Razi University

In many problems related to reliability and survival analysis, the evaluation of uncertainty and information associated with system lifetimes must be performed conditional on the current age (survival condition) of the system. >The aim of this thesis is to study, analyze, and organize the existing knowledge on generalizations of dynamic cumulative information measures and their applications in reliability and model selection. To this end, we first extract the basic definitions of cumulative information measures (including cumulative residual entropy, cumulative residual Fisher information, and past-based versions) and review their analytical relationships with hazard rate and mean residual lifetime functions. Then, the theoretical properties of these measures are compared in specific models (equilibrium and proportional hazards). Next, nonparametric estimation methods (particularly kernel-based estimators) and Monte Carlo simulation results for various distributions are collected and evaluated. Finally, the practical application of dynamic cumulative information measures in selecting competing lifetime distributions (with emphasis on real reliability data) is described, and their performance is compared with classical criteria such as AIC and BIC.