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Complexity index-based graph network estimation for adapting control programs in cyber-physical production systems
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DOI：10.1080/0951192X.2026.2657827.png)
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Abstract
En 中文
In today's dynamic industrial environment, shaped by volatile markets and resource competition, manufacturers must adapt swiftly to remain viable. These circumstances often demand physical changes that may affect the underlying Control Program (CP). Adapting the CP entails reconfiguring systems between operational states, where the associated complexity and effort are crucial factor for evaluating the economic feasibility of alternative strategies. While effort estimation has been extensively explored in software engineering, existing approaches do not quantify the adaptation effort of CP, particularly in Cyber-Physical Production Systems (CPPSs). This paper introduces a complexity index-based graph model for CP adaptation effort estimation and operationalises it via scaling index-to-time-factor to produce quantitative time and cost estimates under scarce industrial data. Unlike architecture-led task listings and qualitative frameworks, the approach yields scenario-level quantitative KPIs that capture change propagation across physical, functional, and code layers. A network-graph model encapsulates these indices as scenario-specific state graphs, enabling change tracking and visualisation. The quantification method then computes adaptation effort from graph differences. The approach is validated through adaptation estimates for one lab-scale and three industrial automation cells. Results demonstrate the approach effectiveness in evaluating architecture, implementation, and runtime effort, offering a practical tool for strategic adaptation decisions.
Keywords:
Effort estimation
adaptive cyber-physical production system
control program complexity
Industry 4.0
system complexity
network graph
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