The Information Entropy Performance Indicator (IEPI): A Deterministic BPMN Analytics Artifact for Routing-Uncertainty Diagnostics and Viability Assessment

Business Process Management (BPM) process models represent routing behaviour through control-flow constructs, yet BPMN 2.0 does not provide a native mechanism for quantifying uncertainty associated with routing decisions. This study presents the Information Entropy Performance Indicator (IEPI) as a deterministic BPMN analytics artifact for evaluating routing uncertainty under externally specified routing probabilities. The IEPI framework integrates construct-level routing diagnostics, viability assessment, diagnostic flagging, compositional uncertainty propagation, and process-level reporting within a unified analytical workflow. The IEPI engine accepts as input a BPMN 2.0 process representation, a routing-probability map, and analyst-specified viability thresholds. It computes (i) construct-level diagnostics based on normalized entropy and responsiveness, (ii) block-level uncertainty and responsiveness quantities using fixed composition rules for XOR, OR, and LOOP routing constructs, and (iii) a bounded process-level viability-band reporting index. The framework is evaluated using four analytically constructed BPMN authorisation workflows designed to exercise the complete routing-construct taxonomy supported by the artifact. Results demonstrate that construct-level classifications, propagated uncertainty quantities, and process-level IEPI values are well defined and reproducible under fixed inputs. Threshold sensitivity analysis shows that local viability classifications and aggregate reporting outputs vary deterministically with threshold settings and remain consistent with the underlying routing diagnostics. The findings highlight the distinction between uncertainty propagation and viability-band compliance. While propagated uncertainty quantities characterize the accumulation of routing uncertainty within a process structure, the IEPI score provides a reporting-oriented assessment of aggregate compliance with analyst-defined viability criteria. The proposed artifact offers a reproducible and extensible analytical framework for routing-uncertainty evaluation in BPMN-based process models.