Petri Net Method Captures Hidden Similarities in Manufacturing Processes

Modern manufacturers are drowning in their own process documentation. Large enterprises routinely accumulate hundreds or even thousands of manufacturing processes covering everything from product design and production planning to quality inspection, and the ability to plan, review, recommend, merge and reuse those processes efficiently has become a genuine competitive necessity. A study published in Cluster Computing by Qianqian Wang of Anhui Science and Technology University and Chifeng Shao of Anhui University of Science and Technology now offers a substantially more accurate way to answer a deceptively simple question: when are two manufacturing processes truly alike, and where exactly do they differ?

The problem, the researchers argue, is that most existing similarity and difference analysis techniques rely on relatively single analysis criteria. Traditional methods typically consider only the dependency relations between activities in a process model. That works reasonably well for general business workflows, but manufacturing processes have a distinctive feature that such approaches ignore: the execution of every operation is accompanied by the consumption of a series of components and changes in their states. Two processes may look behaviorally identical on paper while consuming entirely different parts, or use identical parts while ordering their operations in critically different ways. When screening large process libraries for similar models, these blind spots cause numerous processes to be mistakenly flagged as highly similar, inflating review workloads and obscuring the real differences that matter for quality control.

To address this, the team first reformulated manufacturing processes as Petri net models, a formalism in which places represent products such as raw materials, items in progress or finished goods, transitions represent operations, and arcs capture the flow between them. Crucially, the model includes a function that assigns sets of components to each operation. Building on this representation, the authors introduce the concept of an operation profile, which characterizes how pairs of operations relate when a process executes. Five relations are distinguished: a strict relation in which one operation always precedes another, an interleaving relation that splits into circulation and parallel subtypes depending on whether the operations loop back to each other, and an exclusive relation in which two operations can never occur in the same execution.

A motivating example in the paper shows why a single criterion fails. When only operation profiles are compared, two processes with identical ordering relations score a similarity of exactly 1.0, implying equivalence, even though the components attached to their operations are not the same. Conversely, two processes sharing the same operation items but differing in whether two operations run strictly in sequence or in parallel are also hard to separate under a parts-only view. The lesson is that neither operation items nor operation profiles alone can deliver reliable judgments; both must be weighed together.

From this insight the researchers derive three similarity measurement methods. The operation items, or OI-based, method scores the similarity of corresponding operations by the Jaccard coefficient of their component sets, capturing how much the parts consumed by matching operations overlap. The operation profile, or OP-based, method instead counts how many operation pairs share the same occurrence relation, normalized by the number of possible pairs. The centerpiece, however, is the operation-aware profile, or COP-based, method, which fuses the two perspectives: for every operation pair it multiplies the pair’s component similarity by a binary indicator of whether the occurrence relation matches, then aggregates across the whole process. In a worked example, two processes that scored a perfect 1.0 under profile-only analysis drop to 0.87 once component differences are counted, and processes differing in both dimensions fall to 0.84, exactly the kind of downward correction that prevents false positives in process screening.

The same machinery extends to difference analysis. Given a newly created process, the method first retrieves all processes in the library whose COP similarity exceeds a threshold, set at 0.8 in the study. The operation profile matrices of these similar variants are aggregated into a single weighted matrix whose entries record the frequency of each occurrence relation across the variant set. Two quantitative indicators then drive an iterative clustering procedure. A separation value, computed with a weighted cosine measure, identifies which operations are most suitable to merge together, while a deviation value, measured against benchmark vectors for each relation type, determines which occurrence relation best characterizes the merged pair. Because different relations carry different constraint strength, from the weakly constrained interleaving relation to the strongly constrained exclusive relation, the weights are calibrated by combining domain rules with data-driven optimization rather than manual assignment. The result is a candidate operation profile matrix that summarizes the typical behavior of the whole variant family, against which the new process is compared entry by entry to expose every structural difference.

To test the approach, the team assembled a dataset of low-cost rapid manufacturing temperature sensors, establishing 12 reference processes with 4 variants each, drawn largely from the published literature and converted into Petri net form. A benchmark for true similarity was set with the help of eight experienced modelers, and the methods were evaluated on precision, recall, F1-score and accuracy. The COP method achieved a perfect precision of 1.0 in every case where similar variants existed, correctly rejecting dissimilar processes that the single-criterion methods accepted. The OP method, by contrast, reached recall of 1.0 in most cases, but its broad matching strategy came at the cost of substantial noise, with accuracy in some cases falling as low as 0.25. The COP method attained an average accuracy of 0.83 while the older OTV approach, which considers only part of the profile information, trailed behind in precision.

Statistical validation reinforced the picture. Paired t-tests at a significance level of 0.05 showed that the COP method’s improvements over the OI and OP methods were significant across both precision and accuracy, with all p-values below 0.05. Against the advanced OTV method, COP retained a statistically significant advantage in precision, while the difference in accuracy was not significant, with a p-value of approximately 0.1039, indicating at least comparable overall performance. The authors note that COP nonetheless offers greater theoretical completeness and interpretability, since it fully integrates both operation-component relations and the complete set of occurrence relations rather than a subset.

Perhaps the most practically significant finding concerns the method’s strictness toward small deviations. Rapid manufacturing processes are sensitive to environmental factors, and minor non-standard changes in operation sequence or execution logic frequently arise in production. The t-test results confirmed that when such substandard structural changes occur, the COP method assigns markedly lower similarity scores, flagging potential quality risks that looser methods gloss over. The authors therefore position the OI method for production resource arrangement and equipment scheduling, the OP method for macroscopic process planning and template construction, and the COP method for compliance verification and production quality control, where catching hidden deviations matters most.

In terms of difference mining, simulation experiments on grouped process models demonstrated that the iterative aggregation and clustering procedure correctly recovers candidate operation profiles, even when one process variant dominates the population with a 70 percent share, and that comparing candidate operation items against a new process pinpoints exactly which components deviate from established practice. The work was supported by the National Natural Science Foundation of China and several Anhui provincial programs. The authors acknowledge that, constrained by the availability of real industrial data and privacy limits, the evaluation relied on benchmark datasets from the literature; future work will apply the model to actual production logs with noise in real manufacturing workshops. If those trials succeed, factories could gain a rigorous, quantitative tool for managing sprawling process libraries, promoting reuse, and standardizing production on a scale that manual review has never been able to match.

Subject of Research: A Petri net-based method for measuring similarity and detecting differences between manufacturing processes by jointly analyzing operation profiles and operation-component relations.

Article Title: Analysis of similarity and difference in manufacturing processes based on petri nets

Article References: Analysis of similarity and difference in manufacturing processes based on petri nets. (n.d.). https://doi.org/10.1007/s10586-026-06494-y

Image Credits: AI Generated

DOI: 10.1007/s10586-026-06494-y

Keywords: Petri nets, manufacturing processes, similarity measurement, operation profile, process mining, difference analysis, behavioral profiles, process optimization, Cluster Computing, t-test, rapid manufacturing, precision and recall