Large-scale operations, defined here as multi-site, high-volume production and service systems characterized by organizational complexity and distributed decision rights, confront a persistent paradox. Improvement methodologies that produced substantial gains in single-plant settings frequently fail to replicate at enterprise scale, even as the process data available to these organizations has grown by orders of magnitude. This paper develops a conceptual framework integrating Six Sigma, Lean, and data analytics into a single quality management architecture for large-scale contexts. Drawing on the resource-based view, dynamic capabilities, information processing theory, complementarity theory, absorptive capacity, and organizational ambidexterity, the framework specifies four layers: a foundation of governance, culture, and data infrastructure; a diagnostic layer that decomposes operational loss and classifies it by problem signature; a methodological engine that routes each loss pool to Lean, Six Sigma, or analytical treatment according to that signature; and a learning layer that codifies solutions with their validation conditions and propagates them across sites. The central contribution is a problem-signature routing logic treating the three methodologies as complements addressing distinct classes of operational pathology rather than as competing philosophies to be blended indiscriminately. Fourteen testable propositions, a phased implementation roadmap, and a multi-level measurement architecture are developed, and boundary conditions and an agenda for empirical testing are set out.