## 6 Conclusions  
We have presented the development of a systematic and scalable mathematical model to predict SOIC package misalignment during automated high-voltage IC testing in a dielectric fluid, achieving an impressive reliability of 99.64%, with a margin of error below 4.78%. This model comprehensively analyzes mechanical and hydrodynamic factors, including the crucial aspects of misalignment during the insertion and extraction of SOIC packages from ZIF sockets. This study furthered the knowledge in the development of an energy model for high-voltage test speed calculation that seeks to improve the handling of SOIC packages in dielectric fluids in an advanced automated system, offering vital information on the rate-limiting hydrodynamic effects and precision in handling of SOIC packages. A thorough analysis of the physical properties of dielectric fluids, including viscosity, surface tension, and density, was conducted to understand their influence on the misalignment experienced by the packages during the insertion and removal process. The proposed configuration was evaluated consistently across three types of certified dielectric fluids (FR3 vegetable oil, DPMS silicone, and DTE-150 mineral oil) and different SOIC packages, which included SOP16, SOP20, and SOP24, aligned to JEDEC's standard MC-012 [44], significantly defining the understanding of fluid dynamics and ensuring the reliability and repeatability of the results. This study introduced novel knowledge by analyzing the forces acting on SOIC packages in air and dielectric fluid environments, including the interface between these two mediums. It developed a model to quantify energy losses in each environment where SOIC packages operate. This research highlighted the advantages and limitations of various trapezoidal motion patterns, particularly in high-speed operations, emphasizing their potential to expedite automated high-voltage testing processes. Figure 12: Descriptive statistics of the relative standard errors. This research also explored the mechanics of the ZIF socket and the potential effects of cavitation and splash formation when inserting the SOIC package into the dielectric fluid. This study evidenced that the DUT geometry and fluid properties significantly influence these phenomena. This study applied [PERSON]'s alpha for robust statistical reliability validation, effectively confirming Gaussian distribution patterns and linear deviation correlations. It also analyzed and comprehensively evaluated misalignment probabilities, analyzing factors such as surface tension, sloshing, cavity formation, and bubble dynamics during DUT handling. This study represents a significant contribution to the semiconductor industry in the field of high-voltage IC testing, providing an advanced model for predicting SOIC package misalignment with a resource-efficient approach that outperforms traditional trial-and-error models, improving the automated handling and validation of high-voltage isolation tests for SOIC packages. Conceptualization, Y.A.A. and M.J.; methodology, M.J.; writing--original draft, Y.A.A. ; review and editing, Y.A.A. and M.J.; experimentation, Y.A.A. ; data treatment and statistical analyses, Y.A.A. ; tables and figures preparation, Y.A.A. All authors have read and agreed to the published version of the manuscript. This research was supported in part by Texas Instruments, Inc. under the UPRM-TI Collaborative Program. Any opinions, findings, conclusions, or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of the sponsor. Not applicable. The data presented in this study are openly available in [Data Testing deviation HV-SOIC.csv] at [[[https://github.com/YAAMNAY/Data_SOIC_DF_deviation.git](https://github.com/YAAMNAY/Data_SOIC_DF_deviation.git)]([https://github.com/YAAMNAY/Data_SOIC_DF_deviation.git](https://github.com/YAAMNAY/Data_SOIC_DF_deviation.git))] (accessed on 29 March 2024). The authors declare no conflicts of interest.