Results on Cumulative Entropic Properties of Consecutive Systems

This paper reveals some properties of the cumulative entropy of consecutive k-out-of-n:F system's lifetime. First, we introduce a method for calculating the cumulative entropy of their lifetime and explore its preservation properties using established stochastic orders. Ad- ditionally, we obtain useful bounds that can used in situations where the distribution function of the system's component lifetimes are complicated or systems have large components. To support practical applications, we present two nonparametric estimators for the cumulative entropy of these systems. The efficiency and performance of these estimators are illustrated with simulated datasets and further validated with real data sets.