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This paper investigates the Fisher information (FI) structure of the Kimeldorf–Sampson (KS) bivariate family and its role in parameter estimation and reliability inference. While the KS copula has been used to model weakly dependent systems, the FI for its order statistics (OSs) and their concomitants has not been previously derived or analyzed. Our work addresses this gap by developing closed-form expressions for the FI and the FI matrix (FIM). We examine their behavior for two specific marginal distributions: The KS–exponential (KSE) model, corresponding to a mean parameter, and the KS–power (KSP) model, corresponding to a shape parameter. Numerical evaluations show that the FI increases with the dependence parameter α up to moderate levels (|α| ≤ 0.3), beyond which the information gain plateaus. This indicates a limited sensitivity to stronger dependence. A comparison reveals that the KSP model consistently yields higher FI values than the KSE model, suggesting greater estimation precision for shape-related parameters. In an application to a real computer system dataset, we find a weak negative dependence (ρXY = –0.054) between processor and memory degradation, which aligns with the mild-correlation property of the KS copula. Overall, this analysis provides new quantitative insights into the behavior of FI under mild dependence and establishes a framework for evaluating estimation efficiency in bivariate reliability models based on OSs and their concomitants.