Work

A Multistage Sufficiency Test for Selecting Energy Performance Indicators in Industry: Beyond R2 Toward the Variable Associated with Significant Energy Use

Year: 2026

Type: article

Abstract: Under ISO 50001, energy performance is monitored through Energy Performance Indicators (EnPIs) and energy baselines. In practice, the energy-to-production ratio (kWh/t) is commonly adopted by default and validated solely by the coefficient of determination (R2), which is insensitive to systematic bias, to the base load contained in the intercept, and to the residual structure that reveals an omitted explanatory variable. This work organizes well-established statistical and engineering checks into a sequential, four-outcome decision procedure anchored to the diagnosis of Significant Energy Uses (SEUs): retain the simple ratio, adopt a regression baseline with the same variable, switch to the SEU-associated variable, or reject the model as structurally misspecified. Relative to common practice, the procedure makes three methodological corrections explicit: in-sample NMBE is identically zero for OLS models with an intercept and is therefore defined out of sample; residual diagnostics are evaluated against exact, design-specific Durbin–Watson critical values with a Šidák-corrected family-wise error of 0.044–0.050 (versus ≈0.14 uncorrected); and the candidate-variable step uses a partial F-test on nested models, since the naive residual-versus-variable regression is attenuated by collinearity with production. The procedure is characterized on synthetic data with known truth (N=1000 replicates per cell): against an interannual drift of ≈2%/yr, its sensitivity reaches 1.00 at n=72 months while an R2-only criterion has sensitivity 0.00, and with a base-load fraction of ≈0.28 the R2-only rule retains the biased ratio in 100% of the replicates; specificity under a correct ratio is 0.95–0.96, and the adopted thresholds lie in a stable region of the (R2, f0) sensitivity sweep. The procedure is then demonstrated on six industrial cases; most notably, in a fuel oil power plant a pooled baseline with R2=0.998 is rejected (Durbin–Watson =0.79 versus an exact critical value of 1.64; runs test p<0.001) because of drift in specific fuel consumption that R2 cannot detect, and its out-of-sample validation over 37 rolling origins shows that an aggregated bias of +0.31% can mask an origin-to-origin drift from −1.7% to +2.1%. The contribution is not a new indicator or a new statistic, but the integration of indicator selection and multistage statistical validation into a single auditable decision procedure whose operating characteristics are quantified.

Source: Processes

DOI: 10.3390/pr14162676