Properties, Bounds, and Estimation of Rényi Entropy in Consecutive k-out-of-n:G Systems

This study investigates the Renyi entropy properties of consecutive k-out-of-n:G systems. Initially, a formula for the Renyi entropy of the lifetime of a consecutive k-out-of-n:G system is derived, offering a thorough insight into its Renyi entropy characteristics. A comparative analysis is performed between two consecutive k-out-of-n:G systems with varying component lifetimes. Moreover, some useful bounds for the Renyi entropy of the lifetime of these systems are established, augmenting the comprehension of Renyi entropy variability within such systems. To aid practical implementation, nonparametric estimators for the novel Renyi entropy measure are devised. The efficiency of the estimators is showcased through the utilization of simulated datasets and then numerical demonstrations are conducted using real-world datasets.