Copula-Based Bayesian Reliability Analysis of a Product of a Probability and a Frequency Model for Parallel Systems When Components Are Dependent

While the dependence assumption among the components is naturally important in evaluating the reliability of a system, studies investigating the issues of aggregation errors in Bayesian reliability analyses have been focused mainly on systems with independent components. This study developed a copula-based Bayesian reliability model to formulate dependency between components of a parallel system and to estimate the failure rate of the system. In particular, we integrated Monte Carlo simulation and classification tree learning to identify key factors that affect the magnitude of errors in the estimation of posterior means of system reliability (for different Bayesian analysis approaches—aggregate analysis, disaggregate analysis, and simplified disaggregate analysis) to provide important guidelines for choosing the most appropriate approach for analyzing a model of products of a probability and a frequency for parallel systems with dependent components.

Empirical Bayes Before-After Study to Develop Crash Modification Factors and Functions for High Friction Surface Treatments on Curves and Ramps

The intent of the study was to fill a knowledge void by developing high quality crash modification factors (CMFs) and benefit/cost (B/C) ratios for high friction surface treatment (HFST). The state-of-the-art empirical Bayes (EB) before-after methodology was applied to evaluate the effects of this treatment on crashes of various types using data from West Virginia (curve sites), Pennsylvania (curve sites), Kentucky (curve and ramp sites), and Arkansas (ramp sites). The results for curve sites generally indicate substantial and highly significant safety benefits. This is especially so for the primary crash types targeted by HFST programs: run-off-road, wet road, and head-on side-swipe opposite direction crashes (HOSSOD). The results for ramp sites were inconsistent, with substantial benefits for all crashes and injury crashes for Kentucky, negligible effects for these crashes in Arkansas, and substantial and highly significant reductions in wet weather crashes in both states. A disaggregate analysis of the CMF results for curve sites indicated a logical and consistent relationship between CMFs and three variables: friction improvement, traffic volume, and expected crash frequency before treatment. These variables, and an innovative methodology, were used in developing crash modification functions (CMFunctions) that can be applied to determine where, and under what conditions, the treatment can be used most effectively. Such functions are typically not provided for the vast majority of treatments for which CMFs are available, so, in itself, developing them is a significant contribution of this research.