Measurable Coupling: Figures of Merit for Relationships Between Engineered Systems and Their Environments

Abstract

A prior position paper proposed that measurable relationships between engineered systems and the elements and environments with which they interact be treated as explicit objects of engineering design, and identified two results as the natural first tests of whether that proposal can be made rigorous: the well-posedness of a bounded relationship-quality index, and a defensible figure of merit relating the benefit of an engineered relationship to its cost. This paper takes up those two problems for a particular and consequential class of relationship — the coupling between an engineered system and the physical medium in which it operates. We first establish what the neighboring disciplines already provide, and identify precisely what they do not: a general, normalized, cost-aware figure of merit by which competing designs of a system–environment coupling can be compared. We then characterize such a coupling through four measurable attributes — observability, influenceability, strength, and cost — and state the conditions under which each is meaningful. On that basis we construct a bounded coupling-quality index and a benefit-per-cost figure of merit, establishing the normalization, weighting, sign, and accounting conditions under which each is well defined, and identifying the circumstances in which neither is. We illustrate the constructs against a single demonstration domain, the coupling between a vehicle and the atmosphere through which it moves, and close with the limitations of the present treatment and the questions it leaves open. The contribution is formal groundwork rather than empirical validation: the aim is to make coupling quality a quantity that can be stated, compared, and — in principle — falsified.