<![CDATA[Organizations that hold certifications against several ISO management system standards increasingly face duplicated compliance costs and audit fatigue, yet the central Annex SL claim that integration yields more than the sum of individual standards has rarely been tested using formal interaction terms. Existing studies remain largely qualitative or model integration as a single latent construct, leaving the individual, integrative, and synergistic contributions of multiple standards to IMS effectiveness quantitatively unspecified. This study develops and validates a quantitative additive model grounded in the Annex SL framework to evaluate IMS effectiveness across ISO 9001, ISO/IEC 27001, ISO/IEC 27701, ISO 22301, and ISO/IEC 20000-1. The model introduces a Tiered Integration Weight (λk = 1 + 0.10·ln k) that represents diminishing integration benefits as the number of integrated standards increases, separates integrable (approximately 60%) from non-integrable (approximately 40%) requirement elements, and incorporates pairwise interaction terms to capture synergy. Validation was conducted through a numerical simulation of 100 organizational profiles whose parameters were calibrated to reported characteristics of multi-standard adopters; no field survey data were collected at this stage. The simulated data were estimated using hierarchical regression. All five direct effects are positive and significant (p < 0.001). Adding the interaction terms raises the coefficient of determination from R² = 0.917 to R² = 0.938 (ΔR² = 0.021; F-change(4, 88) = 7.438; p < 0.001). The strongest synergy occurs in the ISO/IEC 27001 × ISO/IEC 27701 pair (β = 1.544; p < 0.001), while the other three pairs are not significant, indicating that synergy is selective rather than automatic. Subgroup analysis shows that this synergy is stronger in younger firms (β = 2.560) than in large mature firms (β = 0.839). The study contributes a replicable quantitative framework that distinguishes integrable from non-integrable factors; empirical validation using field data is the next stage of this research.]]>
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