## 3 Methodology
Verification and validation of the results are the subsequent steps after the data implementation process within the Digital Twin (DT) development. These steps are needed to ensure that the created digital model accurately represents the real system reflecting the operational dynamics, that the simulation results are reliable and applicable in a real-world context, and to identify and correct any discrepancies between the virtual and real worlds. Without rigorous verification and validation, the Digital Twin risks providing inaccurate results, compromising the operational and strategic decisions based on it. Verification is the process of confirming that the digital model has been constructed correctly and that it functions as intended. This involves a comprehensive analysis of the simulation code, parameter configurations, and the consistency of the input data. During this phase, various debugging techniques are employed to identify and resolve any errors in the model. * Model inspection: A manual model check is conducted to ensure that all elements have been implemented correctly and that there are no inconsistencies or logical errors. * Sensitivity testing: Tests are conducted to check how the model responds to variations in input parameters. This process enables the identification of any instabilities in the model and the confirmation of the consistency of the responses with the expected outcomes. * Cross-validation: The model's results are compared with historical data to check the consistency and accuracy of the Digital Twin. Validation ensures that the model meets the requirements for which it was created and that simulation results are accurate to the real system. This process includes various steps:  
* Comparison with actual data: The results of the Digital Twin simulations are compared with the actual operating data. This comparison allows for the identification of discrepancies and the calibration of the model to improve its accuracy. * Performance analysis: A performance analysis is conducted to evaluate the Digital Twin's efficacy in predicting the performance of the real system under various operational scenarios. Iterative feedback: The validation process is iterative, whereby the analysis results are employed to implement modifications and enhancements to the model, which is then subjected to further verification and validation. * To achieve effective verification and validation, several methodologies are employed, each with a specific application and set of benefits:
* Statistical validation: The objective is to ascertain the degree of correlation between the results of a simulation and those of a real-world scenario. Tests such as Chi-Square, Kolmogorov-Smirnov, and Anderson-Darling tests are employed. * Trend analysis: This is a statistical method used to identify patterns in data over time by comparing trends in simulated data with real data over time. This methodology is useful for verifying that the model correctly captures the temporal dynamics of the real system. Several studies have underscored the significance of verification and validation in industrial simulation models. For example, an analysis conducted by [PERSON] et al. in 2015 demonstrated that rigorous validation of simulation models is essential to guarantee their applicability in a real-world context [15]. Similarly, a study by [PERSON] and [PERSON] in 2016 highlighted the importance of verifying input parameters and simulation results to ensure DT reliability [10]. The growing complexity of industrial systems and the evolution of simulation technologies underscore the increasing necessity for robust methodologies for model verification and validation. This enhances the Digital Twin's reliability and permits the comprehensive potential of simulations to be leveraged for optimizing production processes. The conclusion of the method entails an analysis of the underlying causes of inefficiency, based on the identification, evaluation, and resolution of factors that impede productivity and increase operating costs.