The measurement of time-zero failure current with a constant current ramping rate was proposed from the first-order Joule heating model as a new method of monitoring failures in metal lines. The failure current almost linearly increased with increasing metal-linewidth when the width was larger than the thickness and the square of failure current linearly decreased with increased measuring temperature. This time-zero metal failure (TZMF) method was found to be in good agreement with experimental results. For Al-1%Si-0.5%Cu lines with the photo-reworked process and with rectangular-shaped pittings, the failure current probability by the TZMF method showed the same trend as that of the median-time to failure by the conventional electromigration method. Therefore, the failure current measurement by the TZMF method was found to be a useful in-line monitoring and screening tool for the defective aluminum and copper lines.