Evidence-Density-Weighted Multi-Criteria Decision Analysis: A Mathematical Framework with Application to Comparative Evaluation of Managed Pressure Drilling Approaches

Abstract

Standard multi-criteria decision analysis (MCDA) treats criterion weights as exogenous to the underlying evidence base, producing decision-support outputs that do not communicate the strength of the evidence on which they rest. This is a limitation in real-world decision contexts where evidence density and consistency vary systematically across criteria. This paper develops an evidence-density-weighted extension of the standard weighted-sum MCDA aggregation in which criterion weights are made endogenous to the frequency (density) and the agreement (consistency) of the supporting evidence. The framework introduces an evidence-density factor, an evidence-consistency factor, and a combined evidence-confidence weight, supplemented by a three-tier confidence calibration of decision-support outputs. The framework reduces to the standard weighted-sum aggregation in the limiting case of uniform evidence density and consistency, establishing it as a proper generalisation. The framework is demonstrated through application to a corpus of fourteen Managed Pressure Drilling (MPD) case studies from the SPE and IADC literature of 2015-2025, producing an evaluation matrix, a cross-case synthesis, and an application-domain selection map with explicit confidence-tier calibration. The principal substantive finding is that MPD achieves detection sensitivity approximately one to two orders of magnitude superior to conventional drilling, a finding cross-validated against a Gaussian detection-sensitivity model. The framework is computationally tractable with complexity linear in the problem size, generalises to adjacent engineering-comparison problems, and offers an operationally accessible alternative to more complex evidence-aware MCDA methods while addressing the same underlying concern of evidence heterogeneity across criteria.