Iterative Refinement of a Hybrid Process Discovery Algorithm: From Structural Failure to Competitive Conformance, A Case Study on a Real SAP Purchase-to-Pay Log

This paper documents the iterative development of the Precision Hybrid Miner (PHM), a process discovery algorithm combining elements of the Alpha algorithm and the Heuristic Miner, applied for the first time to a real, unfiltered SAP Purchase-to-Pay (P2P) event log (1,165 cases, 24 activities). Rather than presenting a single validated result, the paper traces five successive corrective versions (v1 to v5), each triggered by a concrete, diagnosable failure: the original implementation discovered only 2 causal relations and achieved a self-reported fitness of 0.008, a result traced to unnormalized activity labels, a fixed dependency threshold incompatible with the log's real score distribution, and a Petri-net construction that produced a structurally deadlocked model. Each defect is corrected in turn, and a converter from the PHM model to a pm4py PetriNet object is built to obtain token-based-replay fitness and precision directly comparable to the Alpha Miner and Heuristics Miner baselines on the same log. Under this common, replay-based evaluation, PHM v5 achieved fitness 0.566 and precision 0.364, exceeding the Alpha Miner (0.390/0.280) while remaining behind the Heuristics Miner (0.791/0.819), whose larger net relies on invisible transitions and loop constructs that PHM does not yet model. The paper's main contribution is methodological rather than a state-of-the-art claim: it documents (1) the specific real-world data-quality and structural-modeling defects that caused a plausible hybrid algorithm to fail on real data, (2) the isolated, measurable effect of each correction, and (3) an honest, apples-to-apples benchmark against two established baselines, including the discovery that PHM's own internal quality metrics are heuristic proxies not validated by trace replay, a comparability gap that is treated as a finding in itself rather than elided. Concrete, falsifiable limitations are reported alongside the results: unresolved output-side XOR-splits, absent loop/skip modeling, and a single-dataset, single-run evaluation scope.