Optimization of Diversity Redundancy Systems Based on Modified Shannon Index

Abstract

Diversity redundancy in information systems aims to reduce systemic risk by distributing critical resources (e.g., servers, communication channels, and services) across heterogeneous component types so that a single vulnerability is less likely to compromise many assets simultaneously. This paper proposes a vulnerability-aware diversification framework based on an entropy-inspired indicator Hs that combines (i) deployment shares of component types and (ii) time-accumulated resilience derived from compromise probabilities over a planning horizon. The approach includes a practical allocation principle that prioritizes more resilient technologies while allowing minimum-diversity constraints when required, as well as a deterministic integer allocation procedure (floor-and-carry) suitable for layered architectures under a fixed instance budget. Using a stationary compromise model for comparative planning, we illustrate how resilience-prioritized allocations can improve H_s relative to uniform allocation. To avoid substituting the optimization target, we also report the corresponding system-level survival probability under the same assumptions, showing that improvements in H_s are accompanied by improved system survival in the examples. The proposed methodology is intended as a decision-support tool for architecture planning and what-if analysis; practical use requires parameter estimation from operational data and assessment of modeling assumptions, especially when strong dependencies or correlated compromises are present.