This study provides a detailed investigation into the properties of the cumulative residual entropy of \(k\) -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 \(k\) -out-of- \(n:\text{G}\) system. Based on this formula, we then investigate the cumulative residual entropy of \(k\) -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 \(k\) -out-of- \(n\) : 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.
