Retrospective phase-based index of fire response complexity at fuel and energy facilities

Introduction. Fires at fuel and energy complex (FEC) facilities are not only emergency events but also complex management situations characterized by long active suppression phases, a high resource load and the need to coordinate many responding units. The formal criteria of a large fire (damage, area, formal categorization) do not always reflect the tactical complexity of the response, which complicates retrospective analysis and personnel training. The problem of constructing a reproducible complexity measure whose feature weights are not assigned by experts remains insufficiently developed.

Goals and objectives. The aim of the work is to build a retrospective phase-oriented complexity index of fire response at FEC facilities, in which the weights of features and blocks are determined statistically, without expert assignment of coefficients. The objectives include forming the block structure of the index (temporal, resource, tactical, contextual and organizational blocks), the statistical computation of within-block and between-block weights, evaluating their robustness to the choice of correlation measure, and cross-block and proxy validation of the resulting complexity scale.

Methods. A sample of 194 completed fires was used, together with robust normalization of numerical features clipped at the Q0.05 and Q0.95 quantiles, two-level weighting by the CRITIC method, cross-block validation, repeated out-of-fold cross-validation, the Mann – Whitney test, Cliff’s delta, the Benjamini – Hochberg (FDR) correction and Fisher’s exact test with the Haldane – Anscombe correction. The source data were taken from the federal “Fires” database for 1999–2021; confidence intervals were estimated by bootstrap resampling, and a Pareto front over active-suppression time, the number of fire vehicles and the number of nozzles was built for comparison with an alternative multi-criteria approach.

Results and discussion. A reproducible index combining the temporal, resource, tactical, contextual and organizational blocks was obtained. Cross-block validation showed that the index without the temporal block retains its association with protracted scenarios (area under the ROC curve, AUC 0.772; the full index reaches 0.914), while high complexity levels are robustly associated with special fire equipment, monitor nozzles and a more complex organizational structure (the involvement of several types of fire protection). The between-block weights proved robust to the choice of correlation measure (Pearson and Spearman), and the comparison with the Pareto front showed that the index does not replace the multi-criteria formulation but provides an ordered complexity scale for all records in the sample.

Conclusion. The proposed index provides a statistically reproducible basis for the retrospective analysis of response complexity, the selection of complex fire scenarios and subsequent external validation of construct validity. Eliminating expert-assigned weights makes it possible to use the index in a digital twin of fire and rescue response, in the training of incident commanders, and in improving response processes.

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