Global and Dynamic Information Measures for Reliability

Abstract

In modeling a duration variable, such as the lifetime of an object as it ages, consideration of the age partitions the support of the lifetime distribution progressively and induces truncated distributions for the past and residual lifetimes. Global information measures of the distribution of the entire lifetime do not change with the age, and thus are static. Information measures of the past and residual lifetime distributions are functions of the age, and hence are dynamic. This article presents an overview of the global and dynamic Shannon entropy, Kullback–Leibler information, and mutual information. Examples include information measures for parallel and series systems, proportional hazard, exponential, and Pareto models.