Nonparametric Estimation of Negative Cumulative Extropy for Linear Consecutive Systems: Reliability Properties and Image-Processing Application

Information measures for linear consecutive k-out-of-n:F systems (LCSk,n:F) quantify the uncertainty in reliability structures that fail when a run of consecutive components fails. Such measures support maintenance scheduling and risk assessment in telecommunication networks, pipeline integrity monitoring systems, and particle accelerator vacuum systems. Motivated by this, this paper conducts an extensive analysis of the negative cumulative extropy (NegCEx) of LCSk,n:F as an information-theoretic measure of uncertainty in reliability engineering. For 2k≥n, an explicit representation of the NegCEx of these systems is obtained in terms of the quantile and probability density functions of the component lifetimes. This representation facilitates establishing fundamental stochastic ordering properties and characterization results. Furthermore, we establish several bounds, providing practical tools for estimation and comparison when closed-form expressions are unavailable. We present two nonparametric estimators for the NegCEx. We prove the strong consistency of both estimators under mild regularity conditions and investigate their finite-sample performance through extensive simulation studies across various lifetime distributions (exponential, Pareto, and Rayleigh). Finally, we apply the proposed measure to two illustrative problems: an image-processing application, in which the NegCEx of intensity transformations of a benchmark image identifies the affine-transformed image as the closest to the reference and, unlike location-invariant density-based entropy indices, separates brightening from darkening transformations; and a real repair-time dataset.