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The construction of supply chain control dashboards frequently ignores the informational redundancy generated by including metrics algebraically derived from pre-existing variables, creating a false perception of diagnostic breadth. This study aimed to evaluate the underlying structure of a logistics metric set, quantify their informational overlap, and propose an efficient design ensuring the statistical independence of its components. Using a quantitative comparative approach, synthetic inventory data (150 SKUs evaluated over 1,095 days) were analyzed. These data were created in Python through generative modeling (SDV) from historical records of a real distribution center, preserving their original empirical statistical properties. A full system of six indicators including derived constructs such as the Operational Resilience Index (ORI) and the Logistics Efficiency Index (LEI) was contrasted against a reduced scheme of four base variables using Principal Component Analysis (PCA). Empirical results demonstrate that mathematical transformations on base metrics do not provide new diagnostic value but rather saturate the same latent dimension: the first component of the full system concentrated 58.2% of total variance (evidence of structural redundancy), with identical loadings for dependent indicators. In contrast, the reduced system achieved greater informational efficiency (KMO = 0.619; cumulative variance = 90.2% with two components). It is concluded that empirical statistical validation is an unavoidable prerequisite to mere conceptual differentiation. Auditing dimensionality through multivariate techniques ensures orthogonal managerial instruments that are analytically superior and free from biases caused by duplication.