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A model has been developed that shares the steady-state and the dynamic voltage-current (V-I) characteristics of a xenon head lamp in a motor vehicle. This study proposes the modelling method, which is based on the spline interpolation algorithms including a major factor such as its temperature that is responsible for the design of an high-intensity discharge (HID) ballast during a hot re-strike. As the model simulates the transition process of an HID lamp, the simulation system that includes the HID ballast and the lamp model will be illustrated in detail. The results from the simulation and the experiments will lead to the model validation at the end of the study. This study provides a valuable approach for the optimisation of the HID ballast and the design of a system controller.