Shannon differential entropy properties of consecutive k-out-of-n:G systems

This research delves into the Shannon differential entropy properties of consecutive $k$-out-of-$n$:G. Initially, an expression for the entropy of the lifetime of a consecutive $k$-out-of-$n$:G system is formulated, providing a comprehensive understanding of its entropy characteristics. A characterization outcome is also derived. Furthermore, useful bounds are provided for the entropy of the lifetime of these systems. A nonparametric estimator for the new entropy metric is developed to assist in practical application. The effectiveness of this estimator is demonstrated through the use of simulated datasets, followed by a numerical illustration using a real-world dataset.