Cumulative Residual Entropy of Linear Consecutive $$k$$ k -out-of- $$n$$ n :G Systems and their Applications

This study provides a detailed investigation into the properties of the cumulative residual entropy of $$k$$ k -out-of-n:G systems with consecutive structure. We first derive a useful formula to compute the cumulative residual entropy of the lifetime of a consecutive $$k$$ k -out-of- $$n:\text{G}$$ n : G system. Based on this formula, we then investigate the cumulative residual entropy of $$k$$ k -out-of-n:G systems with consecutive structure in terms of well-known stochastic orders. We also derive some useful bounds. For practical applications, we introduce two nonparametric estimators of the cumulative residual entropy of consecutive $$k$$ k -out-of- $$n$$ n : G systems. The efficiency and performance of these estimators are demonstrated through the use of simulated datasets, and in addition through an image processing application.