Predicting failure in mammalian enamel

Dentition is a vital element of human and animal function, yet there is little fundamental knowledge about how tooth enamel endures under stringent oral conditions. This paper describes a novel approach to the issue. Model glass dome specimens fabricated from glass and back­filled with polymer resin are used as representative of the basic enamel/dentine shell structure. Contact loading is used to deform the dome structures to failure, in simulation of occlusal loading with opposing dentition or food bolus. To investigate the role of enamel microstructure, additional contact tests are conducted on two­phase materials that capture the essence of the mineralized­rod/organic­sheath structure of dental enamel. These materials include dental glass­ceramics and biomimicked composites fabricated from glass fibers infiltrated with epoxy. The tests indicate how enamel is likely to deform and fracture along easy sliding and fracture paths within the binding phase between the rods. Analytical relations describing the critical loads for each damage mode are presented in terms of material properties (hardness, modulus, toughness) and tooth geometry variables (enamel thickness, cusp radius). Implications in dentistry and evolutionary biology are discussed.

A Fully Bayesian Approach for Combining Multilevel Failure Information in Fault Tree Quantification and Corresponding Optimal Resource Allocation

This paper presents a fully Bayesian approach that simultaneously combines basic event and statistically independent higher event-level failure data in fault tree quantification. Such higher-level data could correspond to train, sub-system or system failure events. The full Bayesian approach also allows the highest-level data that are usually available for existing facilities to be automatically propagated to lower levels. A simple example illustrates the proposed approach. The optimal allocation of resources for collecting additional data from a choice of different level events is also presented. The optimization is achieved using a genetic algorithm.

On the Accelerated Failure Time Model for Current Status and Interval Censored Data

This paper introduces a novel approach to making inference about the regression parameters in the accelerated failure time (AFT) model for current status and interval censored data. The estimator is constructed by inverting a Wald type test for testing a null proportional hazards model. A numerically efficient Markov chain Monte Carlo (MCMC) based resampling method is proposed to simultaneously obtain the point estimator and a consistent estimator of its variance-covariance matrix. We illustrate our approach with interval censored data sets from two clinical studies. Extensive numerical studies are conducted to evaluate the finite sample performance of the new estimators.