censoring mechanism depends on preceding observations. This arises naturally in load-sharing systems when component failure under increased load can initiate a series of component failures due to load transfer from the failed components, causing the subsequent component strengths to be interval censored. Here the intervals are determined by the breaking stress that initiates the series of failures. The partition-based nonparametric priors developed in 2009 by Sethuraman and Hollander are a class of natural conjugate priors for this situation. Load-sharing systems are used to model fibrous composite materials. The modeling approach is based on some remarkable experiments conducted in 1964 and 1965 by Rosen, who discovered that load could not be supported through the composite matrix material around a fiber break beyond a distance referred to as the ineffective length. The ineffective length is used to discretize the composite into a system of components for which the load-sharing is determined by mechanical considerations. A Bayesian analysis of the components’ strength distribution of the data from Rosen’s experiment is given based on a partition-based prior. This article has supplementary material.

• Bayes
• Dirichlet processes
• Load-sharing systems
• Nonparametric priors

ACKNOWLEDGMENTS

The first and third authors were partially supported by NSF Grant DMS 1106435, the second and third authors were partially supported by NSF Grants DMS 0243594 and DMS 0805809, and the third author was also partially supported by NSF Grant DMS 0914921. In addition, some of the work of the third author was done while he was a Research Fellow at the Statistical and Applied Mathematical Sciences Institute (SAMSI). The authors thank Walter Rosen for kindly providing copies of photographs from his experiment, and Caroline Grego for GIS assistance. We thank the reviewers, associate editor, and editor, whose thorough work and suggestions greatly improved the presentation of the material.