A stochastic framework for evaluating ranking robustness and decision consistency under uncertainty

Engineering asset prioritisation commonly relies on deterministic multi-criteria decision-making (MCDM) methods that generate a single ranking from fixed indicator weights, although uncertainty in weight estimation can affect operational decisions. This study proposes a stochastic ranking–decision consistency (DC) framework that explicitly models weight uncertainty and jointly evaluates ranking robustness and decision reliability. The framework combines stochastic weight perturbation with Monte Carlo simulation to generate probabilistic ranking distributions and introduces complementary measures: Structural Stability Index, pairwise reversal rate, average rank shift, ranking entropy, DC, and decision change rate. The methodology is demonstrated using maintenance prioritisation for 1000 engineering assets under four weighting strategies: equal weighting, entropy weighting, principal component analysis, and random forest. Bootstrap resampling and perturbation sensitivity analysis assess reproducibility and numerical stability. Results show that weighting strategies producing similar deterministic rankings can exhibit substantially different levels of ranking robustness and decision reliability under uncertainty. Furthermore, ranking robustness and decision robustness are shown to be complementary rather than interchangeable properties. By linking probabilistic ranking behaviour with operational DC, the proposed weighting-method-independent framework provides a general methodology for uncertainty-aware decision support that complements existing MCDM, optimisation, and machine-learning approaches.